rfc9881.original.xml   rfc9881.xml 
<?xml version='1.0' encoding='utf-8'?> <?xml version='1.0' encoding='UTF-8'?>
<!DOCTYPE rfc [ <!DOCTYPE rfc [
<!ENTITY nbsp "&#160;"> <!ENTITY nbsp "&#160;">
<!ENTITY zwsp "&#8203;"> <!ENTITY zwsp "&#8203;">
<!ENTITY nbhy "&#8209;"> <!ENTITY nbhy "&#8209;">
<!ENTITY wj "&#8288;"> <!ENTITY wj "&#8288;">
]> ]>
<?xml-stylesheet type="text/xsl" href="rfc2629.xslt" ?>
<!-- generated by https://github.com/cabo/kramdown-rfc version 1.7.29 (Ruby 3.4. <rfc xmlns:xi="http://www.w3.org/2001/XInclude" ipr="trust200902" docName="draft
4) --> -ietf-lamps-dilithium-certificates-13" number="9881" updates="" obsoletes="" xml
<rfc xmlns:xi="http://www.w3.org/2001/XInclude" ipr="trust200902" docName="draft :lang="en" category="std" consensus="true" submissionType="IETF" tocInclude="tru
-ietf-lamps-dilithium-certificates-13" category="std" consensus="true" submissio e" sortRefs="true" symRefs="true" version="3">
nType="IETF" tocInclude="true" sortRefs="true" symRefs="true" version="3">
<!-- xml2rfc v2v3 conversion 3.30.2 -->
<front> <front>
<title abbrev="ML-DSA in Certificates">Internet X.509 Public Key Infrastruct <title abbrev="ML-DSA in Certificates">Internet X.509 Public Key Infrastruct
ure - Algorithm Identifiers for the Module-Lattice-Based Digital Signature Algor ure -- Algorithm Identifiers for the Module-Lattice-Based Digital Signature Algo
ithm (ML-DSA)</title> rithm (ML-DSA)</title>
<seriesInfo name="Internet-Draft" value="draft-ietf-lamps-dilithium-certific <seriesInfo name="RFC" value="9881"/>
ates-13"/>
<author initials="J." surname="Massimo" fullname="Jake Massimo"> <author initials="J." surname="Massimo" fullname="Jake Massimo">
<organization>AWS</organization> <organization>AWS</organization>
<address> <address>
<postal> <postal>
<country>US</country> <country>United States of America</country>
</postal> </postal>
<email>jakemas@amazon.com</email> <email>jakemas@amazon.com</email>
</address> </address>
</author> </author>
<author initials="P." surname="Kampanakis" fullname="Panos Kampanakis"> <author initials="P." surname="Kampanakis" fullname="Panos Kampanakis">
<organization>AWS</organization> <organization>AWS</organization>
<address> <address>
<postal> <postal>
<country>US</country> <country>United States of America</country>
</postal> </postal>
<email>kpanos@amazon.com</email> <email>kpanos@amazon.com</email>
</address> </address>
</author> </author>
<author initials="S." surname="Turner" fullname="Sean Turner"> <author initials="S." surname="Turner" fullname="Sean Turner">
<organization>sn3rd</organization> <organization>sn3rd</organization>
<address> <address>
<email>sean@sn3rd.com</email> <email>sean@sn3rd.com</email>
</address> </address>
</author> </author>
<author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan"> <author initials="B. E." surname="Westerbaan" fullname="Bas Westerbaan">
<organization>Cloudflare</organization> <organization>Cloudflare</organization>
<address> <address>
<email>bas@cloudflare.com</email> <email>bas@cloudflare.com</email>
</address> </address>
</author> </author>
<date year="2025" month="September" day="30"/> <date year="2025" month="October"/>
<area>SEC</area> <area>SEC</area>
<workgroup>LAMPS WG</workgroup> <workgroup>lamps</workgroup>
<keyword>ML-DSA Certificate X.509 PKIX</keyword> <keyword>ML-DSA</keyword>
<abstract> <keyword>Certificate</keyword>
<?line 147?> <keyword>X.509</keyword>
<keyword>PKIX</keyword>
<t>Digital signatures are used within X.509 certificates, Certificate <abstract>
<t>Digital signatures are used within X.509 certificates and Certificate
Revocation Lists (CRLs), and to sign messages. This document specifies Revocation Lists (CRLs), and to sign messages. This document specifies
the conventions for using FIPS 204, the Module-Lattice-Based Digital the conventions for using FIPS 204, the Module-Lattice-Based Digital
Signature Algorithm (ML-DSA) in Internet X.509 certificates and Signature Algorithm (ML-DSA) in Internet X.509 certificates and
certificate revocation lists. The conventions for the associated CRLs. The conventions for the associated
signatures, subject public keys, and private key are also described.</t> signatures, subject public keys, and private key are also described.</t>
</abstract> </abstract>
<note removeInRFC="true">
<name>About This Document</name>
<t>
The latest revision of this draft can be found at <eref target="https://
lamps-wg.github.io/dilithium-certificates/#go.draft-ietf-lamps-dilithium-certifi
cates.html"/>.
Status information for this document may be found at <eref target="https
://datatracker.ietf.org/doc/draft-ietf-lamps-dilithium-certificates/"/>.
</t>
<t>
Discussion of this document takes place on the
Limited Additional Mechanisms for PKIX and SMIME (lamps) Working Group m
ailing list (<eref target="mailto:spasm@ietf.org"/>),
which is archived at <eref target="https://mailarchive.ietf.org/arch/bro
wse/spasm/"/>.
Subscribe at <eref target="https://www.ietf.org/mailman/listinfo/spasm/"
/>.
</t>
<t>Source for this draft and an issue tracker can be found at
<eref target="https://github.com/lamps-wg/dilithium-certificates"/>.</t>
</note>
</front> </front>
<middle> <middle>
<?line 156?>
<section anchor="introduction"> <section anchor="introduction">
<name>Introduction</name> <name>Introduction</name>
<t>The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a <t>The Module-Lattice-Based Digital Signature Algorithm (ML-DSA) is a
quantum-resistant digital signature scheme standardized by the US quantum-resistant digital signature scheme standardized by the US
National Institute of Standards and Technology (NIST) PQC project National Institute of Standards and Technology (NIST) PQC project
<xref target="NIST-PQC"/> in <xref target="FIPS204"/>. This document <xref target="NIST-PQC"/> in <xref target="FIPS204"/>. This document
specifies the use of the ML-DSA in Public Key Infrastructure X.509 (PKIX) specifies the use of the ML-DSA in Public Key Infrastructure X.509 (PKIX)
certificates and Certificate Revocation Lists (CRLs) at three security certificates and Certificate Revocation Lists (CRLs) at three security
levels: ML-DSA-44, ML-DSA-65, and ML-DSA-87.</t> levels: ML-DSA-44, ML-DSA-65, and ML-DSA-87.</t>
<t><xref target="FIPS204"/> defines two variants of ML-DSA: a pure and a p re-hash variant. <t><xref target="FIPS204"/> defines two variants of ML-DSA: pure and pre-h ash.
Only the former is specified in this document. Only the former is specified in this document.
See <xref target="sec-disallow-hash"/> for the rationale. See <xref target="sec-disallow-hash"/> for the rationale.
The pure variant of ML-DSA supports the typical pre-hash flow. Refer to The pure variant of ML-DSA supports the typical pre-hash flow. Refer to
<xref target="externalmu"/> for more details.</t> <xref target="externalmu"/> for more details.</t>
<t>Prior to standardisation, ML-DSA was known as Dilithium. ML-DSA and <t>Prior to standardization, ML-DSA was known as Dilithium. ML-DSA and
Dilithium are not compatible.</t> Dilithium are not compatible.</t>
<section anchor="requirements-language"> <section anchor="requirements-language">
<name>Requirements Language</name> <name>Requirements Language</name>
<t>The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>", "<bcp <t>
14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>",
NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>", "<bcp14>RECO "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL NOT</bcp14>
MMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>", ",
"<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to be i "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>",
nterpreted as "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
described in BCP 14 <xref target="RFC2119"/> <xref target="RFC8174"/> when, and "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to
only when, they be
appear in all capitals, as shown here.</t> interpreted as described in BCP&nbsp;14 <xref target="RFC2119"/> <xref
<?line -18?> target="RFC8174"/> when, and only when, they appear in all capitals, as
shown here.
</section> </t>
</section>
</section> </section>
<section anchor="oids"> <section anchor="oids">
<name>Identifiers</name> <name>Identifiers</name>
<t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC59 12"/> as follows:</t> <t>The <tt>AlgorithmIdentifier</tt> type is defined in <xref target="RFC59 12"/> as follows:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::= AlgorithmIdentifier{ALGORITHM-TYPE, ALGORITHM-TYPE:AlgorithmSet} ::=
SEQUENCE { SEQUENCE {
algorithm ALGORITHM-TYPE.id({AlgorithmSet}), algorithm ALGORITHM-TYPE.&id({AlgorithmSet}),
parameters ALGORITHM-TYPE. parameters ALGORITHM-TYPE.
Params({AlgorithmSet}{@algorithm}) OPTIONAL &Params({AlgorithmSet}{@algorithm}) OPTIONAL
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with
the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for th e 1988 ASN.1 the 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for th e 1988 ASN.1
syntax.</t> syntax.</t>
</aside> </aside>
<t>The fields in AlgorithmIdentifier have the following meanings:</t> <t>The fields in AlgorithmIdentifier have the following meanings:</t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t><tt>algorithm</tt> identifies the cryptographic algorithm with an o bject <t><tt>algorithm</tt> identifies the cryptographic algorithm with an o bject
identifier (OID).</t> identifier (OID).</t>
</li> </li>
<li> <li>
<t><tt>parameters</tt>, which are optional, are the associated paramet ers for the <t><tt>parameters</tt>, which are optional, are the associated paramet ers for the
algorithm identifier in the algorithm field.</t> algorithm identifier in the algorithm field.</t>
</li> </li>
</ul> </ul>
<t>The NIST registered OIDs <xref target="CSOR"/> are:</t> <t>The NIST-registered OIDs <xref target="CSOR"/> are:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
id-ml-dsa-44 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) id-ml-dsa-44 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3) country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) } nistAlgorithm(4) sigAlgs(3) id-ml-dsa-44(17) }
id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) id-ml-dsa-65 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3) country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) } nistAlgorithm(4) sigAlgs(3) id-ml-dsa-65(18) }
id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) id-ml-dsa-87 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
country(16) us(840) organization(1) gov(101) csor(3) country(16) us(840) organization(1) gov(101) csor(3)
nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19) } nistAlgorithm(4) sigAlgs(3) id-ml-dsa-87(19) }]]></sourcecode>
]]></artwork>
<t>The contents of the <tt>parameters</tt> component for each <tt>algorith m</tt> <bcp14>MUST</bcp14> be <t>The contents of the <tt>parameters</tt> component for each <tt>algorith m</tt> <bcp14>MUST</bcp14> be
absent.</t> absent.</t>
</section> </section>
<section anchor="ml-dsa-signatures-in-pkix"> <section anchor="ml-dsa-signatures-in-pkix">
<name>ML-DSA Signatures in PKIX</name> <name>ML-DSA Signatures in PKIX</name>
<t>ML-DSA is a digital signature scheme built upon the <t>ML-DSA is a digital signature scheme built upon the
Fiat-Shamir-with-aborts framework <xref target="Fiat-Shamir"/>. The security is based Fiat-Shamir-with-aborts framework <xref target="Fiat-Shamir"/>. The security is based
upon the hardness of lattice problems over module lattices <xref target="Dilithi um"/>. upon the hardness of lattice problems over module lattices <xref target="Dilithi um"/>.
ML-DSA provides three parameter sets for the NIST PQC security categories ML-DSA provides three parameter sets for the NIST PQC security categories
2, 3 and 5.</t> 2, 3, and 5.</t>
<t>Signatures are used in a number of different ASN.1 structures. As shown <t>Signatures are used in a number of different ASN.1 structures. As shown
in the ASN.1 representation from <xref target="RFC5280"/> below, in an X.509 in the ASN.1 equivalent to that in <xref target="RFC5280"/> below, in an X.509
certificate, a signature is encoded with an algorithm identifier in the certificate, a signature is encoded with an algorithm identifier in the
<tt>signatureAlgorithm</tt> attribute and a <tt>signatureValue</tt> attribute th at contains <tt>signatureAlgorithm</tt> attribute and a <tt>signatureValue</tt> attribute th at contains
the actual signature.</t> the actual signature.</t>
<artwork><![CDATA[
<sourcecode type="asn.1"><![CDATA[
Certificate ::= SIGNED{ TBSCertificate } Certificate ::= SIGNED{ TBSCertificate }
SIGNED{ToBeSigned} ::= SEQUENCE { SIGNED{ToBeSigned} ::= SEQUENCE {
toBeSigned ToBeSigned, toBeSigned ToBeSigned,
algorithmIdentifier SEQUENCE { algorithmIdentifier SEQUENCE {
algorithm SIGNATURE-ALGORITHM. algorithm SIGNATURE-ALGORITHM.
&id({SignatureAlgorithms}), &id({SignatureAlgorithms}),
parameters SIGNATURE-ALGORITHM. parameters SIGNATURE-ALGORITHM.
&Params({SignatureAlgorithms} &Params({SignatureAlgorithms}
{@algorithmIdentifier.algorithm}) {@algorithmIdentifier.algorithm})
OPTIONAL OPTIONAL
}, },
signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value( signature BIT STRING (CONTAINING SIGNATURE-ALGORITHM.&Value(
{SignatureAlgorithms} {SignatureAlgorithms}
{@algorithmIdentifier.algorithm})) {@algorithmIdentifier.algorithm}))
} }]]></sourcecode>
]]></artwork> <t>Signatures are also used in the CRL list ASN.1; the representation belo
<t>Signatures are also used in the CRL list ASN.1 representation from w is equivalent to that in <xref target="RFC5280"/>. In an X.509 CRL, a signatur
<xref target="RFC5280"/> below. In a X.509 CRL, a signature is encoded with an e is encoded with an
algorithm identifier in the <tt>signatureAlgorithm</tt> attribute and a algorithm identifier in the <tt>signatureAlgorithm</tt> attribute and a
<tt>signatureValue</tt> attribute that contains the actual signature.</t> <tt>signatureValue</tt> attribute that contains the actual signature.</t>
<artwork><![CDATA[
CertificateList ::= SIGNED{ TBSCertList } <sourcecode type="asn.1"><![CDATA[
]]></artwork> CertificateList ::= SIGNED{ TBSCertList }]]></sourcecode>
<t>The following <tt>SIGNATURE-ALGORITHM</tt> ASN.1 classes are for ML-DSA -44, <t>The following <tt>SIGNATURE-ALGORITHM</tt> ASN.1 classes are for ML-DSA -44,
ML-DSA-65, and ML-DSA-87:</t> ML-DSA-65, and ML-DSA-87:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= { sa-ml-dsa-44 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-ml-dsa-44 IDENTIFIER id-ml-dsa-44
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-44 } PUBLIC-KEYS { pk-ml-dsa-44 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-44 }
} }
sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= { sa-ml-dsa-65 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-ml-dsa-65 IDENTIFIER id-ml-dsa-65
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-65 } PUBLIC-KEYS { pk-ml-dsa-65 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 }
} }
sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= { sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-ml-dsa-87 IDENTIFIER id-ml-dsa-87
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-87 } PUBLIC-KEYS { pk-ml-dsa-87 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 }
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t>The identifiers defined in <xref target="oids"/> can be used as the <t>The identifiers defined in <xref target="oids"/> can be used as the
<tt>AlgorithmIdentifier</tt> in the <tt>signatureAlgorithm</tt> field in the seq uence <tt>AlgorithmIdentifier</tt> in the <tt>signatureAlgorithm</tt> field in the seq uence
<tt>Certificate</tt>/<tt>CertificateList</tt> and the <tt>signature</tt> field i n the sequence <tt>Certificate</tt>/<tt>CertificateList</tt> and in the <tt>signature</tt> fiel d in the sequence
<tt>TBSCertificate</tt>/<tt>TBSCertList</tt> in certificates and CRLs, respectiv ely, <tt>TBSCertificate</tt>/<tt>TBSCertList</tt> in certificates and CRLs, respectiv ely,
<xref target="RFC5280"/>. The <tt>parameters</tt> of these signature algorithms <bcp14>MUST</bcp14> be <xref target="RFC5280"/>. The <tt>parameters</tt> of these signature algorithms <bcp14>MUST</bcp14> be
absent, as explained in <xref target="oids"/>. That is, the <tt>AlgorithmIdentif ier</tt> absent, as explained in <xref target="oids"/>. That is, the <tt>AlgorithmIdentif ier</tt>
<bcp14>SHALL</bcp14> be a <tt>SEQUENCE</tt> of one component, the OID id -ml-dsa-*, where * <bcp14>SHALL</bcp14> be a <tt>SEQUENCE</tt> of one component, the OID id -ml-dsa-*, where *
is 44, 65, or 87 - see <xref target="oids"/>.</t> is 44, 65, or 87 -- see <xref target="oids"/>.</t>
<t>The <tt>signatureValue</tt> field contains the corresponding ML-DSA sig <t>The <tt>signatureValue</tt> field contains the corresponding ML-DSA sig
nature nature computed upon the ASN.1 DER-encoded <tt>TBSCertificate</tt>/<tt>TBSCertLi
computed upon the ASN.1 DER encoded <tt>tbsCertificate</tt>/<tt>tbsCertList</tt> st</tt> <xref target="RFC5280"/>. The optional context string (ctx) parameter
<xref target="RFC5280"/>. The optional context string (ctx) parameter
as defined in Section 5.2 of <xref target="FIPS204"/> is left to its default val ue: as defined in Section 5.2 of <xref target="FIPS204"/> is left to its default val ue:
the empty string.</t> the empty string.</t>
<t>Conforming Certification Authority (CA) implementations <bcp14>MUST</bc p14> specify <t>Conforming Certification Authority (CA) implementations <bcp14>MUST</bc p14> specify
the algorithms explicitly by using the OIDs specified in <xref target="oids"/> w hen the algorithms explicitly by using the OIDs specified in <xref target="oids"/> w hen
encoding ML-DSA signatures in certificates and CRLs. Conforming client encoding ML-DSA signatures in certificates and CRLs. Conforming client
implementations that process certificates and CRLs using ML-DSA <bcp14>MUST</bcp 14> implementations that process certificates and CRLs using ML-DSA <bcp14>MUST</bcp 14>
recognize the corresponding OIDs. Encoding rules for ML-DSA signature recognize the corresponding OIDs. Encoding rules for ML-DSA signature
values are specified in <xref target="oids"/>.</t> values are specified in <xref target="oids"/>.</t>
</section> </section>
<section anchor="ML-DSA-PublicKey"> <section anchor="ML-DSA-PublicKey">
<name>ML-DSA Public Keys in PKIX</name> <name>ML-DSA Public Keys in PKIX</name>
<t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has t he <t>In the X.509 certificate, the <tt>subjectPublicKeyInfo</tt> field has t he
<tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t> <tt>SubjectPublicKeyInfo</tt> type, which has the following ASN.1 syntax:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE { SubjectPublicKeyInfo {PUBLIC-KEY: IOSet} ::= SEQUENCE {
algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}}, algorithm AlgorithmIdentifier {PUBLIC-KEY, {IOSet}},
subjectPublicKey BIT STRING subjectPublicKey BIT STRING
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning: </t> <t>The fields in <tt>SubjectPublicKeyInfo</tt> have the following meaning: </t>
<ul spacing="normal"> <ul spacing="normal">
<li> <li>
<t><tt>algorithm</tt> is the algorithm identifier and parameters for t he <t><tt>algorithm</tt> is the algorithm identifier and parameters for t he
public key (see above).</t> public key (see above).</t>
</li> </li>
skipping to change at line 266 skipping to change at line 253
</li> </li>
</ul> </ul>
<t>Algorithm 22 in Section 7.2 of <xref target="FIPS204"/> defines the raw byte string <t>Algorithm 22 in Section 7.2 of <xref target="FIPS204"/> defines the raw byte string
encoding of an ML-DSA public key. When used in a <tt>SubjectPublicKeyInfo</tt> t ype, encoding of an ML-DSA public key. When used in a <tt>SubjectPublicKeyInfo</tt> t ype,
the <tt>subjectPublicKey BIT STRING</tt> contains this raw byte string encoding of the the <tt>subjectPublicKey BIT STRING</tt> contains this raw byte string encoding of the
public key. When an ML-DSA public key appears outside of a <tt>SubjectPublicKeyI nfo</tt> type in an public key. When an ML-DSA public key appears outside of a <tt>SubjectPublicKeyI nfo</tt> type in an
environment that uses ASN.1 encoding, it could be encoded as an <tt>OCTET STRING </tt> by environment that uses ASN.1 encoding, it could be encoded as an <tt>OCTET STRING </tt> by
using the <tt>ML-DSA-44-PublicKey</tt>, <tt>ML-DSA-65-PublicKey</tt>, and <tt>ML -DSA-87-PublicKey</tt> types using the <tt>ML-DSA-44-PublicKey</tt>, <tt>ML-DSA-65-PublicKey</tt>, and <tt>ML -DSA-87-PublicKey</tt> types
corresponding to the correct key size defined below.</t> corresponding to the correct key size defined below.</t>
<t>The <tt>PUBLIC-KEY</tt> ASN.1 types for ML-DSA are defined here:</t> <t>The <tt>PUBLIC-KEY</tt> ASN.1 types for ML-DSA are defined here:</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
pk-ml-dsa-44 PUBLIC-KEY ::= { pk-ml-dsa-44 PUBLIC-KEY ::= {
IDENTIFIER id-ml-dsa-44 IDENTIFIER id-ml-dsa-44
-- KEY no ASN.1 wrapping -- -- KEY no ASN.1 wrapping --
CERT-KEY-USAGE CERT-KEY-USAGE
{ digitalSignature, nonRepudiation, keyCertSign, cRLSign } { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
PRIVATE-KEY ML-DSA-44-PrivateKey } -- defined in Section 6 PRIVATE-KEY ML-DSA-44-PrivateKey } -- defined in Section 6
pk-ml-dsa-65 PUBLIC-KEY ::= { pk-ml-dsa-65 PUBLIC-KEY ::= {
IDENTIFIER id-ml-dsa-65 IDENTIFIER id-ml-dsa-65
-- KEY no ASN.1 wrapping -- -- KEY no ASN.1 wrapping --
skipping to change at line 292 skipping to change at line 279
IDENTIFIER id-ml-dsa-87 IDENTIFIER id-ml-dsa-87
-- KEY no ASN.1 wrapping -- -- KEY no ASN.1 wrapping --
CERT-KEY-USAGE CERT-KEY-USAGE
{ digitalSignature, nonRepudiation, keyCertSign, cRLSign } { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
PRIVATE-KEY ML-DSA-87-PrivateKey } -- defined in Section 6 PRIVATE-KEY ML-DSA-87-PrivateKey } -- defined in Section 6
ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312)) ML-DSA-44-PublicKey ::= OCTET STRING (SIZE (1312))
ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952)) ML-DSA-65-PublicKey ::= OCTET STRING (SIZE (1952))
ML-DSA-87-PublicKey ::= OCTET STRING (SIZE (2592)) ML-DSA-87-PublicKey ::= OCTET STRING (SIZE (2592))]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t><xref target="RFC5958"/> specifies the Asymmetric Key Package's <tt>One AsymmetricKey</tt> type for <t><xref target="RFC5958"/> specifies the Asymmetric Key Package's <tt>One AsymmetricKey</tt> type for
encoding asymmetric keypairs. When an ML-DSA private key or keypair is encoded a s encoding asymmetric keypairs. When an ML-DSA private key or keypair is encoded a s
a <tt>OneAsymmetricKey</tt>, it follows the description in <xref target="priv-ke y"/>.</t> a <tt>OneAsymmetricKey</tt>, it follows the description in <xref target="priv-ke y"/>.</t>
<t>When the ML-DSA private key appears outside of an Asymmetric Key Packag e in an <t>When the ML-DSA private key appears outside of an Asymmetric Key Packag e in an
environment that uses ASN.1 encoding, it can be encoded using one of the environment that uses ASN.1 encoding, it can be encoded using one of the
the <tt>ML-DSA-PrivateKey CHOICE</tt> formats defined in <xref target="priv-key" />. The <tt>seed</tt> format <tt>ML-DSA-PrivateKey CHOICE</tt> formats defined in <xref target="priv-key"/>. The <tt>seed</tt> format
is <bcp14>RECOMMENDED</bcp14> as it efficiently stores both the private and publ ic key.</t> is <bcp14>RECOMMENDED</bcp14> as it efficiently stores both the private and publ ic key.</t>
<t><xref target="examples"/> contains example ML-DSA public keys encoded u sing the <t><xref target="examples"/> contains example ML-DSA public keys encoded u sing the
textual encoding defined in <xref target="RFC7468"/>.</t> textual encoding defined in <xref target="RFC7468"/>.</t>
</section> </section>
<section anchor="key-usage-bits"> <section anchor="key-usage-bits">
<name>Key Usage Bits</name> <name>Key Usage Bits</name>
<t>The intended application for the key is indicated in the <tt>keyUsage</ tt> <t>The intended application for the key is indicated in the <tt>keyUsage</ tt>
certificate extension; see <xref section="4.2.1.3" sectionFormat="of" target="RF C5280"/>. If the certificate extension; see <xref section="4.2.1.3" sectionFormat="of" target="RF C5280"/>. If the
<tt>keyUsage</tt> extension is present in a certificate that includes <tt>id-ml- dsa-*</tt> <tt>keyUsage</tt> extension is present in a certificate that includes <tt>id-ml- dsa-*</tt>
(where * is 44, 65, or 87 - see <xref target="oids"/>) in the <tt>SubjectPublicK eyInfo</tt>, (where * is 44, 65, or 87 -- see <xref target="oids"/>) in the <tt>SubjectPublic KeyInfo</tt>,
then the subject public key can only be used then the subject public key can only be used
for verifying digital signatures on certificates or CRLs, or those used in an for verifying digital signatures on certificates or CRLs, or those used in an
entity authentication service, a data origin authentication service, an entity authentication service, a data origin authentication service, an
integrity service, and/or a non-repudiation service that protects against integrity service, and/or a non-repudiation service that protects against
the signing entity falsely denying some action. This means that the the signing entity falsely denying some action. This means that the
<tt>keyUsage</tt> extention <bcp14>MUST</bcp14> have at least one of the followi <tt>keyUsage</tt> extension <bcp14>MUST</bcp14> have at least one of the followi
ng bits set:</t> ng bits set:</t>
<artwork><![CDATA[
digitalSignature <ul spacing="normal">
nonRepudiation <li>digitalSignature</li>
keyCertSign <li>nonRepudiation</li>
cRLSign <li>keyCertSign</li>
]]></artwork> <li>cRLSign</li>
</ul>
<t>ML-DSA subject public keys cannot be used to establish keys or encrypt data, so the <t>ML-DSA subject public keys cannot be used to establish keys or encrypt data, so the
<tt>keyUsage</tt> extention <bcp14>MUST NOT</bcp14> have any of following bits s <tt>keyUsage</tt> extension <bcp14>MUST NOT</bcp14> have any of the following bi
et:</t> ts set:</t>
<artwork><![CDATA[
keyEncipherment, <ul spacing="normal">
dataEncipherment, <li>keyEncipherment</li>
keyAgreement, <li>dataEncipherment</li>
encipherOnly, and <li>keyAgreement</li>
decipherOnly. <li>encipherOnly</li>
]]></artwork> <li>decipherOnly</li>
</ul>
<t>Requirements about the <tt>keyUsage</tt> extension bits defined in <xre f target="RFC5280"/> <t>Requirements about the <tt>keyUsage</tt> extension bits defined in <xre f target="RFC5280"/>
still apply.</t> still apply.</t>
</section> </section>
<section anchor="priv-key"> <section anchor="priv-key">
<name>Private Key Format</name> <name>Private Key Format</name>
<t><xref target="FIPS204"/> specifies two formats for an ML-DSA private ke y: a 32-octet <t><xref target="FIPS204"/> specifies two formats for an ML-DSA private ke y: a 32-octet
seed (xi) and an (expanded) private key. The expanded private key (and public ke y) seed (<tt>xi</tt>) and an (expanded) private key. The expanded private key (and public key)
is computed from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt> (algorithm 6 ).</t> is computed from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt> (algorithm 6 ).</t>
<t>"Asymmetric Key Packages" <xref target="RFC5958"/> specifies how to enc ode a private <t>"Asymmetric Key Packages" <xref target="RFC5958"/> specifies how to enc ode a private
key in a structure that both identifies what algorithm the private key key in a structure that both identifies what algorithm the private key
is for and allows for the public key and additional attributes about the is for and allows for the public key and additional attributes about the
key to be included as well. For illustration, the ASN.1 structure key to be included as well. For illustration, the ASN.1 structure
<tt>OneAsymmetricKey</tt> is replicated below.</t> <tt>OneAsymmetricKey</tt> is replicated below.</t>
<artwork><![CDATA[ <sourcecode type="asn.1"><![CDATA[
OneAsymmetricKey ::= SEQUENCE { OneAsymmetricKey ::= SEQUENCE {
version Version, version Version,
privateKeyAlgorithm SEQUENCE { privateKeyAlgorithm SEQUENCE {
algorithm PUBLIC-KEY.&id({PublicKeySet}), algorithm PUBLIC-KEY.&id({PublicKeySet}),
parameters PUBLIC-KEY.&Params({PublicKeySet} parameters PUBLIC-KEY.&Params({PublicKeySet}
{@privateKeyAlgorithm.algorithm}) {@privateKeyAlgorithm.algorithm})
OPTIONAL} OPTIONAL}
privateKey OCTET STRING (CONTAINING privateKey OCTET STRING (CONTAINING
PUBLIC-KEY.&PrivateKey({PublicKeySet} PUBLIC-KEY.&PrivateKey({PublicKeySet}
{@privateKeyAlgorithm.algorithm})), {@privateKeyAlgorithm.algorithm})),
attributes [0] Attributes OPTIONAL, attributes [0] Attributes OPTIONAL,
..., ...,
[[2: publicKey [1] BIT STRING (CONTAINING [[2: publicKey [1] BIT STRING (CONTAINING
PUBLIC-KEY.&Params({PublicKeySet} PUBLIC-KEY.&Params({PublicKeySet}
{@privateKeyAlgorithm.algorithm}) {@privateKeyAlgorithm.algorithm})
OPTIONAL ]], OPTIONAL ]],
... ...
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5958"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5958"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>.</t> 2021 ASN.1 syntax <xref target="X680"/>.</t>
</aside> </aside>
<t>For ML-DSA private keys, the <tt>privateKey</tt> field in <tt>OneAsymme tricKey</tt> contains one of <t>For ML-DSA private keys, the <tt>privateKey</tt> field in <tt>OneAsymme tricKey</tt> contains one of
the following DER-encoded <tt>CHOICE</tt> structures. The <tt>seed</tt> format i s a the following DER-encoded <tt>CHOICE</tt> structures. The <tt>seed</tt> format i s a
fixed 32 byte <tt>OCTET STRING</tt> (34 bytes total with the <tt>0x8020</tt> tag and fixed 32-byte <tt>OCTET STRING</tt> (34 bytes total with the <tt>0x8020</tt> tag and
length) for all security levels, while the <tt>expandedKey</tt> and <tt>both</tt > formats length) for all security levels, while the <tt>expandedKey</tt> and <tt>both</tt > formats
vary in size by security level:</t> vary in size by security level:</t>
<artwork><![CDATA[
<sourcecode type="asn.1"><![CDATA[
ML-DSA-44-PrivateKey ::= CHOICE { ML-DSA-44-PrivateKey ::= CHOICE {
seed [0] OCTET STRING (SIZE (32)), seed [0] OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (2560)), expandedKey OCTET STRING (SIZE (2560)),
both SEQUENCE { both SEQUENCE {
seed OCTET STRING (SIZE (32)), seed OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (2560)) expandedKey OCTET STRING (SIZE (2560))
} }
} }
ML-DSA-65-PrivateKey ::= CHOICE { ML-DSA-65-PrivateKey ::= CHOICE {
skipping to change at line 404 skipping to change at line 392
} }
} }
ML-DSA-87-PrivateKey ::= CHOICE { ML-DSA-87-PrivateKey ::= CHOICE {
seed [0] OCTET STRING (SIZE (32)), seed [0] OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (4896)), expandedKey OCTET STRING (SIZE (4896)),
both SEQUENCE { both SEQUENCE {
seed OCTET STRING (SIZE (32)), seed OCTET STRING (SIZE (32)),
expandedKey OCTET STRING (SIZE (4896)) expandedKey OCTET STRING (SIZE (4896))
} }
} }]]></sourcecode>
]]></artwork>
<aside> <aside>
<t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the <t>NOTE: The above syntax is from <xref target="RFC5912"/> and is compat ible with the
2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t> 2021 ASN.1 syntax <xref target="X680"/>. See <xref target="RFC5280"/> for the 1988 ASN.1 syntax.</t>
</aside> </aside>
<t>The <tt>CHOICE</tt> allows three representations of the private key:</t > <t>The <tt>CHOICE</tt> allows three representations of the private key:</t >
<ol spacing="normal" type="1"><li> <ol spacing="normal" type="1"><li>
<t>The <tt>seed</tt> format (tag <tt>[0]</tt>) contains just the 32-by te seed value (xi) <t>The <tt>seed</tt> format (tag <tt>[0]</tt>) contains just the 32-by te seed value (<tt>xi</tt>)
from which both the expanded private key and public key can be derived from which both the expanded private key and public key can be derived
using <tt>ML-DSA.KeyGen_internal(xi)</tt>.</t> using <tt>ML-DSA.KeyGen_internal(xi)</tt>.</t>
</li> </li>
<li> <li>
<t>The <tt>expandedKey</tt> format contains the expanded private key t hat was <t>The <tt>expandedKey</tt> format contains the expanded private key t hat was
derived from the seed.</t> derived from the seed.</t>
</li> </li>
<li> <li>
<t>The <tt>both</tt> format contains both the seed and expanded privat e key, allowing for <t>The <tt>both</tt> format contains both the seed and expanded privat e key, allowing for
for interoperability; some may want to use and retain the seed and interoperability; some may want to use and retain the seed and
others may only support expanded private keys.</t> others may only support expanded private keys.</t>
</li> </li>
</ol> </ol>
<t>When encoding an ML-DSA private key in a <tt>OneAsymmetricKey</tt> obje ct, any of <t>When encoding an ML-DSA private key in a <tt>OneAsymmetricKey</tt> obje ct, any of
these three formats may be used, though the seed format is <bcp14>RECOMMENDED</b cp14> these three formats may be used, though the seed format is <bcp14>RECOMMENDED</b cp14>
for storage efficiency.</t> for storage efficiency.</t>
<t>The <tt>privateKeyAlgorithm</tt> field uses the <tt>AlgorithmIdentifier </tt> structure with <t>The <tt>privateKeyAlgorithm</tt> field uses the <tt>AlgorithmIdentifier </tt> structure with
the appropriate OID as defined in <xref target="oids"/>. If present, the <tt>pub licKey</tt> the appropriate OID as defined in <xref target="oids"/>. If present, the <tt>pub licKey</tt>
field will hold the encoded public key as defined in <xref target="ML-DSA-Public Key"/>.</t> field will hold the encoded public key as defined in <xref target="ML-DSA-Public Key"/>.</t>
<aside>
<t>NOTE: While the private key can be stored in multiple formats, the seed -only <t>NOTE: While the private key can be stored in multiple formats, the seed -only
format is <bcp14>RECOMMENDED</bcp14> as it is the most compact representation. B oth the format is <bcp14>RECOMMENDED</bcp14> as it is the most compact representation. B oth the
expanded private key and the public key can be deterministically derived expanded private key and the public key can be deterministically derived
from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt>. Alternatively, the publ ic from the seed using <tt>ML-DSA.KeyGen_internal(xi)</tt>. Alternatively, the publ ic
key can be generated from the private key. While the <tt>publicKey</tt> field key can be generated from the private key. While the <tt>publicKey</tt> field
and <tt>expandedKey</tt> format are technically redundant when using the seed-on ly and <tt>expandedKey</tt> format are technically redundant when using the seed-on ly
format, they <bcp14>MAY</bcp14> be included to enable keypair consistency checks during format, they <bcp14>MAY</bcp14> be included to enable keypair consistency checks during
import operations.</t> import operations.</t>
</aside>
<t>When parsing the private key, the ASN.1 tag explicitly indicates which <t>When parsing the private key, the ASN.1 tag explicitly indicates which
variant of <tt>CHOICE</tt> is present. Implementations should use the context-sp ecific tag <tt>IMPLICIT [0]</tt> variant of <tt>CHOICE</tt> is present. Implementations should use the context-sp ecific tag <tt>IMPLICIT [0]</tt>
(raw value <tt>0x80</tt>) for <tt>seed</tt>, <tt>OCTET STRING</tt> (<tt>0x04</tt >) for <tt>expandedKey</tt>, and (raw value <tt>0x80</tt>) for <tt>seed</tt>, <tt>OCTET STRING</tt> (<tt>0x04</tt >) for <tt>expandedKey</tt>, and
<tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, ra ther than any <tt>SEQUENCE</tt> (<tt>0x30</tt>) for <tt>both</tt> to parse the private key, ra ther than any
other heuristic like length of the enclosing <tt>OCTET STRING</tt>.</t> other heuristic like length of the enclosing <tt>OCTET STRING</tt>.</t>
<t><xref target="examples"/> contains example ML-DSA private keys encoded using the <t><xref target="examples"/> contains example ML-DSA private keys encoded using the
textual encoding defined in <xref target="RFC7468"/>.</t> textual encoding defined in <xref target="RFC7468"/>.</t>
</section> </section>
<section anchor="iana-considerations"> <section anchor="iana-considerations">
<name>IANA Considerations</name> <name>IANA Considerations</name>
<t>For the ASN.1 module in <xref target="asn1"/>, IANA is requested to ass <t>For the ASN.1 module in <xref target="asn1"/>, IANA has assigned the fo
ign an object llowing object identifier (OID) in the "SMI Security for PKIX Module Identifier"
identifier (OID) for the module identifier (TBD1) with a Description registry (1.3.6.1.5.5.7.0): </t>
of "id-mod-x509-ml-dsa-2025". The OID for the module should be
allocated in the "SMI Security for PKIX Module Identifier" registry <table anchor="oid">
(1.3.6.1.5.5.7.0).</t> <name>Registered ASN.1 Module</name>
<thead>
<tr>
<th>Decimal</th>
<th>Description</th>
<th>Reference</th>
</tr>
</thead>
<tbody>
<tr>
<td>119</td>
<td>id-mod-x509-ml-dsa-2025</td>
<td>RFC 9881</td>
</tr>
</tbody>
</table>
</section> </section>
<section anchor="operational-considerations"> <section anchor="operational-considerations">
<name>Operational Considerations</name> <name>Operational Considerations</name>
<section anchor="private-key-format"> <section anchor="private-key-format">
<name>Private Key Format</name> <name>Private Key Format</name>
<t>An <tt>ML-DSA.KeyGen seed (xi)</tt> represents the <bcp14>RECOMMENDED </bcp14> format for storing <t>An <tt>ML-DSA.KeyGen seed (xi)</tt> represents the <bcp14>RECOMMENDED </bcp14> format for storing
and transmitting ML-DSA private keys. This format is explicitly permitted and transmitting ML-DSA private keys. This format is explicitly permitted
by <xref target="FIPS204"/> as an acceptable representation of a keypair. In par ticular, by <xref target="FIPS204"/> as an acceptable representation of a keypair. In par ticular,
generating the seed in one cryptographic module and then importing or generating the seed in one cryptographic module and then importing or
exporting it into another cryptographic module is allowed. The internal exporting it into another cryptographic module is allowed. The internal
key generation function <tt>ML-DSA.KeyGen_internal(xi)</tt> can be accessed for key-generation function <tt>ML-DSA.KeyGen_internal(xi)</tt> can be accessed for
this purpose.</t> this purpose.</t>
<t>Note also that unlike other private key compression methods in other algorithms, <t>Note also that unlike other private key compression methods in other algorithms,
expanding a private key from a seed is a one-way function, meaning that once a expanding a private key from a seed is a one-way function, meaning that once a
full key is expanded from seed and the seed discarded, the seed cannot be full key is expanded from seed and the seed discarded, the seed cannot be
re-created even if the full expanded private key is available. For this reason recreated, even if the full expanded private key is available. For this reason,
it is <bcp14>RECOMMENDED</bcp14> that implementations retain and export the seed , it is <bcp14>RECOMMENDED</bcp14> that implementations retain and export the seed ,
even when also exporting the expanded private key. ML-DSA seed extraction can be even when also exporting the expanded private key. ML-DSA seed extraction can be
implemented by including the seed xi randomly generated at line 1 of Algorithm 1 implemented by including the seed xi that is randomly generated at line 1 of Alg orithm 1
<tt>ML-DSA.KeyGen</tt> in the returned output.</t> <tt>ML-DSA.KeyGen</tt> in the returned output.</t>
<t>When encoding an ML-DSA private key in a OneAsymmetricKey object, any <t>When encoding an ML-DSA private key in a <tt>OneAsymmetricKey</tt> ob ject, any
of these three formats may be used, though the seed format is of these three formats may be used, though the seed format is
<bcp14>RECOMMENDED</bcp14> for storage efficiency.</t> <bcp14>RECOMMENDED</bcp14> for storage efficiency.</t>
</section> </section>
<section anchor="private-key-consistency-testing"> <section anchor="private-key-consistency-testing">
<name>Private Key Consistency Testing</name> <name>Private Key Consistency Testing</name>
<t>When receiving a private key that contains both the seed and the <t>When receiving a private key that contains both the <tt>seed</tt> and
expandedKey, the recipient <bcp14>SHOULD</bcp14> perform a seed consistency chec the
k to <tt>expandedKey</tt>, the recipient <bcp14>SHOULD</bcp14> perform a seed consist
ency check to
ensure that the sender properly generated the private key. Recipients ensure that the sender properly generated the private key. Recipients
that do not perform this seed consistency check avoid keygen that do not perform this seed consistency check avoid keygen
and compare operations, but are unable to ensure that the <tt>seed</tt> and and compare operations, but are unable to ensure that the <tt>seed</tt> and
<tt>expandedKey</tt> match.</t> <tt>expandedKey</tt> match.</t>
<t>If the check is done and the <tt>seed</tt> and the <tt>expandedKey</t t> are not consistent, <t>If the check is done and the <tt>seed</tt> and the <tt>expandedKey</t t> are not consistent,
the recipient <bcp14>MUST</bcp14> reject the private key as malformed.</t> the recipient <bcp14>MUST</bcp14> reject the private key as malformed.</t>
<t>The seed consistency check consists of regenerating the expanded form from <t>The seed consistency check consists of regenerating the expanded form from
the seed via <tt>ML-DSA.KeyGen_internal</tt> and ensuring it is bytewise equal t o the seed via <tt>ML-DSA.KeyGen_internal</tt>, and ensuring it is bytewise equal to
the value presented in the private key.</t> the value presented in the private key.</t>
<t><xref target="example-bad"/> includes some examples of inconsistent s eeds and expanded private <t><xref target="example-bad"/> includes some examples of inconsistent s eeds and expanded private
keys.</t> keys.</t>
</section> </section>
<section anchor="sec-disallow-hash"> <section anchor="sec-disallow-hash">
<name>Rationale for disallowing HashML-DSA</name> <name>Rationale for Disallowing HashML-DSA</name>
<t>The HashML-DSA mode defined in Section 5.4 of <xref target="FIPS204"/ > <bcp14>MUST NOT</bcp14> be <t>The HashML-DSA mode defined in Section 5.4 of <xref target="FIPS204"/ > <bcp14>MUST NOT</bcp14> be
used; in other words, public keys identified by used; in other words, public keys identified by
<tt>id-hash-ml-dsa-44-with-sha512</tt>, <tt>id-hash-ml-dsa-65-with-sha512</tt>, and <tt>id-hash-ml-dsa-44-with-sha512</tt>, <tt>id-hash-ml-dsa-65-with-sha512</tt>, and
<tt>id-hash-ml-dsa-87-with-sha512</tt> <bcp14>MUST NOT</bcp14> be in X.509 certi ficates used for <tt>id-hash-ml-dsa-87-with-sha512</tt> <bcp14>MUST NOT</bcp14> be in X.509 certi ficates used for
CRLs, OCSP, certificate issuance and related PKIX protocols. This restriction CRLs, OCSP, certificate issuance, and related PKIX protocols. This restriction
is primarily to increase interoperability.</t> is primarily to increase interoperability.</t>
<t>ML-DSA and HashML-DSA are incompatible algorithms that require <t>ML-DSA and HashML-DSA are incompatible algorithms that require
different <tt>Verify()</tt> routines. This introduces the complexity of different <tt>Verify()</tt> routines. This introduces the complexity of
informing the verifier whether to use <tt>ML-DSA.Verify()</tt> or informing the verifier whether to use <tt>ML-DSA.Verify()</tt> or
<tt>HashML-DSA.Verify()</tt>. Additionally, since <tt>HashML-DSA.Verify()</tt>. Additionally, since
the same OIDs are used to identify the ML-DSA the same OIDs are used to identify the ML-DSA
public keys and ML-DSA signature algorithms, an implementation would public keys and ML-DSA signature algorithms, an implementation would
need to commit a given public key to be either of type <tt>ML-DSA</tt> or need to commit a given public key to be either of type <tt>ML-DSA</tt> or
<tt>HashML-DSA</tt> at the time of certificate creation. This is anticipated <tt>HashML-DSA</tt> at the time of certificate creation. This is anticipated
to cause operational issues in contexts where the operator does not to cause operational issues in contexts where the operator does not
know whether the key will need to produce pure or pre-hashed signatures know whether the key will need to produce pure or pre-hashed signatures
at key generation time. The External μ (mu) mode described in <xref target="exte rnalmu"/> at key-generation time. The External <u>μ</u> mode described in <xref target="ex ternalmu"/>
avoids all of these operational concerns.</t> avoids all of these operational concerns.</t>
<t>A minor security reason for disallowing HashML-DSA is that the design of the <t>A minor security reason for disallowing HashML-DSA is that the design of the
ML-DSA algorithm provides enhanced resistance against collision attacks, ML-DSA algorithm provides enhanced resistance against collision attacks,
compared with HashML-DSA or conventional RSA or ECDSA signature algorithms. compared with HashML-DSA or conventional RSA or ECDSA signature algorithms.
Specifically, ML-DSA prepends the SHAKE256 hash of the public key (<tt>tr</tt>) Specifically, ML-DSA prepends the SHAKE256 hash of the public key (<tt>tr</tt>)
to the message to-be-signed prior to hashing, as described in to the message to-be-signed prior to hashing, as described in
line 6 of Algorithm 7 of <xref target="FIPS204"/>. This means that in the unlike ly line 6 of Algorithm 7 of <xref target="FIPS204"/>. This means that in the unlike ly
discovery of a collision attack against the SHA-3 family, an attacker discovery of a collision attack against the SHA-3 family, an attacker
would have to perform a public-key-specific collision search in order would have to perform a public-key-specific collision search in order
to find message pairs such that <tt>H(tr || m1) = H(tr || m2)</tt> since a to find message pairs such that <tt>H(tr || m1) = H(tr || m2)</tt>, because a
direct hash collision <tt>H(m1) = H(m2)</tt> will not suffice. direct hash collision <tt>H(m1) = H(m2)</tt> will not suffice.
HashML-DSA removes this enhanced security property. HashML-DSA removes this enhanced security property.
In spite of its lack of targeted collision protection, the practical In spite of its lack of targeted collision protection, the practical
security risk of using HashML-DSA in X.509 signatures would be security risk of using HashML-DSA in X.509 signatures would be
immaterial. That is because a hash of the issuing CA's public key immaterial. This is because a hash of the issuing CA's public key
is already included in the Authority Key Identifier (AKI) extension which is already included in the Authority Key Identifier (AKI) extension, which
is signed as part of the tbsCertificate structure. is signed as part of the TBSCertificate structure.
Even when it is a SHA-1 hash, general second pre-images against Even when it is a SHA-1 hash, general second pre-images against
the AKI hash of existing issuing CAs would be impractical.</t> the AKI hash of existing issuing CAs would be impractical.</t>
</section> </section>
</section> </section>
<section anchor="security-considerations"> <section anchor="security-considerations">
<name>Security Considerations</name> <name>Security Considerations</name>
<t>The Security Considerations section of <xref target="RFC5280"/> applies to this <t>The Security Considerations section of <xref target="RFC5280"/> applies to this
specification as well.</t> specification as well.</t>
<t>The ML-DSA signature scheme is strongly unforgeable under chosen messag e <t>The ML-DSA signature scheme is strongly unforgeable under chosen messag e
attacks (SUF-CMA). For the purpose of estimating security strength, it has attacks (SUF-CMA). For the purpose of estimating security strength, it has
been assumed that the attacker has access to signatures for no more been assumed that the attacker has access to signatures for no more
than 2^{64} chosen messages.</t> than 2^{64} chosen messages.</t>
<t>ML-DSA depends on high quality random numbers that are suitable for <t>ML-DSA depends on high quality random numbers that are suitable for
use in cryptography. The use of inadequate pseudo-random number use in cryptography. The use of inadequate pseudo-random number
generators (PRNGs) to generate such values can significantly undermine generators (PRNGs) to generate such values can significantly undermine
various security properties. For instance, using an inadequate PRNG various security properties. For instance, using an inadequate PRNG
for key generation, might allow an attacker to efficiently recover for key generation might allow an attacker to efficiently recover
the private key by trying a small set of possibilities, rather than the private key by trying a small set of possibilities, rather than
brute force search the whole keyspace. The generation of random brute-force searching the whole keyspace. The generation of random
numbers of a sufficient level of quality for use in cryptography numbers of a sufficient level of quality for use in cryptography
is difficult; see Section 3.6.1 of <xref target="FIPS204"/> for some additional is difficult; see Section 3.6.1 of <xref target="FIPS204"/> for some additional
information.</t> information.</t>
<t>In the design of ML-DSA, care has been taken to make side-channel <t>In the design of ML-DSA, care has been taken to make side-channel
resilience easier to achieve. For instance, ML-DSA does not depend resilience easier to achieve. For instance, ML-DSA does not depend
on Gaussian sampling. Implementations must still take great care on Gaussian sampling. Implementations must still take great care
not to leak information via various side channels. While deliberate not to leak information via various side channels. While deliberate
design decisions such as these can help to deliver a greater ease design decisions such as these can help to deliver a
of secure implementation - particularly against side-channel secure implementation with greater ease -- particularly against side-channel
attacks - it does not necessarily provide resistance to more attacks -- it does not necessarily provide resistance to more
powerful attacks such as differential power analysis. Some amount powerful attacks such as differential power analysis. Some amount
of side-channel leakage has been demonstrated in parts of the of side-channel leakage has been demonstrated in parts of the
signing algorithm (specifically the bit-unpacking function), from signing algorithm (specifically the bit-unpacking function), from
which a demonstration of key recovery has been made over a large which a demonstration of key recovery has been made over a large
sample of signatures. Masking countermeasures exist for sample of signatures. Masking countermeasures exist for
ML-DSA, but come with a performance overhead.</t> ML-DSA, but comes with performance overhead.</t>
<t>ML-DSA offers both deterministic and randomized signing. Signatures <t>ML-DSA offers both deterministic and randomized signing. Signatures
generated with either mode are compatible and a verifyer can't tell generated with either mode are compatible and a verifier cannot tell
them apart. In the deterministic case, a signature only depends them apart. In the deterministic case, a signature only depends
on the private key and the message to be signed. This makes on the private key and the message to be signed. This makes
the implementation easier to test and does not require the implementation easier to test and does not require
a randomness source during signing. In the randomized case, a randomness source during signing. In the randomized case,
signing mixes in a 256-bit random string from an approved random bit signing mixes in a 256-bit random string from an approved random bit
generator (RBG). When randomized, ML-DSA is easier to harden generator (RBG). When randomized, ML-DSA is easier to harden
against fault and hardware side-channel attacks.</t> against fault and hardware side-channel attacks.</t>
<t>A security property also associated with digital
<t>A security property that is also associated with digital
signatures is non-repudiation. Non-repudiation refers to the signatures is non-repudiation. Non-repudiation refers to the
assurance that the owner of a signature key pair that was assurance that the owner of a signature keypair that was
capable of generating an existing signature corresponding to capable of generating an existing signature corresponding to
certain data cannot convincingly deny having signed the data, certain data cannot convincingly deny having signed the data,
unless its private key was compromised. unless its private key was compromised.
The digital signature scheme ML-DSA possess three security The digital signature scheme ML-DSA possesses three security
properties beyond unforgeability, that are associated with properties beyond unforgeability, that are associated with
non-repudiation. These are exclusive ownership, message-bound non-repudiation. These are exclusive ownership, message-bound
signatures, and non-resignability. These properties are based signatures, and non-resignability. These properties are based
tightly on the assumed collision resistance of the hash tightly on the assumed collision resistance of the hash
function used (in this case SHAKE-256). A full discussion function used (in this case SHAKE-256). A full discussion
of these properties in ML-DSA can be found at <xref target="CDFFJ21"/>.</t> of these properties in ML-DSA can be found at <xref target="CDFFJ21"/>.</t>
</section> </section>
</middle> </middle>
<back> <back>
<references anchor="sec-combined-references"> <references anchor="sec-combined-references">
skipping to change at line 608 skipping to change at line 614
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.680"/> <seriesInfo name="ITU-T Recommendation" value="X.680"/>
<seriesInfo name="ISO/IEC" value="8824-1:2021"/> <seriesInfo name="ISO/IEC" value="8824-1:2021"/>
</reference> </reference>
<reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690"> <reference anchor="X690" target="https://www.itu.int/rec/T-REC-X.690">
<front> <front>
<title>Information Technology -- Abstract Syntax Notation One (ASN.1 ): ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title> <title>Information Technology -- ASN.1 encoding rules: Specification of Basic Encoding Rules (BER), Canonical Encoding Rules (CER) and Distinguished Encoding Rules (DER)</title>
<author> <author>
<organization>ITU-T</organization> <organization>ITU-T</organization>
</author> </author>
<date year="2021" month="February"/> <date year="2021" month="February"/>
</front> </front>
<seriesInfo name="ITU-T Recommendation" value="X.690"/> <seriesInfo name="ITU-T Recommendation" value="X.690"/>
<seriesInfo name="ISO/IEC" value="8825-1:2021"/> <seriesInfo name="ISO/IEC" value="8825-1:2021"/>
</reference> </reference>
<reference anchor="CSOR" target="https://csrc.nist.gov/projects/computer
-security-objects-register/algorithm-registration"> <reference anchor="FIPS204" target="https://nvlpubs.nist.gov/nistpubs/FI
PS/NIST.FIPS.204.pdf">
<front> <front>
<title>Computer Security Objects Register</title> <title>Module-Lattice-Based Digital Signature Standard</title>
<author initials="" surname="NIST" fullname="National Institute of S <author>
tandards and Technology"> <organization abbrev="NIST">National Institute of Standards and Te
<organization/> chnology</organization>
</author> </author>
<date year="2024" month="August" day="20"/> <date day="13" year="2024" month="August"/>
</front> </front>
<seriesInfo name="NIST FIPS" value="204"/>
<seriesInfo name="DOI" value="10.6028/NIST.FIPS.204 "/>
</reference> </reference>
<reference anchor="FIPS204">
<reference anchor="CSOR" target="https://csrc.nist.gov/projects/computer
-security-objects-register/algorithm-registration">
<front> <front>
<title>Module-lattice-based digital signature standard</title> <title>Computer Security Objects Register (CSOR)</title>
<author> <author>
<organization/> <organization abbrev="NIST">National Institute of Standards and Te chnology</organization>
</author> </author>
<date month="August" year="2024"/> <date year="2025" month="June" day="13"/>
</front>
<seriesInfo name="DOI" value="10.6028/nist.fips.204"/>
<refcontent>National Institute of Standards and Technology (U.S.)</ref
content>
</reference>
<reference anchor="RFC2119">
<front>
<title>Key words for use in RFCs to Indicate Requirement Levels</tit
le>
<author fullname="S. Bradner" initials="S." surname="Bradner"/>
<date month="March" year="1997"/>
<abstract>
<t>In many standards track documents several words are used to sig
nify the requirements in the specification. These words are often capitalized. T
his document defines these words as they should be interpreted in IETF documents
. This document specifies an Internet Best Current Practices for the Internet Co
mmunity, and requests discussion and suggestions for improvements.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="2119"/>
<seriesInfo name="DOI" value="10.17487/RFC2119"/>
</reference>
<reference anchor="RFC8174">
<front>
<title>Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words</ti
tle>
<author fullname="B. Leiba" initials="B." surname="Leiba"/>
<date month="May" year="2017"/>
<abstract>
<t>RFC 2119 specifies common key words that may be used in protoco
l specifications. This document aims to reduce the ambiguity by clarifying that
only UPPERCASE usage of the key words have the defined special meanings.</t>
</abstract>
</front>
<seriesInfo name="BCP" value="14"/>
<seriesInfo name="RFC" value="8174"/>
<seriesInfo name="DOI" value="10.17487/RFC8174"/>
</reference>
<reference anchor="RFC5912">
<front>
<title>New ASN.1 Modules for the Public Key Infrastructure Using X.5
09 (PKIX)</title>
<author fullname="P. Hoffman" initials="P." surname="Hoffman"/>
<author fullname="J. Schaad" initials="J." surname="Schaad"/>
<date month="June" year="2010"/>
<abstract>
<t>The Public Key Infrastructure using X.509 (PKIX) certificate fo
rmat, and many associated formats, are expressed using ASN.1. The current ASN.1
modules conform to the 1988 version of ASN.1. This document updates those ASN.1
modules to conform to the 2002 version of ASN.1. There are no bits-on-the-wire c
hanges to any of the formats; this is simply a change to the syntax. This docume
nt is not an Internet Standards Track specification; it is published for informa
tional purposes.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5912"/>
<seriesInfo name="DOI" value="10.17487/RFC5912"/>
</reference>
<reference anchor="RFC5280">
<front>
<title>Internet X.509 Public Key Infrastructure Certificate and Cert
ificate Revocation List (CRL) Profile</title>
<author fullname="D. Cooper" initials="D." surname="Cooper"/>
<author fullname="S. Santesson" initials="S." surname="Santesson"/>
<author fullname="S. Farrell" initials="S." surname="Farrell"/>
<author fullname="S. Boeyen" initials="S." surname="Boeyen"/>
<author fullname="R. Housley" initials="R." surname="Housley"/>
<author fullname="W. Polk" initials="W." surname="Polk"/>
<date month="May" year="2008"/>
<abstract>
<t>This memo profiles the X.509 v3 certificate and X.509 v2 certif
icate revocation list (CRL) for use in the Internet. An overview of this approac
h and model is provided as an introduction. The X.509 v3 certificate format is d
escribed in detail, with additional information regarding the format and semanti
cs of Internet name forms. Standard certificate extensions are described and two
Internet-specific extensions are defined. A set of required certificate extensi
ons is specified. The X.509 v2 CRL format is described in detail along with stan
dard and Internet-specific extensions. An algorithm for X.509 certification path
validation is described. An ASN.1 module and examples are provided in the appen
dices. [STANDARDS-TRACK]</t>
</abstract>
</front>
<seriesInfo name="RFC" value="5280"/>
<seriesInfo name="DOI" value="10.17487/RFC5280"/>
</reference>
<reference anchor="RFC5958">
<front>
<title>Asymmetric Key Packages</title>
<author fullname="S. Turner" initials="S." surname="Turner"/>
<date month="August" year="2010"/>
<abstract>
<t>This document defines the syntax for private-key information an
d a content type for it. Private-key information includes a private key for a sp
ecified public-key algorithm and a set of attributes. The Cryptographic Message
Syntax (CMS), as defined in RFC 5652, can be used to digitally sign, digest, aut
henticate, or encrypt the asymmetric key format content type. This document obso
letes RFC 5208. [STANDARDS-TRACK]</t>
</abstract>
</front> </front>
<seriesInfo name="RFC" value="5958"/>
<seriesInfo name="DOI" value="10.17487/RFC5958"/>
</reference> </reference>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.2
119.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.8
174.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
912.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
280.xml"/>
<xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.5
958.xml"/>
</references> </references>
<references anchor="sec-informative-references"> <references anchor="sec-informative-references">
<name>Informative References</name> <name>Informative References</name>
<reference anchor="Dilithium" target="https://pq-crystals.org/dilithium/ data/dilithium-specification-round3-20210208.pdf"> <reference anchor="Dilithium" target="https://pq-crystals.org/dilithium/ data/dilithium-specification-round3-20210208.pdf">
<front> <front>
<title>CRYSTALS-Dilithium Algorithm Specifications and Supporting Do cumentation</title> <title>CRYSTALS-Dilithium Algorithm Specifications and Supporting Do cumentation (Version 3.1)</title>
<author initials="S." surname="Bai"> <author initials="S." surname="Bai">
<organization/> <organization/>
</author> </author>
<author initials="L." surname="Ducas"> <author initials="L." surname="Ducas">
<organization/> <organization/>
</author> </author>
<author initials="E." surname="Kiltz">
<organization/>
</author>
<author initials="T." surname="Lepoint"> <author initials="T." surname="Lepoint">
<organization/> <organization/>
</author> </author>
<author initials="V." surname="Lyubashevsky"> <author initials="V." surname="Lyubashevsky">
<organization/> <organization/>
</author> </author>
<author initials="P." surname="Schwabe"> <author initials="P." surname="Schwabe">
<organization/> <organization/>
</author> </author>
<author initials="G." surname="Seiler"> <author initials="G." surname="Seiler">
<organization/> <organization/>
</author> </author>
<author initials="D." surname="Stehlé"> <author initials="D." surname="Stehlé">
<organization/> <organization/>
</author> </author>
<date year="2021"/> <date day="8" month="2" year="2021"/>
</front> </front>
</reference> </reference>
<reference anchor="Fiat-Shamir" target="https://www.iacr.org/archive/asi acrypt2009/59120596/59120596.pdf"> <reference anchor="Fiat-Shamir" target="https://www.iacr.org/archive/asi acrypt2009/59120596/59120596.pdf">
<front> <front>
<title>Fiat-Shamir with aborts: Applications to lattice and factorin g-based signatures</title> <title>Fiat-Shamir with aborts: Applications to lattice and factorin g-based signatures</title>
<author initials="V." surname="Lyubashevsky"> <author initials="V." surname="Lyubashevsky">
<organization/> <organization/>
</author> </author>
<date year="2009"/> <date year="2009"/>
</front> </front>
<seriesInfo name="International Conference on the Theory and Applicati on of Cryptology and Information Security" value=""/> <refcontent>International Conference on the Theory and Application of Cryptology and Information Security</refcontent>
</reference> </reference>
<reference anchor="CDFFJ21" target="https://eprint.iacr.org/2020/1525.pd
f"> <reference anchor="CDFFJ21" target="https://eprint.iacr.org/archive/2020
/1525/20231023:114351">
<front> <front>
<title>BUFFing signature schemes beyond unforgeability and the case of post-quantum signatures</title> <title>BUFFing signature schemes beyond unforgeability and the case of post-quantum signatures</title>
<author initials="C." surname="Cremers"> <author initials="C." surname="Cremers">
<organization/> <organization/>
</author> </author>
<author initials="S." surname="Düzlü"> <author initials="S." surname="Düzlü">
<organization/> <organization/>
</author> </author>
<author initials="R." surname="Fiedler"> <author initials="R." surname="Fiedler">
<organization/> <organization/>
</author> </author>
<author initials="M." surname="Fischlin"> <author initials="M." surname="Fischlin">
<organization/> <organization/>
</author> </author>
<author initials="C." surname="Janson"> <author initials="C." surname="Janson">
<organization/> <organization/>
</author> </author>
<date year="2021"/> <date month="October" year="2023"/>
</front> </front>
<seriesInfo name="In Proceedings of the 42nd IEEE Symposium on Securit y and Privacy" value=""/> <refcontent>Cryptology ePrint Archive, Paper 2020/1525</refcontent>
</reference> </reference>
<reference anchor="NIST-PQC" target="https://csrc.nist.gov/Projects/post -quantum-cryptography"> <reference anchor="NIST-PQC" target="https://csrc.nist.gov/Projects/post -quantum-cryptography">
<front> <front>
<title>Post-Quantum Cryptography Project</title> <title>Post-Quantum Cryptography (PQC)</title>
<author> <author>
<organization>National Institute of Standards and Technology (NIST )</organization> <organization abbrev="NIST">National Institute of Standards and Te chnology</organization>
</author> </author>
<date year="2016" month="December" day="20"/> <date year="2025" month="July" day="28"/>
</front> </front>
</reference> </reference>
<reference anchor="FIPS204-ExternalMuFAQ" target="https://csrc.nist.gov/ csrc/media/Projects/post-quantum-cryptography/documents/faq/fips204-sec6-0319202 5.pdf"> <reference anchor="FIPS204-ExternalMuFAQ" target="https://csrc.nist.gov/ csrc/media/Projects/post-quantum-cryptography/documents/faq/fips204-sec6-0319202 5.pdf">
<front> <front>
<title>FIPS 204 Section 6 FAQ</title> <title>FIPS 204 Section 6 FAQ</title>
<author> <author>
<organization>National Institute of Standards and Technology (NIST )</organization> <organization abbrev="NIST">National Institute of Standards and Te chnology</organization>
</author> </author>
<date year="2025"/> <date year="2025"/>
</front> </front>
</reference> </reference>
<reference anchor="RFC7468"> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.7
<front> 468.xml"/>
<title>Textual Encodings of PKIX, PKCS, and CMS Structures</title> <xi:include href="https://bib.ietf.org/public/rfc/bibxml/reference.RFC.3
<author fullname="S. Josefsson" initials="S." surname="Josefsson"/> 647.xml"/>
<author fullname="S. Leonard" initials="S." surname="Leonard"/>
<date month="April" year="2015"/>
<abstract>
<t>This document describes and discusses the textual encodings of
the Public-Key Infrastructure X.509 (PKIX), Public-Key Cryptography Standards (P
KCS), and Cryptographic Message Syntax (CMS). The textual encodings are well-kno
wn, are implemented by several applications and libraries, and are widely deploy
ed. This document articulates the de facto rules by which existing implementatio
ns operate and defines them so that future implementations can interoperate.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="7468"/>
<seriesInfo name="DOI" value="10.17487/RFC7468"/>
</reference>
<reference anchor="RFC3647">
<front>
<title>Internet X.509 Public Key Infrastructure Certificate Policy a
nd Certification Practices Framework</title>
<author fullname="S. Chokhani" initials="S." surname="Chokhani"/>
<author fullname="W. Ford" initials="W." surname="Ford"/>
<author fullname="R. Sabett" initials="R." surname="Sabett"/>
<author fullname="C. Merrill" initials="C." surname="Merrill"/>
<author fullname="S. Wu" initials="S." surname="Wu"/>
<date month="November" year="2003"/>
<abstract>
<t>This document presents a framework to assist the writers of cer
tificate policies or certification practice statements for participants within p
ublic key infrastructures, such as certification authorities, policy authorities
, and communities of interest that wish to rely on certificates. In particular,
the framework provides a comprehensive list of topics that potentially (at the w
riter's discretion) need to be covered in a certificate policy or a certificatio
n practice statement. This document supersedes RFC 2527.</t>
</abstract>
</front>
<seriesInfo name="RFC" value="3647"/>
<seriesInfo name="DOI" value="10.17487/RFC3647"/>
</reference>
</references> </references>
</references> </references>
<?line 726?>
<section anchor="asn1"> <section anchor="asn1">
<name>ASN.1 Module</name> <name>ASN.1 Module</name>
<t>This appendix includes the ASN.1 module <xref target="X680"/> for the M L-DSA. Note that <t>This appendix includes the ASN.1 module <xref target="X680"/> for the M L-DSA. Note that
as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rul es; see as per <xref target="RFC5280"/>, certificates use the Distinguished Encoding Rul es; see
<xref target="X690"/>. This module imports objects from <xref target="RFC5912"/> .</t> <xref target="X690"/>. This module imports objects from <xref target="RFC5912"/> .</t>
<sourcecode markers="true"><![CDATA[ <sourcecode type="asn.1" markers="true"><![CDATA[
X509-ML-DSA-2025 X509-ML-DSA-2025
{ iso(1) identified-organization(3) dod(6) { iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0) internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-x509-ml-dsa-2025(TBD1) } id-mod-x509-ml-dsa-2025(119) }
DEFINITIONS IMPLICIT TAGS ::= BEGIN DEFINITIONS IMPLICIT TAGS ::= BEGIN
EXPORTS ALL; EXPORTS ALL;
IMPORTS IMPORTS
PUBLIC-KEY, SIGNATURE-ALGORITHM PUBLIC-KEY, SIGNATURE-ALGORITHM
FROM AlgorithmInformation-2009 -- [RFC 5912] FROM AlgorithmInformation-2009 -- [RFC 5912]
{ iso(1) identified-organization(3) dod(6) internet(1) { iso(1) identified-organization(3) dod(6) internet(1)
skipping to change at line 968 skipping to change at line 890
PUBLIC-KEYS { pk-ml-dsa-65 } PUBLIC-KEYS { pk-ml-dsa-65 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-65 }
} }
sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= { sa-ml-dsa-87 SIGNATURE-ALGORITHM ::= {
IDENTIFIER id-ml-dsa-87 IDENTIFIER id-ml-dsa-87
PARAMS ARE absent PARAMS ARE absent
PUBLIC-KEYS { pk-ml-dsa-87 } PUBLIC-KEYS { pk-ml-dsa-87 }
SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 } SMIME-CAPS { IDENTIFIED BY id-ml-dsa-87 }
} }
END]]></sourcecode>
END
]]></sourcecode>
</section> </section>
<section anchor="security-strengths"> <section anchor="security-strengths">
<name>Security Strengths</name> <name>Security Strengths</name>
<t>Instead of defining the strength of a quantum algorithm <t>Instead of defining the strength of a quantum algorithm
in a traditional manner using the imprecise notion of bits using the common but imprecise notion of bits
of security, NIST has instead elected to define security of security, NIST has instead elected to define security
levels by picking a reference scheme, which NIST expects levels by picking a reference scheme, which NIST expects
to offer notable levels of resistance to both quantum and to offer notable levels of resistance to both quantum and
classical attack. To wit, an algorithm that achieves NIST PQC classical attacks. To wit, an algorithm that achieves NIST PQC
security level 1 must require computational resources to security level 1 must require computational resources to
break the relevant security property, which are greater than break the relevant security property, which are greater than
those required for a brute-force key search on AES-128. those required for a brute-force key search on AES-128.
Levels 3 and 5 use AES-192 and AES-256 as reference respectively. Levels 3 and 5 use AES-192 and AES-256 as references, respectively.
Levels 2 and 4 use collision search for SHA-256 and SHA-384 Levels 2 and 4 use collision search for SHA-256 and SHA-384
as reference.</t> as references.</t>
<t>The parameter sets defined for NIST security levels 2, 3 and 5 <t>The parameter sets defined for NIST security levels 2, 3, and 5
are listed in the Figure 1, along with the resulting signature are listed in Figure 1, along with the resulting signature
size, public key, and private key sizes in bytes. size, public key, and private key sizes in bytes.
Note that these are the sizes of the raw keys, not including Note that these are the sizes of the raw keys, not including
ASN.1 encoding overhead from OneAsymmetricKey and SubjectPublicKeyInfo ASN.1 encoding overhead from <tt>OneAsymmetricKey</tt> and <tt>SubjectPublicKeyI nfo</tt>
wrappers. Private key sizes are shown for both the seed format wrappers. Private key sizes are shown for both the seed format
and expanded format.</t> and expanded format.</t>
<figure anchor="ML-DSAParameters"> <table anchor="ML-DSAParameters">
<name>ML-DSA Parameters</name> <name>ML-DSA Parameters</name>
<artwork><![CDATA[ <thead>
|=======+=======+=====+========+========+==========+==========| <tr>
| Level | (k,l) | eta | Sig. | Public | Private | Private | <th>Level</th>
| | | | (B) | Key(B) | Seed(B) | Expand(B)| <th>(k,l)</th>
|=======+=======+=====+========+========+==========+==========| <th>eta</th>
| 2 | (4,4) | 2 | 2420 | 1312 | 32 | 2560 | <th>Sig. (B)</th>
| 3 | (6,5) | 4 | 3309 | 1952 | 32 | 4032 | <th>Public Key(B)</th>
| 5 | (8,7) | 2 | 4627 | 2592 | 32 | 4896 | <th>Private Seed(B)</th>
|=======+=======+=====+========+========+==========+==========| <th>Private Expand(B)</th>
]]></artwork> </tr>
</figure> </thead>
<tbody>
<tr>
<td>2</td>
<td>(4,4)</td>
<td>2</td>
<td>2420</td>
<td>1312</td>
<td>32</td>
<td>2560</td>
</tr>
<tr>
<td>3</td>
<td>(6,5)</td>
<td>4</td>
<td>3309</td>
<td>1952</td>
<td>32</td>
<td>4032</td>
</tr>
<tr>
<td>5</td>
<td>(8,7)</td>
<td>2</td>
<td>4627</td>
<td>2592</td>
<td>32</td>
<td>4896</td>
</tr>
</tbody>
</table>
</section> </section>
<section anchor="examples"> <section anchor="examples">
<name>Examples</name> <name>Examples</name>
<t>This appendix contains examples of ML-DSA private keys, public keys, <t>This appendix contains examples of ML-DSA private keys, public keys,
certificates, and inconsistent seed and expanded private keys.</t> certificates, and inconsistent seed and expanded private keys.</t>
<section anchor="example-private"> <section anchor="example-private">
<name>Example Private Keys</name> <name>Example Private Keys</name>
<t>The following examples show ML-DSA private keys in different formats, <t>The following examples show ML-DSA private keys in different formats,
all derived from the same seed <tt>000102...1e1f</tt>. For each security level, all derived from the same seed <tt>000102...1e1f</tt>. For each security level,
we show the seed-only format (using a context-specific <tt>[0]</tt> primitive we show the seed-only format (using a context-specific <tt>[0]</tt> primitive
tag with an implicit encoding of <tt>OCTET STRING</tt>), the <tt>expanded</tt> f ormat, tag with an implicit encoding of <tt>OCTET STRING</tt>), the <tt>expanded</tt> f ormat,
and <tt>both</tt> formats together.</t> and <tt>both</tt> formats together.</t>
<aside>
<t>NOTE: All examples use the same seed value, showing how the same seed <t>NOTE: All examples use the same seed value, showing how the same seed
produces different expanded private keys for each security level.</t> produces different expanded private keys for each security level.</t>
</aside>
<section anchor="ml-dsa-44-private-key-examples"> <section anchor="ml-dsa-44-private-key-examples">
<name>ML-DSA-44 Private Key Examples</name> <name>ML-DSA-44 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format"> <section anchor="seed-format">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MDQCAQAwCwYJYIZIAWUDBAMRBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MDQCAQAwCwYJYIZIAWUDBAMRBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4f GhscHR4f
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f` } 5161718191a1b1c1d1e1f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format"> <section anchor="expanded-format">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex
+rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
skipping to change at line 1103 skipping to change at line 1056
wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d178 OCTET_STRING { `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d178
9dafa17024b316e9bec939ce0f7f77f8db5644dcda366bfe4734bd95f435ff9a 9dafa17024b316e9bec939ce0f7f77f8db5644dcda366bfe4734bd95f435ff9a
613aa54aa41c2c694c04329a07b1fabb48f52a309f11a1898f848e2322ffe623 613aa54aa41c2c694c04329a07b1fabb48f52a309f11a1898f848e2322ffe623
skipping to change at line 1194 skipping to change at line 1147
495679adaed70167b50866713a53109db7b6f7d81304ecdfd83b319b1ef24830 495679adaed70167b50866713a53109db7b6f7d81304ecdfd83b319b1ef24830
6b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a893 6b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a893
2878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926b4 2878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926b4
e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe75 e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe75
27e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafca8 27e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafca8
6be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a56 6be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a56
46601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa1063 46601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa1063
98f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c7217 98f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c7217
b0689e21d8eb0ff69668` } b0689e21d8eb0ff69668` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format"> <section anchor="both-format">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8EggoA17K0clSq4NtF55MNSpjSyX2PE5fReJ2voXAksxbp EhMUFRYXGBkaGxwdHh8EggoA17K0clSq4NtF55MNSpjSyX2PE5fReJ2voXAksxbp
vsk5zg9/d/jbVkTc2jZr/kc0vZX0Nf+aYTqlSqQcLGlMBDKaB7H6u0j1KjCfEaGJ vsk5zg9/d/jbVkTc2jZr/kc0vZX0Nf+aYTqlSqQcLGlMBDKaB7H6u0j1KjCfEaGJ
j4SOIyL/5iPsgQ2zvuM2hYVKiCadoyDVEgv8/omhjjD3EU2DqkBKZGtsmXOJhg0S j4SOIyL/5iPsgQ2zvuM2hYVKiCadoyDVEgv8/omhjjD3EU2DqkBKZGtsmXOJhg0S
Ui7gAG4jhIGRhmGbJg0RhmTUpigiGESCQCiYFGFIpmFMQkihkgjCOClRJEgIoSXC Ui7gAG4jhIGRhmGbJg0RhmTUpigiGESCQCiYFGFIpmFMQkihkgjCOClRJEgIoSXC
skipping to change at line 1351 skipping to change at line 1305
306b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a8 306b45ad29e7ddcc863dac56048b5d69ea175011f7614c00a86a863cde1872a8
932878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926 932878b9ac7e1ac5bda4997b72064f0cd75f4c814e034de11acb9013cf7ea926
b4e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe b4e7eaace070c7ba2188efad2e431e1223d45dd05c4d8403c2e45cee6413ecbe
7527e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafc 7527e873e455c4e610a61839aacc0bd56d2483e78f298b66a478eb2f558cbafc
a86be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a a86be847baeb02c5b216c8cd88fea4df249b09e670a20703abac24b0a91abc4a
5646601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa10 5646601442ba10becfd30993880051d07f56a05a9379e7a8e6befee3f22faa10
6398f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c72 6398f7706006e42e9be1ef89d25c272f11a95095c587d713732284de9dbd3c72
17b0689e21d8eb0ff69668` } 17b0689e21d8eb0ff69668` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
<section anchor="ml-dsa-65-private-key-examples"> <section anchor="ml-dsa-65-private-key-examples">
<name>ML-DSA-65 Private Key Examples</name> <name>ML-DSA-65 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format-1"> <section anchor="seed-format-1">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MDQCAQAwCwYJYIZIAWUDBAMSBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MDQCAQAwCwYJYIZIAWUDBAMSBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4f GhscHR4f
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f` } 5161718191a1b1c1d1e1f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format-1"> <section anchor="expanded-format-1">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIP2AIBADALBglghkgBZQMEAxIEgg/EBIIPwEhoPZGXjjHrPd24sEc0gtK4il9i MIIP2AIBADALBglghkgBZQMEAxIEgg/EBIIPwEhoPZGXjjHrPd24sEc0gtK4il9i
WUn9j1ilYeaWvUwn2FP6abgZkCPozWeN2fq/kEdkb/0Ms8x/eVgFpx5w0jcbBWPj WUn9j1ilYeaWvUwn2FP6abgZkCPozWeN2fq/kEdkb/0Ms8x/eVgFpx5w0jcbBWPj
zTNGFJyMnrzyOwpOWpAO6pxlYnkKfGPjhmPaot3bbkgNxAWh5wGUi3SEHvXMHD8r zTNGFJyMnrzyOwpOWpAO6pxlYnkKfGPjhmPaot3bbkgNxAWh5wGUi3SEHvXMHD8r
8yeXLpUQUQzVN17MCFVxdxGHIiGGI4EABCR3gGFHUAdQFxcDVQRRUSVHGDgEYXVy 8yeXLpUQUQzVN17MCFVxdxGHIiGGI4EABCR3gGFHUAdQFxcDVQRRUSVHGDgEYXVy
IkQQiGhghkYBJ0dWcYCHBmaGQzJEQSIENjhmdQKCNjQkQyIFc2QQZFVUdyJ1VoFD IkQQiGhghkYBJ0dWcYCHBmaGQzJEQSIENjhmdQKCNjQkQyIFc2QQZFVUdyJ1VoFD
skipping to change at line 1469 skipping to change at line 1423
j4Q32BOw8SLy+xdgO2k+2cOPF8/VC4FebZ38DtLM8Z9jmSdKFCDyNaWdi/ckNF4U j4Q32BOw8SLy+xdgO2k+2cOPF8/VC4FebZ38DtLM8Z9jmSdKFCDyNaWdi/ckNF4U
5F2eS+iTTfw/qSZ422HXEYv1PLiiIlszX36uUOP5QSN2KNt22Oo493pyrzomyB/k 5F2eS+iTTfw/qSZ422HXEYv1PLiiIlszX36uUOP5QSN2KNt22Oo493pyrzomyB/k
NSOzNVNaXR23w480EIK7VzTQieiuMJz9o6C8tc1bCXETyO35YWqk9uZjG5ElJ2+z NSOzNVNaXR23w480EIK7VzTQieiuMJz9o6C8tc1bCXETyO35YWqk9uZjG5ElJ2+z
9oCjQ0HD22aNxsrUX8k7JwjKKvdczOc0/RkcUAidrVOYL92uAlMf+T4fIf85X8Ch 9oCjQ0HD22aNxsrUX8k7JwjKKvdczOc0/RkcUAidrVOYL92uAlMf+T4fIf85X8Ch
KHTt8GtvlkfpWnMkWGxx39kdkB1iGFgZD+zQDM0RC7rFn5bLiEw8k5lHSKVvQSg7 KHTt8GtvlkfpWnMkWGxx39kdkB1iGFgZD+zQDM0RC7rFn5bLiEw8k5lHSKVvQSg7
/EH7iQUhU6iUWIw8uQF/PWYybJhWN+V1rLgSNGNCZUAl1gLeO6lAwZrBpjPf/al3 /EH7iQUhU6iUWIw8uQF/PWYybJhWN+V1rLgSNGNCZUAl1gLeO6lAwZrBpjPf/al3
tSm4AT4ZwdbQaA9NrmLJJEUK5mqrgvIUcwYdqz1iskf5B+NVGTmtP1Rl6dCKgr/q tSm4AT4ZwdbQaA9NrmLJJEUK5mqrgvIUcwYdqz1iskf5B+NVGTmtP1Rl6dCKgr/q
F+6htrK5I3V0d/mTAAsvQ7cPKKqrH+miatH9M2FhbAsOJC/nZgS3AzofMOl+KPUm F+6htrK5I3V0d/mTAAsvQ7cPKKqrH+miatH9M2FhbAsOJC/nZgS3AzofMOl+KPUm
yjyID+K42dGwyf8YizHLnZdCWsq5shbZimrjVeWD2nHohk7j0WsHWXlhkO9UXB5i yjyID+K42dGwyf8YizHLnZdCWsq5shbZimrjVeWD2nHohk7j0WsHWXlhkO9UXB5i
v++Sr2yhR7EyRNbIkvyO8iOrP0P5JML0Zgl+6A== v++Sr2yhR7EyRNbIkvyO8iOrP0P5JML0Zgl+6A==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `48683d91978e31eb3dddb8b0473482d2b88a5f625949 OCTET_STRING { `48683d91978e31eb3dddb8b0473482d2b88a5f625949
fd8f58a561e696bd4c27d853fa69b8199023e8cd678dd9fabf9047646ffd0cb3 fd8f58a561e696bd4c27d853fa69b8199023e8cd678dd9fabf9047646ffd0cb3
cc7f795805a71e70d2371b0563e3cd3346149c8c9ebcf23b0a4e5a900eea9c65 cc7f795805a71e70d2371b0563e3cd3346149c8c9ebcf23b0a4e5a900eea9c65
skipping to change at line 1606 skipping to change at line 1560
edf06b6f9647e95a7324586c71dfd91d901d621858190fecd00ccd110bbac59f edf06b6f9647e95a7324586c71dfd91d901d621858190fecd00ccd110bbac59f
96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d6632 96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d6632
6c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b529 6c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b529
b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f907 b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f907
e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b70f e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b70f
28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca3c 28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca3c
880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e886 880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e886
4ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223ab 4ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223ab
3f43f924c2f466097ee8` } 3f43f924c2f466097ee8` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format-1"> <section anchor="both-format-1">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIP/gIBADALBglghkgBZQMEAxIEgg/qMIIP5gQgAAECAwQFBgcICQoLDA0ODxAR MIIP/gIBADALBglghkgBZQMEAxIEgg/qMIIP5gQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8Egg/ASGg9kZeOMes93biwRzSC0riKX2JZSf2PWKVh5pa9 EhMUFRYXGBkaGxwdHh8Egg/ASGg9kZeOMes93biwRzSC0riKX2JZSf2PWKVh5pa9
TCfYU/ppuBmQI+jNZ43Z+r+QR2Rv/QyzzH95WAWnHnDSNxsFY+PNM0YUnIyevPI7 TCfYU/ppuBmQI+jNZ43Z+r+QR2Rv/QyzzH95WAWnHnDSNxsFY+PNM0YUnIyevPI7
Ck5akA7qnGVieQp8Y+OGY9qi3dtuSA3EBaHnAZSLdIQe9cwcPyvzJ5culRBRDNU3 Ck5akA7qnGVieQp8Y+OGY9qi3dtuSA3EBaHnAZSLdIQe9cwcPyvzJ5culRBRDNU3
XswIVXF3EYciIYYjgQAEJHeAYUdQB1AXFwNVBFFRJUcYOARhdXIiRBCIaGCGRgEn XswIVXF3EYciIYYjgQAEJHeAYUdQB1AXFwNVBFFRJUcYOARhdXIiRBCIaGCGRgEn
skipping to change at line 1699 skipping to change at line 1652
F2A7aT7Zw48Xz9ULgV5tnfwO0szxn2OZJ0oUIPI1pZ2L9yQ0XhTkXZ5L6JNN/D+p F2A7aT7Zw48Xz9ULgV5tnfwO0szxn2OZJ0oUIPI1pZ2L9yQ0XhTkXZ5L6JNN/D+p
JnjbYdcRi/U8uKIiWzNffq5Q4/lBI3Yo23bY6jj3enKvOibIH+Q1I7M1U1pdHbfD JnjbYdcRi/U8uKIiWzNffq5Q4/lBI3Yo23bY6jj3enKvOibIH+Q1I7M1U1pdHbfD
jzQQgrtXNNCJ6K4wnP2joLy1zVsJcRPI7flhaqT25mMbkSUnb7P2gKNDQcPbZo3G jzQQgrtXNNCJ6K4wnP2joLy1zVsJcRPI7flhaqT25mMbkSUnb7P2gKNDQcPbZo3G
ytRfyTsnCMoq91zM5zT9GRxQCJ2tU5gv3a4CUx/5Ph8h/zlfwKEodO3wa2+WR+la ytRfyTsnCMoq91zM5zT9GRxQCJ2tU5gv3a4CUx/5Ph8h/zlfwKEodO3wa2+WR+la
cyRYbHHf2R2QHWIYWBkP7NAMzRELusWflsuITDyTmUdIpW9BKDv8QfuJBSFTqJRY cyRYbHHf2R2QHWIYWBkP7NAMzRELusWflsuITDyTmUdIpW9BKDv8QfuJBSFTqJRY
jDy5AX89ZjJsmFY35XWsuBI0Y0JlQCXWAt47qUDBmsGmM9/9qXe1KbgBPhnB1tBo jDy5AX89ZjJsmFY35XWsuBI0Y0JlQCXWAt47qUDBmsGmM9/9qXe1KbgBPhnB1tBo
D02uYskkRQrmaquC8hRzBh2rPWKyR/kH41UZOa0/VGXp0IqCv+oX7qG2srkjdXR3 D02uYskkRQrmaquC8hRzBh2rPWKyR/kH41UZOa0/VGXp0IqCv+oX7qG2srkjdXR3
+ZMACy9Dtw8oqqsf6aJq0f0zYWFsCw4kL+dmBLcDOh8w6X4o9SbKPIgP4rjZ0bDJ +ZMACy9Dtw8oqqsf6aJq0f0zYWFsCw4kL+dmBLcDOh8w6X4o9SbKPIgP4rjZ0bDJ
/xiLMcudl0JayrmyFtmKauNV5YPaceiGTuPRawdZeWGQ71RcHmK/75KvbKFHsTJE /xiLMcudl0JayrmyFtmKauNV5YPaceiGTuPRawdZeWGQ71RcHmK/75KvbKFHsTJE
1siS/I7yI6s/Q/kkwvRmCX7o 1siS/I7yI6s/Q/kkwvRmCX7o
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
OCTET_STRING { OCTET_STRING {
SEQUENCE { SEQUENCE {
OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
15161718191a1b1c1d1e1f` } 15161718191a1b1c1d1e1f` }
skipping to change at line 1840 skipping to change at line 1793
9f96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d66 9f96cb884c3c93994748a56f41283bfc41fb89052153a894588c3cb9017f3d66
326c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b5 326c985637e575acb812346342654025d602de3ba940c19ac1a633dffda977b5
29b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f9 29b8013e19c1d6d0680f4dae62c924450ae66aab82f21473061dab3d62b247f9
07e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b7 07e3551939ad3f5465e9d08a82bfea17eea1b6b2b923757477f993000b2f43b7
0f28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca 0f28aaab1fe9a26ad1fd3361616c0b0e242fe76604b7033a1f30e97e28f526ca
3c880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e8 3c880fe2b8d9d1b0c9ff188b31cb9d97425acab9b216d98a6ae355e583da71e8
864ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223 864ee3d16b0759796190ef545c1e62bfef92af6ca147b13244d6c892fc8ef223
ab3f43f924c2f466097ee8` } ab3f43f924c2f466097ee8` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
<section anchor="ml-dsa-87-private-key-examples"> <section anchor="ml-dsa-87-private-key-examples">
<name>ML-DSA-87 Private Key Examples</name> <name>ML-DSA-87 Private Key Examples</name>
<t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by <t>Each of the examples includes the textual encoding <xref target="RF C7468"/> followed by
the so-called "pretty print"; the private keys are the same.</t> the so-called "pretty print"; the private keys are the same.</t>
<section anchor="seed-format-2"> <section anchor="seed-format-2">
<name>Seed Format</name> <name>Seed Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MDQCAQAwCwYJYIZIAWUDBAMTBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ MDQCAQAwCwYJYIZIAWUDBAMTBCKAIAABAgMEBQYHCAkKCwwNDg8QERITFBUWFxgZ
GhscHR4f GhscHR4f
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
OCTET_STRING { OCTET_STRING {
[0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141 [0 PRIMITIVE] { `000102030405060708090a0b0c0d0e0f10111213141
5161718191a1b1c1d1e1f` } 5161718191a1b1c1d1e1f` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="expanded-format-2"> <section anchor="expanded-format-2">
<name>Expanded Format</name> <name>Expanded Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIITOAIBADALBglghkgBZQMEAxMEghMkBIITIJeSvOwvJDBoaoL8zzwvX/Zl53HX MIITOAIBADALBglghkgBZQMEAxMEghMkBIITIJeSvOwvJDBoaoL8zzwvX/Zl53HX
q0G5AljPp+kOyXEk2OnuTpChbGAvXsm8OFF9ww4ynVqydnO9hfTJsDAPd2OJiGdQ q0G5AljPp+kOyXEk2OnuTpChbGAvXsm8OFF9ww4ynVqydnO9hfTJsDAPd2OJiGdQ
tXwk2z/AEuYe3ll1Mzc3T6cSSZFUmvJDSW0GN8s74FpZSCNb95h1+JbY/gyrMMhJ tXwk2z/AEuYe3ll1Mzc3T6cSSZFUmvJDSW0GN8s74FpZSCNb95h1+JbY/gyrMMhJ
SNtNYxWqrxYKxiQ2ZCIBSBYRCREslAKJIkUsYrhFAEUqCJZwkBJuFJNw1EYQhERR SNtNYxWqrxYKxiQ2ZCIBSBYRCREslAKJIkUsYrhFAEUqCJZwkBJuFJNw1EYQhERR
WJaRDKkpgrJByQhxxChoBJaJSECFmyJtHChkWRJBnLiRhASJRJAFyzRioIaQQCaS WJaRDKkpgrJByQhxxChoBJaJSECFmyJtHChkWRJBnLiRhASJRJAFyzRioIaQQCaS
skipping to change at line 1976 skipping to change at line 1928
bEvuv0b8EiIsCy7M1hWdWuqOVU16CWUrBr98ppmnGZ5xbQXdVTBBqPKzA9I2qbq6 bEvuv0b8EiIsCy7M1hWdWuqOVU16CWUrBr98ppmnGZ5xbQXdVTBBqPKzA9I2qbq6
r7n6Uo8oosoqp4C5QDg8CZqmWgB0uD/R8Lxbe15Gwl5Ug4s8vPyV+H8dRxs7qJRD r7n6Uo8oosoqp4C5QDg8CZqmWgB0uD/R8Lxbe15Gwl5Ug4s8vPyV+H8dRxs7qJRD
T6WJUv3Ld/FhNyaTMG26To8hbRyOXK/w/oNgpRxgdjZEFp/caoJn8uP5CaYbKmeL T6WJUv3Ld/FhNyaTMG26To8hbRyOXK/w/oNgpRxgdjZEFp/caoJn8uP5CaYbKmeL
zmrpBAOoNrGnt+jNi1TDcIep4URG2V5pCNLu2/zGU+Av33cfcBp5ueWibtCpR4Qg zmrpBAOoNrGnt+jNi1TDcIep4URG2V5pCNLu2/zGU+Av33cfcBp5ueWibtCpR4Qg
cPO1cBdCIRIZ52F2LDfw0KHRuXUP7ld+EggRXGasB+wJHmo/xKpqJTvLqGjt0xVN cPO1cBdCIRIZ52F2LDfw0KHRuXUP7ld+EggRXGasB+wJHmo/xKpqJTvLqGjt0xVN
yvUWL2FehUkKbKNC80xDrGGj6mv+79hQ4ZDrHY2k0otezusWeMAkM+zV1IslNkBC yvUWL2FehUkKbKNC80xDrGGj6mv+79hQ4ZDrHY2k0otezusWeMAkM+zV1IslNkBC
V+jKe+9YVfK4E+0vTECURaMxfJvho1ri+00rh5IbkEvywU21FM7gRSUc/CdjdNsV V+jKe+9YVfK4E+0vTECURaMxfJvho1ri+00rh5IbkEvywU21FM7gRSUc/CdjdNsV
yZ3qFazeGXxutSSYjjm2Moe+uGdoZaqjutG0O4yrFcvyekmHWeMgOr82npckLwsB yZ3qFazeGXxutSSYjjm2Moe+uGdoZaqjutG0O4yrFcvyekmHWeMgOr82npckLwsB
VBSfFKwjPNtzoit/uPCTJb8qzoO7a124oSGitoIUmmkTHMzlIimECxE/x7C8xYQF VBSfFKwjPNtzoit/uPCTJb8qzoO7a124oSGitoIUmmkTHMzlIimECxE/x7C8xYQF
v+h/H5X/wulvxVllZ+lDZN+qbZ1abrma5N30JA== v+h/H5X/wulvxVllZ+lDZN+qbZ1abrma5N30JA==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
OCTET_STRING { OCTET_STRING {
OCTET_STRING { `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab41 OCTET_STRING { `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab41
b90258cfa7e90ec97124d8e9ee4e90a16c602f5ec9bc38517dc30e329d5ab276 b90258cfa7e90ec97124d8e9ee4e90a16c602f5ec9bc38517dc30e329d5ab276
73bd85f4c9b0300f776389886750b57c24db3fc012e61ede59753337374fa712 73bd85f4c9b0300f776389886750b57c24db3fc012e61ede59753337374fa712
skipping to change at line 2140 skipping to change at line 2092
b5701742211219e761762c37f0d0a1d1b9750fee577e1208115c66ac07ec091e b5701742211219e761762c37f0d0a1d1b9750fee577e1208115c66ac07ec091e
6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61a3 6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61a3
ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257e8 ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257e8
ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2c1 ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2c1
4db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287be 4db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287be
b8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b015414 b8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b015414
9f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a69131c 9f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a69131c
cce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364dfaa cce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364dfaa
6d9d5a6eb99ae4ddf424` } 6d9d5a6eb99ae4ddf424` }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="both-format-2"> <section anchor="both-format-2">
<name>Both Format</name> <name>Both Format</name>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIITXgIBADALBglghkgBZQMEAxMEghNKMIITRgQgAAECAwQFBgcICQoLDA0ODxAR MIITXgIBADALBglghkgBZQMEAxMEghNKMIITRgQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8EghMgl5K87C8kMGhqgvzPPC9f9mXncderQbkCWM+n6Q7J EhMUFRYXGBkaGxwdHh8EghMgl5K87C8kMGhqgvzPPC9f9mXncderQbkCWM+n6Q7J
cSTY6e5OkKFsYC9eybw4UX3DDjKdWrJ2c72F9MmwMA93Y4mIZ1C1fCTbP8AS5h7e cSTY6e5OkKFsYC9eybw4UX3DDjKdWrJ2c72F9MmwMA93Y4mIZ1C1fCTbP8AS5h7e
WXUzNzdPpxJJkVSa8kNJbQY3yzvgWllII1v3mHX4ltj+DKswyElI201jFaqvFgrG WXUzNzdPpxJJkVSa8kNJbQY3yzvgWllII1v3mHX4ltj+DKswyElI201jFaqvFgrG
JDZkIgFIFhEJESyUAokiRSxiuEUARSoIlnCQEm4Uk3DURhCERFFYlpEMqSmCskHJ JDZkIgFIFhEJESyUAokiRSxiuEUARSoIlnCQEm4Uk3DURhCERFFYlpEMqSmCskHJ
skipping to change at line 2251 skipping to change at line 2202
LszWFZ1a6o5VTXoJZSsGv3ymmacZnnFtBd1VMEGo8rMD0japurqvufpSjyiiyiqn LszWFZ1a6o5VTXoJZSsGv3ymmacZnnFtBd1VMEGo8rMD0japurqvufpSjyiiyiqn
gLlAODwJmqZaAHS4P9HwvFt7XkbCXlSDizy8/JX4fx1HGzuolENPpYlS/ct38WE3 gLlAODwJmqZaAHS4P9HwvFt7XkbCXlSDizy8/JX4fx1HGzuolENPpYlS/ct38WE3
JpMwbbpOjyFtHI5cr/D+g2ClHGB2NkQWn9xqgmfy4/kJphsqZ4vOaukEA6g2sae3 JpMwbbpOjyFtHI5cr/D+g2ClHGB2NkQWn9xqgmfy4/kJphsqZ4vOaukEA6g2sae3
6M2LVMNwh6nhREbZXmkI0u7b/MZT4C/fdx9wGnm55aJu0KlHhCBw87VwF0IhEhnn 6M2LVMNwh6nhREbZXmkI0u7b/MZT4C/fdx9wGnm55aJu0KlHhCBw87VwF0IhEhnn
YXYsN/DQodG5dQ/uV34SCBFcZqwH7Akeaj/EqmolO8uoaO3TFU3K9RYvYV6FSQps YXYsN/DQodG5dQ/uV34SCBFcZqwH7Akeaj/EqmolO8uoaO3TFU3K9RYvYV6FSQps
o0LzTEOsYaPqa/7v2FDhkOsdjaTSi17O6xZ4wCQz7NXUiyU2QEJX6Mp771hV8rgT o0LzTEOsYaPqa/7v2FDhkOsdjaTSi17O6xZ4wCQz7NXUiyU2QEJX6Mp771hV8rgT
7S9MQJRFozF8m+GjWuL7TSuHkhuQS/LBTbUUzuBFJRz8J2N02xXJneoVrN4ZfG61 7S9MQJRFozF8m+GjWuL7TSuHkhuQS/LBTbUUzuBFJRz8J2N02xXJneoVrN4ZfG61
JJiOObYyh764Z2hlqqO60bQ7jKsVy/J6SYdZ4yA6vzaelyQvCwFUFJ8UrCM823Oi JJiOObYyh764Z2hlqqO60bQ7jKsVy/J6SYdZ4yA6vzaelyQvCwFUFJ8UrCM823Oi
K3+48JMlvyrOg7trXbihIaK2ghSaaRMczOUiKYQLET/HsLzFhAW/6H8flf/C6W/F K3+48JMlvyrOg7trXbihIaK2ghSaaRMczOUiKYQLET/HsLzFhAW/6H8flf/C6W/F
WWVn6UNk36ptnVpuuZrk3fQk WWVn6UNk36ptnVpuuZrk3fQk
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
INTEGER { 0 } INTEGER { 0 }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
OCTET_STRING { OCTET_STRING {
SEQUENCE { SEQUENCE {
OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314 OCTET_STRING { `000102030405060708090a0b0c0d0e0f1011121314
15161718191a1b1c1d1e1f` } 15161718191a1b1c1d1e1f` }
skipping to change at line 2419 skipping to change at line 2370
1e6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61 1e6a3fc4aa6a253bcba868edd3154dcaf5162f615e85490a6ca342f34c43ac61
a3ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257 a3ea6bfeefd850e190eb1d8da4d28b5eceeb1678c02433ecd5d48b2536404257
e8ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2 e8ca7bef5855f2b813ed2f4c409445a3317c9be1a35ae2fb4d2b87921b904bf2
c14db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287 c14db514cee045251cfc276374db15c99dea15acde197c6eb524988e39b63287
beb8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b0154 beb8676865aaa3bad1b43b8cab15cbf27a498759e3203abf369e97242f0b0154
149f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a6913 149f14ac233cdb73a22b7fb8f09325bf2ace83bb6b5db8a121a2b682149a6913
1ccce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364df 1ccce52229840b113fc7b0bcc58405bfe87f1f95ffc2e96fc5596567e94364df
aa6d9d5a6eb99ae4ddf424` } aa6d9d5a6eb99ae4ddf424` }
} }
} }
} }]]></artwork>
]]></artwork>
</section> </section>
</section> </section>
</section> </section>
<section anchor="example-public"> <section anchor="example-public">
<name>Example Public Keys</name> <name>Example Public Keys</name>
<t>The following is the ML-DSA-44 public key corresponding to the privat e <t>The following is the ML-DSA-44 public key corresponding to the privat e
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
skipping to change at line 2459 skipping to change at line 2409
7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV 7QvAuAGz5ugtzUPpwOn0F0TNmBW9G8iCDYuxI/BPrNGxtoXdWisbjbvz7ZM2cPCV
oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn oYC08ZLQixC4+rvfzCskUY4y7qCl4MkEyoRHgAg/OwzS0Li2r2e8NVuUlAJdx7Cn
j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl j6gOOi2/61EyiFHWB4GY6Uk2Ua54fsAlH5Irow6fUd9iptcnhM890gU5MXbfoySl
Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI Er2Ulwo23TSlFKhnkfDrNvAUWwmrZGUbSgMTsplhGiocSIkWJ1mHaKMRQGC6RENI
bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/ bfUVIqHOiLMJhcIW+ObtF43VZ7MEoNTK+6iCooNC8XqaomrljbYwCD0sNY/fVmw/
XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br XWKkKFZ7yeqM6VyqDzVHSwv6jzOaJQq0388gg76O77wQVeGP4VNw7ssmBWbYP/Br
IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP IRquxDyim1TM0A+IFaJGXvC0ZRXMfkHzEk8J7/9zkwmrWLKaFFmgC85QOOk4yWeP
cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO cusOTuX9quZtn4Vz/Jf8QrSVn0v4th14Qz6GsDNdbpGRxNi/SHs5BcEIz9asJLDO
t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo t9y3z1H4TQ7Wh7lerrHFM8BvDZcCPZKnCCWDe1m6bLfU5WsKh8IDhiro8xW6WSXo
7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI= 7e+meTaaIgJ2YVHxapZfn4Hs52zAcLVYaeTbl4TPBcgwsyQsgxI=
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17 BIT_STRING { `00` `d7b2b47254aae0db45e7930d4a98d2c97d8f1397d17
89dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed51156 89dafa17024b316e9bec94fc9946d42f19b79a7413bbaa33e7149cb42ed51156
93ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa414ba3 93ac041facb988adeb5fe0e1d8631184995b592c397d2294e2e14f90aa414ba3
826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f61e7 826899ac43f4cccacbc26e9a832b95118d5cb433cbef9660b00138e0817f61e7
62ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f72e55 62ca274c36ad554eb22aac1162e4ab01acba1e38c4efd8f80b65b333d0f72e55
skipping to change at line 2508 skipping to change at line 2458
299611a2a1c48891627598768a3114060ba4443486df51522a1ce88b30985c21 299611a2a1c48891627598768a3114060ba4443486df51522a1ce88b30985c21
6f8e6ed178dd567b304a0d4cafba882a28342f17a9aa26ae58db630083d2c358 6f8e6ed178dd567b304a0d4cafba882a28342f17a9aa26ae58db630083d2c358
fdf566c3f5d62a428567bc9ea8ce95caa0f35474b0bfa8f339a250ab4dfcf208 fdf566c3f5d62a428567bc9ea8ce95caa0f35474b0bfa8f339a250ab4dfcf208
3be8eefbc1055e18fe15370eecb260566d83ff06b211aaec43ca29b54ccd00f8 3be8eefbc1055e18fe15370eecb260566d83ff06b211aaec43ca29b54ccd00f8
815a2465ef0b46515cc7e41f3124f09efff739309ab58b29a1459a00bce5038e 815a2465ef0b46515cc7e41f3124f09efff739309ab58b29a1459a00bce5038e
938c9678f72eb0e4ee5fdaae66d9f8573fc97fc42b4959f4bf8b61d78433e86b 938c9678f72eb0e4ee5fdaae66d9f8573fc97fc42b4959f4bf8b61d78433e86b
0335d6e9191c4d8bf487b3905c108cfd6ac24b0ceb7dcb7cf51f84d0ed687b95 0335d6e9191c4d8bf487b3905c108cfd6ac24b0ceb7dcb7cf51f84d0ed687b95
eaeb1c533c06f0d97023d92a70825837b59ba6cb7d4e56b0a87c203862ae8f31 eaeb1c533c06f0d97023d92a70825837b59ba6cb7d4e56b0a87c203862ae8f31
5ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e4db9 5ba5925e8edefa679369a2202766151f16a965f9f81ece76cc070b55869e4db9
784cf05c830b3242c8312` } 784cf05c830b3242c8312` }
} }]]></artwork>
]]></artwork>
<t>The following is the ML-DSA-65 public key corresponding to the privat e <t>The following is the ML-DSA-65 public key corresponding to the privat e
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIHsjALBglghkgBZQMEAxIDggehAEhoPZGXjjHrPd24sEc0gtK4il9iWUn9j1il MIIHsjALBglghkgBZQMEAxIDggehAEhoPZGXjjHrPd24sEc0gtK4il9iWUn9j1il
YeaWvUwn0Fs427Lt8B5mTv2Bvh6ok2iM5oqi1RxZWPi7xutOie5n0sAyCVTVchLK YeaWvUwn0Fs427Lt8B5mTv2Bvh6ok2iM5oqi1RxZWPi7xutOie5n0sAyCVTVchLK
xyKf8dbq8DkovVFRH42I2EdzbH3icw1ZeOVBBxMWCXiGdxG/VTmgv8TDUMK+Vyuv xyKf8dbq8DkovVFRH42I2EdzbH3icw1ZeOVBBxMWCXiGdxG/VTmgv8TDUMK+Vyuv
DuLi+xbM/qCAKNmaxJrrt1k33c4RHNq2L/886ouiIz0eVvvFxaHnJt5j+t0q8Bax DuLi+xbM/qCAKNmaxJrrt1k33c4RHNq2L/886ouiIz0eVvvFxaHnJt5j+t0q8Bax
GRd/o9lxotkncXP85VtndFrwt8IdWX2+uT5qMvNBxJpai+noJQiNHyqkUVXWyK4V GRd/o9lxotkncXP85VtndFrwt8IdWX2+uT5qMvNBxJpai+noJQiNHyqkUVXWyK4V
Nn5OsAO4/feFEHGUlzn5//CQI+r0UQTSqEpFkG7tRnGkTcKNJ5h7tV32np6FYfYa Nn5OsAO4/feFEHGUlzn5//CQI+r0UQTSqEpFkG7tRnGkTcKNJ5h7tV32np6FYfYa
gKcmmVA4Zf7Zt+5yqOF6GcQIFE9LKa/vcDHDpthXFhC0LJ9CEkWojxl+FoErAxFZ gKcmmVA4Zf7Zt+5yqOF6GcQIFE9LKa/vcDHDpthXFhC0LJ9CEkWojxl+FoErAxFZ
tluWh+Wz6TTFIlrpinm6c9Kzmdc1EO/60Z5TuEUPC6j84QEv2Y0mCnSqqhP64kmg tluWh+Wz6TTFIlrpinm6c9Kzmdc1EO/60Z5TuEUPC6j84QEv2Y0mCnSqqhP64kmg
skipping to change at line 2557 skipping to change at line 2508
/am3Uw3AyoZIyNlzc44Burjwi0kF6EqkZBvWAkEM2XUgJl8vIx8rNeFesvoE0r2U /am3Uw3AyoZIyNlzc44Burjwi0kF6EqkZBvWAkEM2XUgJl8vIx8rNeFesvoE0r2U
1ad6uvHg4WEBCpkAh/W0bqmIsrwFEv2g+pI9rdbEXFMB0JSDZzJltasuEPS6Ug9r 1ad6uvHg4WEBCpkAh/W0bqmIsrwFEv2g+pI9rdbEXFMB0JSDZzJltasuEPS6Ug9r
utVkpcPV4nvbCA99IOEylqMYGVTDnGSclD6+F99cH3quCo/hJsR3WFpdTWSKDQCL utVkpcPV4nvbCA99IOEylqMYGVTDnGSclD6+F99cH3quCo/hJsR3WFpdTWSKDQCL
avXozTG+aakpbU8/0l7YbyIeS5P2X1kplnUzYkuSNXUMMHB1ULWFNtEJpxMcWlu+ avXozTG+aakpbU8/0l7YbyIeS5P2X1kplnUzYkuSNXUMMHB1ULWFNtEJpxMcWlu+
SlcVVnwSU0rsdmB2Huu5+uKJHHdFibgOVmrVV93vc2cZa3In6phw7wnd/seda5MZ SlcVVnwSU0rsdmB2Huu5+uKJHHdFibgOVmrVV93vc2cZa3In6phw7wnd/seda5MZ
poebUgXXa/erpazzOvtZ0X/FTmg4PWvloI6bZtpT3N4Ai7KUuFgr0TLNzEmVn9vC poebUgXXa/erpazzOvtZ0X/FTmg4PWvloI6bZtpT3N4Ai7KUuFgr0TLNzEmVn9vC
HlJyGIDIrQNSx58DpDu9hMTN/cbFKQBeHnzZo0mnFoo1Vpul3qgYlo1akUZr1uZO HlJyGIDIrQNSx58DpDu9hMTN/cbFKQBeHnzZo0mnFoo1Vpul3qgYlo1akUZr1uZO
IL9iQXGYr8ToHCjdd+1AKCMjmLUvvehryE9HW5AWcQziqrwRoGtNuskB7BbPNlyj IL9iQXGYr8ToHCjdd+1AKCMjmLUvvehryE9HW5AWcQziqrwRoGtNuskB7BbPNlyj
8tU4E5SKaToPk+ecRspdWm3KPSjKUK0YvRP8pVBZ3ZsYX3n5xHGWpOgbIQS8RgoF 8tU4E5SKaToPk+ecRspdWm3KPSjKUK0YvRP8pVBZ3ZsYX3n5xHGWpOgbIQS8RgoF
HgLy6ERP HgLy6ERP
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594 BIT_STRING { `00` `48683d91978e31eb3dddb8b0473482d2b88a5f62594
9fd8f58a561e696bd4c27d05b38dbb2edf01e664efd81be1ea893688ce68aa2d 9fd8f58a561e696bd4c27d05b38dbb2edf01e664efd81be1ea893688ce68aa2d
51c5958f8bbc6eb4e89ee67d2c0320954d57212cac7229ff1d6eaf03928bd515 51c5958f8bbc6eb4e89ee67d2c0320954d57212cac7229ff1d6eaf03928bd515
11f8d88d847736c7de2730d5978e5410713160978867711bf5539a0bfc4c350c 11f8d88d847736c7de2730d5978e5410713160978867711bf5539a0bfc4c350c
2be572baf0ee2e2fb16ccfea08028d99ac49aebb75937ddce111cdab62fff3ce 2be572baf0ee2e2fb16ccfea08028d99ac49aebb75937ddce111cdab62fff3ce
skipping to change at line 2626 skipping to change at line 2577
48a0d008b6af5e8cd31be69a9296d4f3fd25ed86f221e4b93f65f59299675336 48a0d008b6af5e8cd31be69a9296d4f3fd25ed86f221e4b93f65f59299675336
24b9235750c30707550b58536d109a7131c5a5bbe4a5715567c12534aec76607 24b9235750c30707550b58536d109a7131c5a5bbe4a5715567c12534aec76607
61eebb9fae2891c774589b80e566ad557ddef7367196b7227ea9870ef09ddfec 61eebb9fae2891c774589b80e566ad557ddef7367196b7227ea9870ef09ddfec
79d6b9319a6879b5205d76bf7aba5acf33afb59d17fc54e68383d6be5a08e9b6 79d6b9319a6879b5205d76bf7aba5acf33afb59d17fc54e68383d6be5a08e9b6
6da53dcde008bb294b8582bd132cdcc49959fdbc21e52721880c8ad0352c79f0 6da53dcde008bb294b8582bd132cdcc49959fdbc21e52721880c8ad0352c79f0
3a43bbd84c4cdfdc6c529005e1e7cd9a349a7168a35569ba5dea818968d5a914 3a43bbd84c4cdfdc6c529005e1e7cd9a349a7168a35569ba5dea818968d5a914
66bd6e64e20bf62417198afc4e81c28dd77ed4028232398b52fbde86bc84f475 66bd6e64e20bf62417198afc4e81c28dd77ed4028232398b52fbde86bc84f475
b9016710ce2aabc11a06b4dbac901ec16cf365ca3f2d53813948a693a0f93e79 b9016710ce2aabc11a06b4dbac901ec16cf365ca3f2d53813948a693a0f93e79
c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81b210 c46ca5d5a6dca3d28ca50ad18bd13fca55059dd9b185f79f9c47196a4e81b210
4bc460a051e02f2e8444f` } 4bc460a051e02f2e8444f` }
} }]]></artwork>
]]></artwork>
<t>The following is the ML-DSA-87 public key corresponding to the privat e <t>The following is the ML-DSA-87 public key corresponding to the privat e
key in the previous section. The textual encoding <xref target="RFC7468"/> is key in the previous section. The textual encoding <xref target="RFC7468"/> is
followed by the so-called "pretty print"; the public keys are the same.</t> followed by the so-called "pretty print"; the public keys are the same.</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PUBLIC KEY----- -----BEGIN PUBLIC KEY-----
MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP MIIKMjALBglghkgBZQMEAxMDggohAJeSvOwvJDBoaoL8zzwvX/Zl53HXq0G5AljP
p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt p+kOyXEkpzsyO5uiGrZNdnxDP1pSHv/hj4bkahiJUsRGfgSLcp5/xNEV5+SNoYlt
X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4 X+EZsQ3N3vYssweVQHS0IzblKDbeYdqUH4036misgQb6vhkHBnmvYAhTcSD3B5O4
6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY 6pzA5ue3tMmlx0IcYPJEUboekz2xou4Wx5VZ8hs9G4MFhQqkKvuxPx9NW59INfnY
ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz ffzrFi0O9Kf9xMuhdDzRyHu0ln2hbMh2S2Vp347lvcv/6aTgV0jm/fIlr55O63dz
ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv ti6Phfm1a1SJRVUYRPvYmAakrDab7S0lYQD2iKatXgpwmCbcREnpHiPFUG5kI2Hv
WjE3EvebxLMYaGHKhaS6sX5/lD0bijM6o6584WtEDWAY+eBNr1clx/GpP60aWie2 WjE3EvebxLMYaGHKhaS6sX5/lD0bijM6o6584WtEDWAY+eBNr1clx/GpP60aWie2
eJW9JJqpFoXeIK8yyLfiaMf5aHfQyFABE1pPCo8bgmT6br5aNJ2K7K0aFimczy/Z eJW9JJqpFoXeIK8yyLfiaMf5aHfQyFABE1pPCo8bgmT6br5aNJ2K7K0aFimczy/Z
skipping to change at line 2688 skipping to change at line 2640
citu4VdPLhSdVddE3kiHAk4IURQxwGJ1DhbHSrnzJC8ts/+xKo1hB/qiKdb2NzsH citu4VdPLhSdVddE3kiHAk4IURQxwGJ1DhbHSrnzJC8ts/+xKo1hB/qiKdb2NzsH
8205MrO9sEwZ3WTq3X+Tw8Vkw1ihyB3PHJwx5bBlaPl1RMF9wVaYxcs4mDqa/EJ4 8205MrO9sEwZ3WTq3X+Tw8Vkw1ihyB3PHJwx5bBlaPl1RMF9wVaYxcs4mDqa/EJ4
P6p3OlLJ2CYGkL6eMVaqW8FQneo/aVh2lc1v8XK6g+am2KfWu+u7zaNnJzGYP4m8 P6p3OlLJ2CYGkL6eMVaqW8FQneo/aVh2lc1v8XK6g+am2KfWu+u7zaNnJzGYP4m8
WDHcN8PzxcVvrMaX88sgvV2629cC5UhErC9iaQH+FZ25Pf1Hc9j+c1YrhGwfyFbR WDHcN8PzxcVvrMaX88sgvV2629cC5UhErC9iaQH+FZ25Pf1Hc9j+c1YrhGwfyFbR
gCdihA68cteYi951y8pw0xnTLODMAlO7KtRVcj7gx/RzbObmZlxayjKkgcU4Obwl gCdihA68cteYi951y8pw0xnTLODMAlO7KtRVcj7gx/RzbObmZlxayjKkgcU4Obwl
kWewE9BCM5Xuuaqu4yBhSafVUNZ/xf3+SopcNdJRC2ZDeauPcoVaKvR6vOKmMgSO kWewE9BCM5Xuuaqu4yBhSafVUNZ/xf3+SopcNdJRC2ZDeauPcoVaKvR6vOKmMgSO
r4nly0qI3rxTpZUQOszk8c/xis/wev4etXFqoeQLYxNMOjrpV5+of1Fb4JPC0p22 r4nly0qI3rxTpZUQOszk8c/xis/wev4etXFqoeQLYxNMOjrpV5+of1Fb4JPC0p22
1rZck2YeAGNrWScE0JPMZxbCNC6xhT1IyFxjrIooVEYse3fn470erFvKKP+qALXT 1rZck2YeAGNrWScE0JPMZxbCNC6xhT1IyFxjrIooVEYse3fn470erFvKKP+qALXT
SfilR62HW5aowrKRDJMBMJo/kTilaTER9Vs8AJypR8Od/ILZjrHKpKnL6IX3hvqG SfilR62HW5aowrKRDJMBMJo/kTilaTER9Vs8AJypR8Od/ILZjrHKpKnL6IX3hvqG
5VvgYiIvi6kKl0BzMmsxISrs4KNKYA== 5VvgYiIvi6kKl0BzMmsxISrs4KNKYA==
]]></artwork> -----END PUBLIC KEY-----]]></artwork>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab4 BIT_STRING { `00` `9792bcec2f2430686a82fccf3c2f5ff665e771d7ab4
1b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f86e46 1b90258cfa7e90ec97124a73b323b9ba21ab64d767c433f5a521effe18f86e46
a188952c4467e048b729e7fc4d115e7e48da1896d5fe119b10dcddef62cb3079 a188952c4467e048b729e7fc4d115e7e48da1896d5fe119b10dcddef62cb3079
54074b42336e52836de61da941f8d37ea68ac8106fabe19070679af600853712 54074b42336e52836de61da941f8d37ea68ac8106fabe19070679af600853712
0f70793b8ea9cc0e6e7b7b4c9a5c7421c60f24451ba1e933db1a2ee16c79559f 0f70793b8ea9cc0e6e7b7b4c9a5c7421c60f24451ba1e933db1a2ee16c79559f
skipping to change at line 2777 skipping to change at line 2729
7f3cb20bd5dbadbd702e54844ac2f626901fe159db93dfd4773d8fe73562b846 7f3cb20bd5dbadbd702e54844ac2f626901fe159db93dfd4773d8fe73562b846
c1fc856d1802762840ebc72d7988bde75cbca70d319d32ce0cc0253bb2ad4557 c1fc856d1802762840ebc72d7988bde75cbca70d319d32ce0cc0253bb2ad4557
23ee0c7f4736ce6e6665c5aca32a481c53839bc259167b013d0423395eeb9aaa 23ee0c7f4736ce6e6665c5aca32a481c53839bc259167b013d0423395eeb9aaa
ee3206149a7d550d67fc5fdfe4a8a5c35d2510b664379ab8f72855a2af47abce ee3206149a7d550d67fc5fdfe4a8a5c35d2510b664379ab8f72855a2af47abce
2a632048eaf89e5cb4a88debc53a595103acce4f1cff18acff07afe1eb5716aa 2a632048eaf89e5cb4a88debc53a595103acce4f1cff18acff07afe1eb5716aa
1e40b63134c3a3ae9579fa87f515be093c2d29db6d6b65c93661e00636b59270 1e40b63134c3a3ae9579fa87f515be093c2d29db6d6b65c93661e00636b59270
4d093cc6716c2342eb1853d48c85c63ac8a2854462c7b77e7e3bd1eac5bca28f 4d093cc6716c2342eb1853d48c85c63ac8a2854462c7b77e7e3bd1eac5bca28f
faa00b5d349f8a547ad875b96a8c2b2910c9301309a3f9138a5693111f55b3c0 faa00b5d349f8a547ad875b96a8c2b2910c9301309a3f9138a5693111f55b3c0
09ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a97407 09ca947c39dfc82d98eb1caa4a9cbe885f786fa86e55be062222f8ba90a97407
3326b31212aece0a34a60` } 3326b31212aece0a34a60` }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="example-certificates"> <section anchor="example-certificates">
<name>Example Certificates</name> <name>Example Certificates</name>
<aside> <aside>
<t>The example certificates in this section have key usage bits set to <t>The example certificates in this section have key usage bits set to
<tt>digitalSignature</tt>, <tt>keyCertSign</tt>, and <tt>cRLSign</tt> to lessen the number of <tt>digitalSignature</tt>, <tt>keyCertSign</tt>, and <tt>cRLSign</tt> to lessen the number of
examples, i.e., brevity. Certificate Policies (CPs) <xref target="RFC3647"/> examples, i.e., brevity. Certificate Policies (CPs) <xref target="RFC3647"/>
for production CAs should consider whether this combination is for production CAs should consider whether this combination is
appropriate.</t> appropriate.</t>
</aside> </aside>
<t>The following is a self-signed certificate for the ML-DSA-44 public k ey in the <t>The following is a self-signed certificate for the ML-DSA-44 public k ey in the
previous section. The textual encoding <xref target="RFC7468"/> is followed by t he previous section. The textual encoding <xref target="RFC7468"/> is followed by t he
so-called "pretty print"; the certificates are the same.</t> so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[ <sourcecode type="x509"><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR MIIPlDCCBgqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMR
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
TEFNUFMgV0cwggUyMAsGCWCGSAFlAwQDEQOCBSEA17K0clSq4NtF55MNSpjSyX2P TEFNUFMgV0cwggUyMAsGCWCGSAFlAwQDEQOCBSEA17K0clSq4NtF55MNSpjSyX2P
E5fReJ2voXAksxbpvslPyZRtQvGbeadBO7qjPnFJy0LtURVpOsBB+suYit61/g4d E5fReJ2voXAksxbpvslPyZRtQvGbeadBO7qjPnFJy0LtURVpOsBB+suYit61/g4d
hjEYSZW1ksOX0ilOLhT5CqQUujgmiZrEP0zMrLwm6agyuVEY1ctDPL75ZgsAE44I hjEYSZW1ksOX0ilOLhT5CqQUujgmiZrEP0zMrLwm6agyuVEY1ctDPL75ZgsAE44I
F/YediyidMNq1VTrIqrBFi5KsBrLoeOMTv2PgLZbMz0PcuVd/nHOnB67mInnxWEG F/YediyidMNq1VTrIqrBFi5KsBrLoeOMTv2PgLZbMz0PcuVd/nHOnB67mInnxWEG
wP1zgDoq7P6v3teqPLLO2lTRK9jNNqeM+XWUO0er0l6ICsRS5XQu0ejRqCr6huWQ wP1zgDoq7P6v3teqPLLO2lTRK9jNNqeM+XWUO0er0l6ICsRS5XQu0ejRqCr6huWQ
x1jBWuTShA2SvKGlCQ9ASWWX/KfYuVE/GhvabpUKqpjeRnUH1KT1pPBZkhZYLDVy x1jBWuTShA2SvKGlCQ9ASWWX/KfYuVE/GhvabpUKqpjeRnUH1KT1pPBZkhZYLDVy
skipping to change at line 2878 skipping to change at line 2829
J/11Up4pEegRS/c+Li2OUvQr9Jxi8XGIdEJZY1T8oVpzDJf3C29gpARWSDAXrFn0 J/11Up4pEegRS/c+Li2OUvQr9Jxi8XGIdEJZY1T8oVpzDJf3C29gpARWSDAXrFn0
lgZHnqFyebeC1uDW8r/wGtYmI2EC53+FlOF5AFcH+3LzObZzerqwror4UMOA+B5c lgZHnqFyebeC1uDW8r/wGtYmI2EC53+FlOF5AFcH+3LzObZzerqwror4UMOA+B5c
QMU5vDv1LFcWLzvJHMXJfCHL5nVSukXCMawr+DbeKjrkseG0UX0gpUbQy0vHIH1K QMU5vDv1LFcWLzvJHMXJfCHL5nVSukXCMawr+DbeKjrkseG0UX0gpUbQy0vHIH1K
2geD2xyl3TJ8jCaKOxb/Hu+KfkvtOCsh07TA+cnTV1WHR77svUcMErzHXWOFm8+U 2geD2xyl3TJ8jCaKOxb/Hu+KfkvtOCsh07TA+cnTV1WHR77svUcMErzHXWOFm8+U
omIXALO1EiDbpu38gERRLkC84eMhRBQjKcdmlcBFsmilt3cfIofypuhMRiIFjIke omIXALO1EiDbpu38gERRLkC84eMhRBQjKcdmlcBFsmilt3cfIofypuhMRiIFjIke
00y2GEdQVsZGA/LX1HILqD4dEFDDQI2LPvCG5qe28HTfWspzsqK94IRESzm+Vmdp 00y2GEdQVsZGA/LX1HILqD4dEFDDQI2LPvCG5qe28HTfWspzsqK94IRESzm+Vmdp
IjNzkTyrPI06yMvxaHGajwUtLWCReJOG/uXhswbX7EviVYyqCR4vzDLDVXAulxo/ IjNzkTyrPI06yMvxaHGajwUtLWCReJOG/uXhswbX7EviVYyqCR4vzDLDVXAulxo/
OsHaQhMX8xYOLXontx7SNCBlu/EEBww5QklKUldgd5igr7bDxsvZ6vHy/wcNIzY3 OsHaQhMX8xYOLXontx7SNCBlu/EEBww5QklKUldgd5igr7bDxsvZ6vHy/wcNIzY3
RUdidnuDkpSm1hIoLz4/SW2Tm6C2u9La5evu7xAfIy1ul8LE3/P0AAAAAAAAAAAA RUdidnuDkpSm1hIoLz4/SW2Tm6C2u9La5evu7xAfIy1ul8LE3/P0AAAAAAAAAAAA
AAAAABcmOEM= AAAAABcmOEM=
]]></artwork> -----END CERTIFICATE-----]]></sourcecode>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.17 }
} }
skipping to change at line 3083 skipping to change at line 3034
c2bf836de2a3ae4b1e1b4517d20a546d0cb4bc7207d4ada0783db1ca5dd327c8 c2bf836de2a3ae4b1e1b4517d20a546d0cb4bc7207d4ada0783db1ca5dd327c8
c268a3b16ff1eef8a7e4bed382b21d3b4c0f9c9d357558747beecbd470c12bcc c268a3b16ff1eef8a7e4bed382b21d3b4c0f9c9d357558747beecbd470c12bcc
75d63859bcf94a2621700b3b51220dba6edfc8044512e40bce1e32144142329c 75d63859bcf94a2621700b3b51220dba6edfc8044512e40bce1e32144142329c
76695c045b268a5b7771f2287f2a6e84c4622058c891ed34cb618475056c6460 76695c045b268a5b7771f2287f2a6e84c4622058c891ed34cb618475056c6460
3f2d7d4720ba83e1d1050c3408d8b3ef086e6a7b6f074df5aca73b2a2bde0844 3f2d7d4720ba83e1d1050c3408d8b3ef086e6a7b6f074df5aca73b2a2bde0844
44b39be566769223373913cab3c8d3ac8cbf168719a8f052d2d6091789386fee 44b39be566769223373913cab3c8d3ac8cbf168719a8f052d2d6091789386fee
5e1b306d7ec4be2558caa091e2fcc32c355702e971a3f3ac1da421317f3160e2 5e1b306d7ec4be2558caa091e2fcc32c355702e971a3f3ac1da421317f3160e2
d7a27b71ed2342065bbf104070c3942494a5257607798a0afb6c3c6cbd9eaf1f d7a27b71ed2342065bbf104070c3942494a5257607798a0afb6c3c6cbd9eaf1f
2ff070d233637454762767b839294a6d612282f3e3f496d939ba0b6bbd2dae5e 2ff070d233637454762767b839294a6d612282f3e3f496d939ba0b6bbd2dae5e
beeef101f232d6e97c2c4dff3f40000000000000000000000000017263843` } beeef101f232d6e97c2c4dff3f40000000000000000000000000017263843` }
} }]]></artwork>
]]></artwork>
<t>The following is a self-signed certificate for the ML-DSA-65 public k ey in the <t>The following is a self-signed certificate for the ML-DSA-65 public k ey in the
previous section. The textual encoding <xref target="RFC7468"/> is followed by t he previous section. The textual encoding <xref target="RFC7468"/> is followed by t he
so-called "pretty print"; the certificates are the same.</t> so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[
<sourcecode type="x509"><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIIVjTCCCIqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMS MIIVjTCCCIqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMS
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
TEFNUFMgV0cwggeyMAsGCWCGSAFlAwQDEgOCB6EASGg9kZeOMes93biwRzSC0riK TEFNUFMgV0cwggeyMAsGCWCGSAFlAwQDEgOCB6EASGg9kZeOMes93biwRzSC0riK
X2JZSf2PWKVh5pa9TCfQWzjbsu3wHmZO/YG+HqiTaIzmiqLVHFlY+LvG606J7mfS X2JZSf2PWKVh5pa9TCfQWzjbsu3wHmZO/YG+HqiTaIzmiqLVHFlY+LvG606J7mfS
wDIJVNVyEsrHIp/x1urwOSi9UVEfjYjYR3NsfeJzDVl45UEHExYJeIZ3Eb9VOaC/ wDIJVNVyEsrHIp/x1urwOSi9UVEfjYjYR3NsfeJzDVl45UEHExYJeIZ3Eb9VOaC/
xMNQwr5XK68O4uL7Fsz+oIAo2ZrEmuu3WTfdzhEc2rYv/zzqi6IjPR5W+8XFoecm xMNQwr5XK68O4uL7Fsz+oIAo2ZrEmuu3WTfdzhEc2rYv/zzqi6IjPR5W+8XFoecm
3mP63SrwFrEZF3+j2XGi2Sdxc/zlW2d0WvC3wh1Zfb65Pmoy80HEmlqL6eglCI0f 3mP63SrwFrEZF3+j2XGi2Sdxc/zlW2d0WvC3wh1Zfb65Pmoy80HEmlqL6eglCI0f
KqRRVdbIrhU2fk6wA7j994UQcZSXOfn/8JAj6vRRBNKoSkWQbu1GcaRNwo0nmHu1 KqRRVdbIrhU2fk6wA7j994UQcZSXOfn/8JAj6vRRBNKoSkWQbu1GcaRNwo0nmHu1
skipping to change at line 3206 skipping to change at line 3158
7E3OGjBH4my94VaNx6O8HIEhtY6zq2X18IkRvwUhO9dLIUZqYNAgC5n/8NQrxRqi 7E3OGjBH4my94VaNx6O8HIEhtY6zq2X18IkRvwUhO9dLIUZqYNAgC5n/8NQrxRqi
iY0RxJ9UObtef5YlNsNNoXmL4tXvJ9esMNTMFR5bHLlFW5dpfHd2TCzAZKxRPeGr iY0RxJ9UObtef5YlNsNNoXmL4tXvJ9esMNTMFR5bHLlFW5dpfHd2TCzAZKxRPeGr
uKQ14KFmXfvcmw18tV7YXNTitPtBb+5osiJIX8GBG91eipxNytxK/qoVqvvfjytS uKQ14KFmXfvcmw18tV7YXNTitPtBb+5osiJIX8GBG91eipxNytxK/qoVqvvfjytS
f4Bi0XC/I1E4xQ46UwTvGQKLTtRHyeg3vG+gX5raRK2Ny6IXDJj0scYE79q83TAc f4Bi0XC/I1E4xQ46UwTvGQKLTtRHyeg3vG+gX5raRK2Ny6IXDJj0scYE79q83TAc
uWXH6mJ0D04Edb/ut+2n5xL5VDde/rXlzntbCYTwxa4BbJmYjwQCiKVzDeknXdMj uWXH6mJ0D04Edb/ut+2n5xL5VDde/rXlzntbCYTwxa4BbJmYjwQCiKVzDeknXdMj
xsV0Euw3Okm3CIQp7biPo7108y5keJll6HEpx7sWT37mNOoj4AFdm79wzEJQhl6p xsV0Euw3Okm3CIQp7biPo7108y5keJll6HEpx7sWT37mNOoj4AFdm79wzEJQhl6p
KOo4Bpfj1etTFQAcU6E3weyVD9ROi7WtSBH4EFhFOfgfga1CHD8DHbwDdsa+dhIj KOo4Bpfj1etTFQAcU6E3weyVD9ROi7WtSBH4EFhFOfgfga1CHD8DHbwDdsa+dhIj
9mORCp7dEUPjt5Qi5mimlqQwYFfCHI+ap6VYsrhpzWr3gPi8EENRsbTUEWWezM/n 9mORCp7dEUPjt5Qi5mimlqQwYFfCHI+ap6VYsrhpzWr3gPi8EENRsbTUEWWezM/n
+BH4UnmFmQY7SGZyeHuDvFNzdNIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYNDxMc +BH4UnmFmQY7SGZyeHuDvFNzdNIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAYNDxMc
IA== IA==
]]></artwork> -----END CERTIFICATE-----]]></sourcecode>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.18 }
} }
skipping to change at line 3459 skipping to change at line 3411
2485fc1811bdd5e8a9c4dcadc4afeaa15aafbdf8f2b527f8062d170bf235138c 2485fc1811bdd5e8a9c4dcadc4afeaa15aafbdf8f2b527f8062d170bf235138c
50e3a5304ef19028b4ed447c9e837bc6fa05f9ada44ad8dcba2170c98f4b1c60 50e3a5304ef19028b4ed447c9e837bc6fa05f9ada44ad8dcba2170c98f4b1c60
4efdabcdd301cb965c7ea62740f4e0475bfeeb7eda7e712f954375efeb5e5ce7 4efdabcdd301cb965c7ea62740f4e0475bfeeb7eda7e712f954375efeb5e5ce7
b5b0984f0c5ae016c99988f040288a5730de9275dd323c6c57412ec373a49b70 b5b0984f0c5ae016c99988f040288a5730de9275dd323c6c57412ec373a49b70
88429edb88fa3bd74f32e64789965e87129c7bb164f7ee634ea23e0015d9bbf7 88429edb88fa3bd74f32e64789965e87129c7bb164f7ee634ea23e0015d9bbf7
0cc4250865ea928ea380697e3d5eb5315001c53a137c1ec950fd44e8bb5ad481 0cc4250865ea928ea380697e3d5eb5315001c53a137c1ec950fd44e8bb5ad481
1f810584539f81f81ad421c3f031dbc0376c6be761223f663910a9edd1143e3b 1f810584539f81f81ad421c3f031dbc0376c6be761223f663910a9edd1143e3b
79422e668a696a4306057c21c8f9aa7a558b2b869cd6af780f8bc104351b1b4d 79422e668a696a4306057c21c8f9aa7a558b2b869cd6af780f8bc104351b1b4d
411659ecccfe7f811f852798599063b486672787b83bc537374d200000000000 411659ecccfe7f811f852798599063b486672787b83bc537374d200000000000
00000000000000000000000000000000000060d0f131c20` } 00000000000000000000000000000000000060d0f131c20` }
} }]]></artwork>
]]></artwork>
<t>The following is a self-signed certificate for the ML-DSA-87 public k ey in the <t>The following is a self-signed certificate for the ML-DSA-87 public k ey in the
previous section. The textual encoding <xref target="RFC7468"/> is followed by t he previous section. The textual encoding <xref target="RFC7468"/> is followed by t he
so-called "pretty print"; the certificates are the same.</t> so-called "pretty print"; the certificates are the same.</t>
<artwork><![CDATA[
<sourcecode type="x509"><![CDATA[
-----BEGIN CERTIFICATE----- -----BEGIN CERTIFICATE-----
MIIdMzCCCwqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMT MIIdMzCCCwqgAwIBAgIUFZ/+byL9XMQsUk32/V4o0N44804wCwYJYIZIAWUDBAMT
MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0 MCIxDTALBgNVBAoTBElFVEYxETAPBgNVBAMTCExBTVBTIFdHMB4XDTIwMDIwMzA0
MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI MzIxMFoXDTQwMDEyOTA0MzIxMFowIjENMAsGA1UEChMESUVURjERMA8GA1UEAxMI
TEFNUFMgV0cwggoyMAsGCWCGSAFlAwQDEwOCCiEAl5K87C8kMGhqgvzPPC9f9mXn TEFNUFMgV0cwggoyMAsGCWCGSAFlAwQDEwOCCiEAl5K87C8kMGhqgvzPPC9f9mXn
cderQbkCWM+n6Q7JcSSnOzI7m6Iatk12fEM/WlIe/+GPhuRqGIlSxEZ+BItynn/E cderQbkCWM+n6Q7JcSSnOzI7m6Iatk12fEM/WlIe/+GPhuRqGIlSxEZ+BItynn/E
0RXn5I2hiW1f4RmxDc3e9iyzB5VAdLQjNuUoNt5h2pQfjTfqaKyBBvq+GQcGea9g 0RXn5I2hiW1f4RmxDc3e9iyzB5VAdLQjNuUoNt5h2pQfjTfqaKyBBvq+GQcGea9g
CFNxIPcHk7jqnMDm57e0yaXHQhxg8kRRuh6TPbGi7hbHlVnyGz0bgwWFCqQq+7E/ CFNxIPcHk7jqnMDm57e0yaXHQhxg8kRRuh6TPbGi7hbHlVnyGz0bgwWFCqQq+7E/
H01bn0g1+dh9/OsWLQ70p/3Ey6F0PNHIe7SWfaFsyHZLZWnfjuW9y//ppOBXSOb9 H01bn0g1+dh9/OsWLQ70p/3Ey6F0PNHIe7SWfaFsyHZLZWnfjuW9y//ppOBXSOb9
8iWvnk7rd3O2Lo+F+bVrVIlFVRhE+9iYBqSsNpvtLSVhAPaIpq1eCnCYJtxESeke 8iWvnk7rd3O2Lo+F+bVrVIlFVRhE+9iYBqSsNpvtLSVhAPaIpq1eCnCYJtxESeke
skipping to change at line 3622 skipping to change at line 3575
izLeOXEANQ9YCOF2GmHwg2Gi3Iw88PqvERz0T9/RCI5CiGa+Oli19jjFx2L7J5Ct izLeOXEANQ9YCOF2GmHwg2Gi3Iw88PqvERz0T9/RCI5CiGa+Oli19jjFx2L7J5Ct
6RS+DPYStrO97GuIrM9tGz14xBDAWuURfKECXTLMA6AW8zAjYBjWV5zQuZMLMXou 6RS+DPYStrO97GuIrM9tGz14xBDAWuURfKECXTLMA6AW8zAjYBjWV5zQuZMLMXou
yqK0FJG4JqfSWSJv+DvDvGdmCkxcBiDzO6wDGWpFF65F8z7wHKU7VMzJa3LWjlfO yqK0FJG4JqfSWSJv+DvDvGdmCkxcBiDzO6wDGWpFF65F8z7wHKU7VMzJa3LWjlfO
lIn7fepvuNyI+PK9UyvX0am7R29bxNyCTNJHQuVJv93WrokJX7IHOaZXyY7T4bMj lIn7fepvuNyI+PK9UyvX0am7R29bxNyCTNJHQuVJv93WrokJX7IHOaZXyY7T4bMj
yw0yMsWOanzDyh0y7OGhDgXiJS42y2XU0UH/JGGEZbZlEpfNNNOPYcYvMfuOlwww yw0yMsWOanzDyh0y7OGhDgXiJS42y2XU0UH/JGGEZbZlEpfNNNOPYcYvMfuOlwww
ZTIl7tStk6k0AtZ77tHmw2iu5730yoXlTrKxe72lAdDQlvXLTkdXXw+oxg+O078n ZTIl7tStk6k0AtZ77tHmw2iu5730yoXlTrKxe72lAdDQlvXLTkdXXw+oxg+O078n
Zt5jdDQgFMXYxyqanZgc5scGn3X4Q/uXgZ0QSlhPErGjtIC5/XdAUraYJZNo6lu3 Zt5jdDQgFMXYxyqanZgc5scGn3X4Q/uXgZ0QSlhPErGjtIC5/XdAUraYJZNo6lu3
r2dYCUIfo6xun+6+QnoT7OXpb+hc04Ky4QYHq5EYd60H50ogBiHTzC2QLcqDbpK4 r2dYCUIfo6xun+6+QnoT7OXpb+hc04Ky4QYHq5EYd60H50ogBiHTzC2QLcqDbpK4
rnVLSDqKkbgKCwwRPEiw8SU8WZu5zwG9ygURLGN4obLeSQU8UHyCteEbbpGrstXp rnVLSDqKkbgKCwwRPEiw8SU8WZu5zwG9ygURLGN4obLeSQU8UHyCteEbbpGrstXp
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQMEhUdHiUs AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQMEhUdHiUs
]]></artwork> -----END CERTIFICATE-----]]></sourcecode>
<artwork><![CDATA[ <artwork><![CDATA[
SEQUENCE { SEQUENCE {
SEQUENCE { SEQUENCE {
[0] { [0] {
INTEGER { 2 } INTEGER { 2 }
} }
INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` } INTEGER { `159ffe6f22fd5cc42c524df6fd5e28d0de38f34e` }
SEQUENCE { SEQUENCE {
OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 } OBJECT_IDENTIFIER { 2.16.840.1.101.3.4.3.19 }
} }
skipping to change at line 3936 skipping to change at line 3889
8f2bd532bd7d1a9bb476f5bc4dc824cd24742e549bfddd6ae89095fb20739a65 8f2bd532bd7d1a9bb476f5bc4dc824cd24742e549bfddd6ae89095fb20739a65
7c98ed3e1b323cb0d3232c58e6a7cc3ca1d32ece1a10e05e2252e36cb65d4d14 7c98ed3e1b323cb0d3232c58e6a7cc3ca1d32ece1a10e05e2252e36cb65d4d14
1ff24618465b6651297cd34d38f61c62f31fb8e970c30653225eed4ad93a9340 1ff24618465b6651297cd34d38f61c62f31fb8e970c30653225eed4ad93a9340
2d67beed1e6c368aee7bdf4ca85e54eb2b17bbda501d0d096f5cb4e47575f0fa 2d67beed1e6c368aee7bdf4ca85e54eb2b17bbda501d0d096f5cb4e47575f0fa
8c60f8ed3bf2766de6374342014c5d8c72a9a9d981ce6c7069f75f843fb97819 8c60f8ed3bf2766de6374342014c5d8c72a9a9d981ce6c7069f75f843fb97819
d104a584f12b1a3b480b9fd774052b698259368ea5bb7af675809421fa3ac6e9 d104a584f12b1a3b480b9fd774052b698259368ea5bb7af675809421fa3ac6e9
feebe427a13ece5e96fe85cd382b2e10607ab911877ad07e74a200621d3cc2d9 feebe427a13ece5e96fe85cd382b2e10607ab911877ad07e74a200621d3cc2d9
02dca836e92b8ae754b483a8a91b80a0b0c113c48b0f1253c599bb9cf01bdca0 02dca836e92b8ae754b483a8a91b80a0b0c113c48b0f1253c599bb9cf01bdca0
5112c6378a1b2de49053c507c82b5e11b6e91abb2d5e90000000000000000000 5112c6378a1b2de49053c507c82b5e11b6e91abb2d5e90000000000000000000
0000000000000000000000000000000000000000000040c12151d1e252c` } 0000000000000000000000000000000000000000000040c12151d1e252c` }
} }]]></artwork>
]]></artwork>
</section> </section>
<section anchor="example-bad"> <section anchor="example-bad">
<name>Example Inconsistent Seed and Expanded Private Keys</name> <name>Example Inconsistent Seed and Expanded Private Keys</name>
<aside> <aside>
<t>WARNING: These private keys are purposely bad do not use them in <t>WARNING: These private keys are purposely bad; do not use them in
production systems.</t> production systems.</t>
</aside> </aside>
<t>The following examples demonstrate inconsistent seed and expanded pri vate keys.</t> <t>The following examples demonstrate inconsistent seed and expanded pri vate keys.</t>
<t>Three <tt>ML-DSA-44-PrivateKey</tt> examples of inconsistent seed and <t>Three <tt>ML-DSA-44-PrivateKey</tt> examples of inconsistent seed and
expanded private keys follow:</t> expanded private keys follow:</t>
<ol spacing="normal" type="1"><li> <ol spacing="normal" type="1">
<t>The first <tt>ML-DSA-PrivateKey</tt> example includes the <tt>bot <li>
h CHOICE</tt> , i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are included. <t>The first <tt>ML-DSA-PrivateKey</tt> example includes the <tt>bot
The <tt>seed</tt> and <tt>expanded</tt> values can be checked for inconsistencie h CHOICE</tt> , i.e., both <tt>seed</tt> and <tt>expandedKey</tt> are included.
s.</t> The <tt>seed</tt> and <tt>expandedKey</tt> values can be checked for inconsisten
cies.</t>
</li> </li>
<li> <li>
<t>The second <tt>ML-DSA-PrivateKey</tt> example includes only <tt>e xpandedKey</tt>. The public key fails to match the <tt>tr</tt> hash value in th e private key.</t> <t>The second <tt>ML-DSA-PrivateKey</tt> example includes only <tt>e xpandedKey</tt>. The public key fails to match the <tt>tr</tt> hash value in th e private key.</t>
</li> </li>
<li> <li>
<t>The third <tt>ML-DSA-PrivateKey</tt> example also includes only < tt>expandedKey</tt>. The private <tt>s_1</tt> and <tt>s_2</tt> vectors imply a < tt>t</tt> vector whose private low bits do not match the <tt>t_0</tt> vector por tion of the private key (its high bits <tt>t_1</tt> are the primary content of t he public key).</t> <t>The third <tt>ML-DSA-PrivateKey</tt> example also includes only < tt>expandedKey</tt>. The private <tt>s_1</tt> and <tt>s_2</tt> vectors imply a < tt>t</tt> vector whose private low bits do not match the <tt>t_0</tt> vector por tion of the private key (its high bits <tt>t_1</tt> are the primary content of t he public key).</t>
</li> </li>
</ol> </ol>
<t>The second and third examples would not be detected by implementation s <t>The second and third examples would not be detected by implementation s
that do not regenerate the public key from the private key, or neglect to that do not regenerate the public key from the private key or, when they do, the
then check consistency of <tt>tr</tt> or <tt>t_0</tt>.</t> y neglect to check consistency of <tt>tr</tt> and <tt>t_0</tt>.</t>
<t>The following is the first example:</t> <t>The following is the first example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR MIIKPgIBADALBglghkgBZQMEAxEEggoqMIIKJgQgAAECAwQFBgcICQoLDA0ODxAR
EhMUFRYXGBkaGxwdHh8EggoAUQyb/R3XN09Oiucd1YKBEGqTQS7Y+jV/dLu0Zh7L EhMUFRYXGBkaGxwdHh8EggoAUQyb/R3XN09Oiucd1YKBEGqTQS7Y+jV/dLu0Zh7L
GSHTp1/JO4jvDmqbhRvs7BmZm+gQaMhZ1t8RXGCMFQEXDrbAVcIvYlWSSXbYlaX1 GSHTp1/JO4jvDmqbhRvs7BmZm+gQaMhZ1t8RXGCMFQEXDrbAVcIvYlWSSXbYlaX1
TSw4WWxAPM72+XPiKl+MfCuoNjNEcJCniyK7Qc/e2vvLLt7PkHDM5hLkKrCh8T65 TSw4WWxAPM72+XPiKl+MfCuoNjNEcJCniyK7Qc/e2vvLLt7PkHDM5hLkKrCh8T65
3DwUkDGJwoHgsDHalISCEgijtDDSKEoEByDDRELgQC5EoHEBqSwDJmQSQSQYMiQA 3DwUkDGJwoHgsDHalISCEgijtDDSKEoEByDDRELgQC5EoHEBqSwDJmQSQSQYMiQA
Ii5KlmALGZAiMyBShkUbCEyTGIQZAG1TgAwQpChQBgogBgwjETLSxEDSEgIENIYj Ii5KlmALGZAiMyBShkUbCEyTGIQZAG1TgAwQpChQBgogBgwjETLSxEDSEgIENIYj
lQygtkxbSJGMEoQgGQKRGIEKJRAcoGlgkCgDxjCTBJARuJAERTLBIEzawpDZiCwY lQygtkxbSJGMEoQgGQKRGIEKJRAcoGlgkCgDxjCTBJARuJAERTLBIEzawpDZiCwY
skipping to change at line 4019 skipping to change at line 3973
paZzqkJijn+EH7d+G8RVLGhU0gkbplrNqDAIHAiCnO76b3CuBam2ngtjQzBPUlSU paZzqkJijn+EH7d+G8RVLGhU0gkbplrNqDAIHAiCnO76b3CuBam2ngtjQzBPUlSU
AqXPtG17rJg2B+fzgPKAgh8vuZLEaXP7/XeNMwNe6QsNuU9gfln7Tt+pqYpwm1gH AqXPtG17rJg2B+fzgPKAgh8vuZLEaXP7/XeNMwNe6QsNuU9gfln7Tt+pqYpwm1gH
Wkqor1xYXy+1md2Ct3tLbznupLFIfQ3NVBkeDW+NVvpPvC+CF/NefkSuzOaBPlTa Wkqor1xYXy+1md2Ct3tLbznupLFIfQ3NVBkeDW+NVvpPvC+CF/NefkSuzOaBPlTa
itxMHENeGFxR5cf0Sp43j59iGKdWBtJBCV8uWf4qRgRG8fdbfQ+l1qAJEx4v8r4H itxMHENeGFxR5cf0Sp43j59iGKdWBtJBCV8uWf4qRgRG8fdbfQ+l1qAJEx4v8r4H
2Hsm6eS/CeZlEpe9fnobwS1BBNoczKSL+noqpxcmgAjbcEtZtsBXSJVBsj4OCdt3 2Hsm6eS/CeZlEpe9fnobwS1BBNoczKSL+noqpxcmgAjbcEtZtsBXSJVBsj4OCdt3
fA/6IfpWRsNBIVR1aD2p/a0U/RH3FCZKDhwF2ZhBLeHEWWQOCr1v0W68/rllFuIW fA/6IfpWRsNBIVR1aD2p/a0U/RH3FCZKDhwF2ZhBLeHEWWQOCr1v0W68/rllFuIW
YcyqOojDEup7oFhc0k4aUwdv50HJAWk3ehaPvbP+zlz84DmyVMQjXYJl9gZShi+9 YcyqOojDEup7oFhc0k4aUwdv50HJAWk3ehaPvbP+zlz84DmyVMQjXYJl9gZShi+9
tFV4KJ8aZz/kCdufmWwtLJKHIBuVkX/hqbYO8Xg4XyWv2pZpZIGeW779l8wQE1MI tFV4KJ8aZz/kCdufmWwtLJKHIBuVkX/hqbYO8Xg4XyWv2pZpZIGeW779l8wQE1MI
2Yt6grThI3sytb+dM3JvqUW79clvJ288BqRZMJSNO2vUIo4vPqyM/Wcuy465qS0V 2Yt6grThI3sytb+dM3JvqUW79clvJ288BqRZMJSNO2vUIo4vPqyM/Wcuy465qS0V
ns+zr0zC2uo3z3LqK57arYABNRm8CV2VxaOqH61GvYyUrA== ns+zr0zC2uo3z3LqK57arYABNRm8CV2VxaOqH61GvYyUrA==
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<t>The following is the second example:</t> <t>The following is the second example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQzmgex 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQzmgex
+rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk
ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu
EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi
skipping to change at line 4078 skipping to change at line 4033
wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
<t>The following is the third example:</t> <t>The following is the third example:</t>
<artwork><![CDATA[ <artwork><![CDATA[
-----BEGIN PRIVATE KEY----- -----BEGIN PRIVATE KEY-----
MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX MIIKGAIBADALBglghkgBZQMEAxEEggoEBIIKANeytHJUquDbReeTDUqY0sl9jxOX
0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex 0Xidr6FwJLMW6b7JOc4Pf3f421ZE3No2a/5HNL2V9DX/mmE6pUqkHCxpTAQymgex
+rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA +rtI9SownxGhiY+EjiMi/+Yj7IENs77jNoWFSogmnaMg1RIL/P6JoY4w9xFNg6pA
SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII SmRrbJlziYYNElIu4ABuI4SBkYZhmyYNEYZk1KYoIhhEgkAomBRhSKZhTEJIoZII
wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG wjgpUSRICKElwggxCMRxIBQJFINsGKeAhBBuycBwIrVkCLBhDAcEmBJEUYhpWQBG
IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk IpMgQQYuQrZMARZJFChMQahRgEYKURZRWgggAiJE3JhJ0TJR4TBl08CFkqhREqFk
ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu ADkiCUZiHMcM2Qht0AYmUkCFgEQwkQYsUMgJJMWEGpZtSpgsmQZtpEQyIKdkWjJu
EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi EbVwIJJhJBOOBIUsCkhyyKBR0wgqmSCAWCQgJAdOWRSIEKRkYMBt4LKNGxkJIDQi
skipping to change at line 4137 skipping to change at line 4093
wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr wjev7TsVHEuo6fS964SZowZuJrvGnorwid7HFzHR3FKeqxfvc3RzTA/kdUlMg4Nr
3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC 3TSgO5vImRRxYGG/uY7G5hw+1EOO3K8lJDxkcIa56nAYsNmooLAM7LAKveJJjWnC
M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ M2EBp3LL5PVxUj9RvQWILN81i4ScwUCqH68iQjoShRzg4z/UiXWklZ+lxf5BjJOQ
gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J gZGrbnQbd7/gLL1pjueVxGbWFWGeZEE4LG6sAYNO6atzzqgLviNceNqRvXm2+C+J
l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y l4XWhwDTk+Z1wiJNa3oa0hMgSVZ5ra7XAWe1CGZxOlMQnbe299gTBOzf2Dsxmx7y
SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP SDBrRa0p593Mhj2sVgSLXWnqF1AR92FMAKhqhjzeGHKokyh4uax+GsW9pJl7cgZP
DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs DNdfTIFOA03hGsuQE89+qSa05+qs4HDHuiGI760uQx4SI9Rd0FxNhAPC5FzuZBPs
vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k vnUn6HPkVcTmEKYYOarMC9VtJIPnjymLZqR46y9VjLr8qGvoR7rrAsWyFsjNiP6k
3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q 3ySbCeZwogcDq6wksKkavEpWRmAUQroQvs/TCZOIAFHQf1agWpN556jmvv7j8i+q
EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg= EGOY93BgBuQum+HvidJcJy8RqVCVxYfXE3MihN6dvTxyF7BoniHY6w/2lmg=
]]></artwork> -----END PRIVATE KEY-----]]></artwork>
</section> </section>
</section> </section>
<section anchor="externalmu"> <section anchor="externalmu">
<name>Pre-hashing (Externalμ-ML-DSA)</name> <name>Pre-Hashing (Externalμ-ML-DSA)</name>
<t>Some applications require pre-hashing that ease operational <t>Some applications require pre-hashing that ease operational
requirements around large or inconsistently-sized payloads. requirements around large or inconsistently-sized payloads.
When signing with pre-hashing, the signature generation When signing with pre-hashing, the signature-generation
process can be separated into a pre-hash step requiring only the message process can be separated into a pre-hash step requiring only the message
and other public information, and a core signature and other public information, and a core signature
step which uses the public key.</t> step that uses the public key.</t>
<t>In the context of ML-DSA, pre-hashing can be performed with <t>In the context of ML-DSA, pre-hashing can be performed with
the HashML-DSA algorithm defined in Section 5.4 of <xref target="FIPS204"/>. the HashML-DSA algorithm defined in Section 5.4 of <xref target="FIPS204"/>.
ML-DSA itself supports a External μ pre-hashing mode which ML-DSA itself supports an External μ pre-hashing mode, which
externalizes the message pre-hashing originally performed inside externalizes the message pre-hashing originally performed inside
the signing operation. This mode is also laid out in the signing operation. This mode is also laid out in
<xref target="FIPS204-ExternalMuFAQ"/>. This document specifies <xref target="FIPS204-ExternalMuFAQ"/>. This document specifies
only the use of ML-DSA's External μ mode, and not HashML-DSA, only the use of ML-DSA's External μ mode, and not HashML-DSA,
in PKIX for reasons laid out in <xref target="sec-disallow-hash"/>.</t> in PKIX for reasons laid out in <xref target="sec-disallow-hash"/>.</t>
<t>Implementations of ML-DSA using the External μ pre-hashing mode require s the following <t>Implementations of ML-DSA using the External μ pre-hashing mode require s the following
algorithms, which are modified versions of the algorithms presented in <xref tar get="FIPS204"/>. algorithms, which are modified versions of the algorithms presented in <xref tar get="FIPS204"/>.
The nomenclature used here has been modified from the NIST FAQ <xref target="FIP S204-ExternalMuFAQ"/> The nomenclature used here has been modified from the NIST FAQ <xref target="FIP S204-ExternalMuFAQ"/>
for clarity.</t> for clarity.</t>
<t>Pre-hash operation:</t> <t>Pre-hash operation:</t>
<figure anchor="fig-externalmu-ml-dsa-external"> <figure anchor="fig-externalmu-ml-dsa-external">
<name>Computeμ prehash operation</name> <name>Computeμ Pre-Hash Operation</name>
<artwork><![CDATA[ <sourcecode type="pseudocode"><![CDATA[
Computeμ(pk, M, ctx): Computeμ(pk, M, ctx):
# Referred to as 'Externalμ-ML-DSA.Prehash(pk, M, ctx)' # Referred to as 'ExternalMu-ML-DSA.Prehash(pk, M, ctx)'
# in the FIPS 204 FAQ. # in the FIPS 204 FAQ.
# M is the message, a bit-string # M is the message, a bit-string
# μ and ctx are byte-strings. # μ and ctx are byte-strings.
# ctx is the context string, which defaults to the empy string. # ctx is the context string, which defaults to the empty string.
μ = H(BytesToBits(H(pk, 64) || IntegerToBytes(0, 1) || μ = H(BytesToBits(H(pk, 64) || IntegerToBytes(0, 1) ||
IntegerToBytes(|ctx|, 1) || ctx) || M, 64) IntegerToBytes(|ctx|, 1) || ctx) || M, 64)
# The functions `BytesToBits` and `IntegerToBytes` are defined in FIPS 204. # The functions `BytesToBits` and `IntegerToBytes` are defined
return μ # in FIPS 204.
]]></artwork> return μ]]></sourcecode>
</figure> </figure>
<t>Sign operations:</t> <t>Sign operations:</t>
<figure anchor="fig-externalmu-ml-dsa-internal"> <figure anchor="fig-externalmu-ml-dsa-internal">
<name>The operations for signing μ</name> <name>The Operations for Signing μ</name>
<artwork><![CDATA[
Signμ(sk, μ):
# Referred to as 'Externalμ-ML-DSA.Sign(sk, μ)' <sourcecode type="pseudocode"><![CDATA[Signμ(sk, μ):
# Referred to as 'ExternalMu-ML-DSA.Sign(sk, mu)'
# in the FIPS 204 FAQ. # in the FIPS 204 FAQ.
if |μ| != 64 then if |μ| != 64 then
return error # return an error indication if the input μ is not return error # return an error indication if the input μ is not
# 64 bytes. # 64 bytes.
end if end if
rnd = rand(32) # for the optional deterministic variant, rnd = rand(32) # for the optional deterministic variant,
# set rnd to all zeroes # set rnd to all zeroes
if rnd = NULL then if rnd = NULL then
return error # return an error indication if random bit return error # return an error indication if random bit
# generation failed # generation failed
end if end if
sigma = Signμ_internal(sk, μ, rnd, isExternalμ=true) sigma = Signμ_internal(sk, μ, rnd, isExternalμ=true)
return sigma return sigma
ML-DSA.Signμ_internal(sk, M', rnd, isExternalμ=false): ML-DSA.Signμ_internal(sk, M', rnd, isExternalμ=false):
# μ can be passed as an argument instead of M' # μ is passed to the function via the argument M'.
# defaulting is Externalμ to false means that # Defaulting Externalμ to false means that
# this modified version of Sign_internal can be used # this modified version of Sign_internal can be used
# in place of the original without interfering with # in place of the original without interfering with
# functioning of pure ML-DSA mode. # functioning of pure ML-DSA mode.
# ... identical to FIPS 204 Algorithm 7, but with Line 6 replaced with
# ... identical to FIPS 204 Algorithm 7, but with Line 6
# replaced with
6: if (isExternalμ): 6: if (isExternalμ):
μ = M' μ = M'
else: else:
μ = H(BytesToBits(tr) || M', 64) μ = H(BytesToBits(tr) || M', 64)]]></sourcecode>
]]></artwork>
</figure> </figure>
<t>There is no need to specify an External μ <tt>Verify()</tt> routine bec ause <t>There is no need to specify an External μ <tt>Verify()</tt> routine bec ause
this is identical to the original <tt>ML-DSA.Verify()</tt>. This makes External this is identical to the original <tt>ML-DSA.Verify()</tt>. This makes External
μ mode simply an internal optimization of the signer, and μ mode simply an internal optimization of the signer, and
allows an ML-DSA key to sometimes be used with the "one-shot" <tt>Sign()</tt> allows an ML-DSA key to sometimes be used with the "one-shot" <tt>Sign()</tt>
API and sometimes the External μ API without any interoperability concens.</t> API and to sometimes be used with the External μ API without any interoperabilit y concerns.</t>
<t>The External μ mode requires the <tt>Computeμ</tt> routine to have acce ss to the <t>The External μ mode requires the <tt>Computeμ</tt> routine to have acce ss to the
hash of the signer's public key which may not be available in some architectures , hash of the signer's public key, which may not be available in some architecture s,
or require fetching it. That may allow for mismatches between <tt>tr</tt> and <t t>sk</tt>. or require fetching it. That may allow for mismatches between <tt>tr</tt> and <t t>sk</tt>.
At worst, this will produce a signature which will fail to verify under the At worst, this will produce a signature that will fail to verify under the
intended public key since a compliant <tt>Verify()</tt> routine will intended public key since a compliant <tt>Verify()</tt> routine will
independently compute <tt>tr</tt> from the public key. That independently compute <tt>tr</tt> from the public key. This
is not believed to be a security concern since <tt>μ</tt> is never used as-is is not believed to be a security concern since <tt>μ</tt> is never used as-is
within <tt>ML-DSA.Sign_internal()</tt> (Algorithm 7 in <xref target="FIPS204"/>) . Rather, within <tt>ML-DSA.Sign_internal()</tt> (Algorithm 7 in <xref target="FIPS204"/>) . Rather,
it is hashed with values unknown to an attacker on lines 7 and 15. it is hashed with values unknown to an attacker on lines 7 and 15.
Thus, a signing oracle exposing <tt>Signμ()</tt> does not leak any bits of the s ecret Thus, a signing oracle exposing <tt>Signμ()</tt> does not leak any bits of the s ecret
key. The External μ mode also requires SHAKE256 to be available to the key. The External μ mode also requires SHAKE256 to be available to the
<tt>Computeμ</tt> routine.</t> <tt>Computeμ</tt> routine.</t>
</section> </section>
<section numbered="false" anchor="acknowledgments"> <section numbered="false" anchor="acknowledgments">
<name>Acknowledgments</name> <name>Acknowledgments</name>
<t>The authors wish to thank the following people for their contributions <t>The authors wish to thank the following people for their
to this document: Corey Bonnell, Dierdre Connolly, Viktor Dukhovni, Russ Housley contributions to this document: <contact fullname="Corey Bonnell"/>,
, <contact fullname="Dierdre Connolly"/>, <contact fullname="Viktor
Alicja Kario, Mike Ounsworth, and Daniel Van Geest.</t> Dukhovni"/>, <contact fullname="Russ Housley"/>, <contact
<t>In addition, we would like to thank those who contributed to the privat fullname="Alicja Kario"/>, <contact fullname="Mike Ounsworth"/>, and
e <contact fullname="Daniel Van Geest"/>.</t>
key format discussion: Tony Arcieri, Bob Beck, Dmitry Belyavskiy, David <t>In addition, we would like to thank those who contributed to the
Benjamin, Daniel Bernstein, Uri Blumenthal, Theo Buehler, Stephen Farrell, private key format discussion: <contact fullname="Tony Arcieri"/>,
Jean-Pierre Fiset, Scott Fluhrer, Alex Gaynor, John Gray, Peter Gutmann, <contact fullname="Bob Beck"/>, <contact fullname="Dmitry Belyavskiy"/>,
David Hook, Tim Hudson, Paul Kehrer, John Kemp, Watson Ladd, Adam Langley, <contact fullname="David Benjamin"/>, <contact fullname="Daniel
John Mattsson, Damien Miller, Robert Relyea, Michael Richardson, Bernstein"/>, <contact fullname="Uri Blumenthal"/>, <contact
Markku-Juhani O. Saarinen, Rich Salz, Roland Shoemaker, Sophie Schmieg, fullname="Theo Buehler"/>, <contact fullname="Stephen Farrell"/>,
Simo Sorce, Michael St. Johns, Falko Strenzke, Filippo Valsorda, Loganaden <contact fullname="Jean-Pierre Fiset"/>, <contact fullname="Scott
Velvindron, Carl Wallace, and Wei-Jun Wang.</t> Fluhrer"/>, <contact fullname="Alex Gaynor"/>, <contact fullname="John
Gray"/>, <contact fullname="Peter Gutmann"/>, <contact fullname="David
Hook"/>, <contact fullname="Tim Hudson"/>, <contact fullname="Paul
Kehrer"/>, <contact fullname="John Kemp"/>, <contact fullname="Watson
Ladd"/>, <contact fullname="Adam Langley"/>, <contact fullname="John
Mattsson"/>, <contact fullname="Damien Miller"/>, <contact
fullname="Robert Relyea"/>, <contact fullname="Michael Richardson"/>,
<contact fullname="Markku-Juhani O. Saarinen"/>, <contact fullname="Rich
Salz"/>, <contact fullname="Roland Shoemaker"/>, <contact
fullname="Sophie Schmieg"/>, <contact fullname="Simo Sorce"/>, <contact
fullname="Michael St. Johns"/>, <contact fullname="Falko Strenzke"/>,
<contact fullname="Filippo Valsorda"/>, <contact fullname="Loganaden
Velvindron"/>, <contact fullname="Carl Wallace"/>, and <contact
fullname="Wei-Jun Wang"/>.</t>
</section> </section>
</back>
<!-- ##markdown-source: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<!-- [rfced] Please review <tt> throughout the document for correctness and cons
istent use. Please see the list of <tt> use at the following location:
https://www.rfc-editor.org/authors/rfc9881tt2.txt
The list has been alphabetized and entries are listed only once (that is, if <tt
> is used multiple times for the same term, it is only listed once).
-->
<!-- [rfced] Please review each artwork element and let us know if any should
be marked as sourcecode (or another element) instead.
Please let us know if any instances of <artwork> should be <sourcecode> and whet
her type="" should be set. The current list of types is available at
<https://www.rfc-editor.org/rpc/wiki/doku.php?id=sourcecode-types>. If it does
not contain an applicable type, then feel free to let us know. Note that it is
also acceptable to leave the "type" attribute not set.
--> -->
</back>
</rfc> </rfc>
 End of changes. 173 change blocks. 
3002 lines changed or deleted 410 lines changed or added

This html diff was produced by rfcdiff 1.48.