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Algorithms and Identifiers for Post-Quantum Algorithms

Document Type Replaced Internet-Draft (individual)
Authors Jake Massimo , Panos Kampanakis , Sean Turner , Bas Westerbaan
Last updated 2022-07-08
Replaced by draft-ietf-lamps-dilithium-certificates
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LAMPS WG                                                      J. Massimo
Internet-Draft                                             P. Kampanakis
Intended status: Standards Track                                     AWS
Expires: 9 January 2023                                        S. Turner
                                                           B. Westerbaan
                                                             8 July 2022

         Algorithms and Identifiers for Post-Quantum Algorithms
            in the Internet X.509 Public Key Infrastructure


   Digital signatures are used within X.509 certificates, Certificate
   Revocation Lists (CRLs), and to sign messages.  This document
   describes the conventions for using Dilithium quantum-resistant
   signatures in Internet X.509 certificates and certifiate revocation
   lists.  The conventions for the associated post-quantum signatures,
   subject public keys, and private key are also described.


   [EDNOTE: This draft is not expected to be finalized before the NIST
   PQC Project has standardized PQ algorithms.  After NIST has
   standardized its first algorithms, this document will replace TBD,
   with the appropriate algorithms and parameters before proceeding to
   ratification.  The algorithm Dilithium has been added as an example
   in this draft, to provide a more detailed illustration of the content
   - it by no means indicates its inclusion in the final version.  This
   specification will use object identifiers for the new algorithms that
   are assigned by NIST, and will use placeholders until these are

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at

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   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on 9 January 2023.

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   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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   Please review these documents carefully, as they describe your rights
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   provided without warranty as described in the Revised BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   3
   2.  Identifiers . . . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Dilithium Signatures in PKIX  . . . . . . . . . . . . . . . .   4
   4.  Dilithium Public Keys in PKIX . . . . . . . . . . . . . . . .   5
   5.  Dilithium Private Keys  . . . . . . . . . . . . . . . . . . .   6
   6.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . . . .   6
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .   8
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .   9
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  10
   Appendix A.  Acknowledgements . . . . . . . . . . . . . . . . . .  11
   Appendix B.  Appendix . . . . . . . . . . . . . . . . . . . . . .  11
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  11

1.  Introduction

   The US National Institute of Standards and Technology (NIST) Post-
   Quantum Cryptography (PQC) effort has defined quantum-resistant
   public key cryptographic algorithm standards [NIST-PQC].  This
   document specifies the use of these Post-Quantum public key
   algorithms with Public Key Infrastructure X.509 (PKIX) certificates
   and Certificate Revocation Lists (CRLs) using object identifiers
   algorithms assigned by NIST.

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   This specification includes conventions for the signatureAlgorithm,
   signatureValue, signature, and subjectPublicKeyInfo fields within
   Internet X.509 certificates and CRLs [RFC5280], like [RFC3279] did
   for classic cryptography and [RFC5480] did for elliptic curve
   cryptography.  It describes the encoding of digital signatures and
   public keys generated with quantum-resistant signature algorithm

1.1.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

2.  Identifiers

   This specification uses placeholders for object identifiers until the
   identifiers for the new algorithms are assigned by NIST.

   The AlgorithmIdentifier type, which is included herein for
   convenience, is defined as follows:

      AlgorithmIdentifier  ::=  SEQUENCE  {
          algorithm   OBJECT IDENTIFIER,
          parameters  ANY DEFINED BY algorithm OPTIONAL

      |  NOTE: The above syntax is from [RFC5280] and matches the
      |  version used therein, i.e., the 1988 ASN.1 syntax.  See
      |  [RFC5912] for ASN.1 copmatible with the 2015 ASN.1 syntax.

   The OIDs are:

      id-dilithiumTBD OBJECT IDENTIFIER ::= { joint-iso-itu-t(2)
               country(16) us(840) organization(1) gov(101) csor(3)
               nistAlgorithm(4) sigAlgs(3) TBD }

   The contents of the parameters component for each algorithm are

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3.  Dilithium Signatures in PKIX

   Dilithium is a digital signature scheme built upon the Fiat-Shamir-
   with-aborts framework [Fiat-Shamir].  The security is based upon the
   hardness of lattice problems over module lattices [Dilithium].
   Dilithium provides three parameter sets for the security categories
   2, 3 and 5.

   Signatures are used in a number of different ASN.1 structures.  As
   shown in the ASN.1 representation from [RFC5280] below, in an X.509
   certificate, a signature is encoded with an algorithm identifier in
   the signatureAlgorithm attribute and a signatureValue attribute that
   contains the actual signature.

      Certificate  ::=  SEQUENCE  {
         tbsCertificate       TBSCertificate,
         signatureAlgorithm   AlgorithmIdentifier,
         signatureValue       BIT STRING  }

   Signatures are also used in the CRL list ASN.1 representation from
   [RFC5280] below.  In a X.509 CRL, a signature is encoded with an
   algorithm identifier in the signatureAlgorithm attribute and a
   signatureValue attribute that contains the actual signature.

      CertificateList  ::=  SEQUENCE  {
         tbsCertificate       TBSCertList,
         signatureAlgorithm   AlgorithmIdentifier,
         signatureValue       BIT STRING  }

   The identifiers defined in Section 2 can be used as the
   AlgorithmIdentifier in the signatureAlgorithm field in the sequence
   Certificate/CertificateList and the signature field in the sequence
   TBSCertificate/TBSCertList in certificates CRLs, respectively,
   [RFC5280].  The parameters of these signature algorithms are absent,
   as explained in Section 2.

   The signatureValue field contains the corresponding Dilithium
   signature computed upon the ASN.1 DER encoded tbsCertificate

   Conforming Certification Authority (CA) implementations MUST specify
   the algorithms explicitly by using the OIDs specified in Section 2
   when encoding Dilithium signatures in certificates and CRLs.
   Conforming client implementations that process certificates and CRLs
   using Dilithium MUST recognize the corresponding OIDs.  Encoding
   rules for Dilithium signature values are specified Section 2.

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   When the id-dilithiumTBD identifier appears in the algorithm field as
   an AlgorithmIdentifier, the encoding MUST omit the parameters field.
   That is, the AlgorithmIdentifier SHALL be a SEQUENCE of one
   component, the OID id-dilithiumTBD.

4.  Dilithium Public Keys in PKIX

   In the X.509 certificate, the subjectPublicKeyInfo field has the
   SubjectPublicKeyInfo type, which has the following ASN.1 syntax:

     SubjectPublicKeyInfo  ::=  SEQUENCE  {
         algorithm         AlgorithmIdentifier,
         subjectPublicKey  BIT STRING

   The public parameters for Dilithium are based upon a polynomial ring
   R_q for prime q.  A (k*l) public matrix A is produced, consisting of
   polynomials whose coefficients are sampled uniformly at random from
   the integers modulo q.  This sampling is performed by expanding a
   nonce (rho) using an XOF.

   The Dilithium public key MUST be encoded using the ASN.1 type

     DilithiumPublicKey ::= OCTET STRING

   where DilithiumPublicKey is a concatenation of rho and t1.  Here, rho
   is the nonce used to seed the XOF to produce the matrix A, and t1 is
   a vector encoded in 320*k bytes where k is the rank of the vector
   over the polynomial ring R_q.  These parameters MUST be encoded as a
   single OCTET STRING.  The size required to hold a DilithiumPublicKey
   public key element is therefore 32+320*k bytes.

   The id-dilithiumTBD identifier defined in Section 2 MUST be used as
   the algorithm field in the SubjectPublicKeyInfo sequence [RFC5280] to
   identify a Dilithium public key.

   The intended application for the key is indicated in the keyUsage
   certificate extension; see Section of [RFC5280].  If the
   keyUsage extension is present in a certificate that indicates id-
   dilithiumTBD in the SubjectPublicKeyInfo, then the at least one of
   following MUST be present:

     digitalSignature; or
     nonRepudiation; or
     keyCertSign; or

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   Requirements about the keyUsage extension bits defined in [RFC5280]
   still apply.

   Conforming CA implementations MUST specify the X.509 public key
   algorithm explicitly by using the OIDs specified in Section 2 when
   using Dilithium public keys in certificates and CRLs.  Conforming
   client implementations that process Dilithium public keys when
   processing certificates and CRLs MUST recognize the corresponding

5.  Dilithium Private Keys

   A Dilithium private key is encoded as DilithiumPrivateKey in the
   privateKey field as an OCTET STRING.  Dilithium public keys are
   optionally distributed in the publicKey field of the PrivateKeyInfo

   The ASN.1 encoding for a Dilithium private key is as follows:

     DilithiumPrivateKey ::= SEQUENCE {
         rho         BIT STRING,         - nonce/seed
         K           BIT STRING,         - key/seed
         tr          BIT STRING,         - PRF bytes (CRH in spec.)
         s1          BIT STRING,         - vector l
         s2          BIT STRING,         - vector k
         t0          BIT STRING,         - encoded vector
         PublicKey   IMPLICIT DilithiumPublicKey OPTIONAL

   Dilithium offers both deterministic and randomized signing.  The
   deterministic version creates a signature based on a function of the
   key K and the message, whereas the randomized version instead selects
   these values at random.  The randomized version can be invoked by
   leaving K as EMPTY.

   A fully populated Dilithium private key consists of 6 parameters.
   The size necessary to hold all private key elements is
   32+32+32+32*[(k+l)*ceiling(log(2*eta+1))+13*k] bytes.  The
   description of k, l, and eta as well as public key and secret key
   sizes for security levels 2, 3, and 5 can be found in Figure 1 of the

6.  ASN.1 Module

   This section includes the ASN.1 module for Post-Quantum algorithms in
   X.509.  This module does not come from any previously existing RFC.
   This module references [RFC5912].

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   [ EDNOTE: Add ASN.1 here ]

     PKIX1-PQ-Algorithms { iso(1) identified-organization(3) dod(6)
        internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
        id-mod-pkix1-PQ-algorithms(X) }



     -- EXPORTS ALL;


     -- FROM RFC 5912

     FROM AlgorithmInformation-2009
       { iso(1) identified-organization(3) dod(6) internet(1)
         security(5) mechanisms(5) pkix(7) id-mod(0)
         id-mod-algorithmInformation-02(58) }

     -- Public Key (pk-) Algorithms
     PublicKeys PUBLIC-KEY ::= {
       -- This expands PublicKeys from RFC 5912
       pk-dilithiumTBD |

     -- The hashAlgorithm is mda-shake256
     -- The XOF seed rho is 32 bytes
     -- The vector t1 is 320*k bytes
     -- These are encoded as a single string
     pk-dilithiumTBD PUBLIC-KEY ::= {
       IDENTIFIER id-dilithiumTBD
       KEY DilithiumPublicKey
       PARAMS ARE absent
       CERT-KEY-USAGE { nonRepudiation, digitalSignature,
                       keyCertSign, cRLSign }
       PRIVATE-KEY DilithiumPrivateKey


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7.  IANA Considerations

   Extensions in certificates and CRLs are identified using object
   Identifiers (OIDs).  The creation and delegation of these arcs is to
   be determined.

   IANA is requested to register the id-mod-pkix1-PQ-algorithms OID for
   the ASN.1 module identifier found in Section 5 in the "SMI Security
   for PKIX Module Identifier" registry.

8.  Security Considerations

   The Security Considerations section of [RFC5280] applies to this
   specification as well.

   The digital signature scheme defined within this document are modeled
   under existentially unforgeable digital signatures with respect to an
   adaptive chosen message attack (EUF-CMA).  For the purpose of
   estimating security strength, it has been assumed that the attacker
   has access to signatures for no more than 2^{64} chosen messages.

   EDNOTE: Discuss implications of not hash-then-sign.  Implications in
   performance too.

   Within the hash-then-sign paradigm, hash functions are used as a
   domain restrictor over the message to be signed.  By pre-hashing, the
   onus of resistance to existential forgeries becomes heavily reliant
   on the collision-resistance of the hash function in use.  As well as
   this security goal, the hash-then-sign paradigm also has the ability
   to improve performance by reducing the size of signed messages.  As a
   corollary, hashing remains mandatory even for short messages and
   assigns a further computational requirement onto the verifier.  This
   makes the performance of hash-then-sign schemes more consistent, but
   not necessarily more efficient.  Dilithium diverges from the hash-
   then-sign paradigm by hashing the message during the signing
   procedure (at the point in which the challenge polynomial).  However,
   due to the fact that Dilithium signatures may require the signing
   procedure to be repeated several times for a signature to be
   produced, Dilithium implementations can make use of pre-hashing the
   message to prevent rehashing with each attempt.

   EDNOTE: Discuss side-channels for Dilithium. .

   Dilithium has been designed to provide side-channel resilience by
   eliminating a reliance on Gaussian sampling.  While deliberate design
   decisions such as these can help to deliver a greater ease of secure
   implementation - particularly against side-channel attacks - it does
   not necessarily provide resistance to more powerful attacks such as

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   differential power analysis.  Some amount of side-channel leakage has
   been demonstrated in parts of the signing algorithm (specifically the
   bit-unpacking function), from which a demonstration of key recovery
   has been made over a large sample of signatures.  Masking
   countermeasures exist for Dilithium, but come with a performance

   A fundamental security property also associated with digital
   signatures is non-repudiation.  Non-repudiation refers to the
   assurance that the owner of a signature key pair that was capable of
   generating an existing signature corresponding to certain data cannot
   convincingly deny having signed the data.  The digital signature
   scheme Dilithium possess three security properties beyond
   unforgeability, that are associated with non-repudiation.  These are
   exclusive ownership, message-bound signatures, and non-resignability.
   These properties are based tightly on the assumed collision
   resistance of the hash function used (in this case SHAKE-256).
   Exclusive ownership is a property in which a signature sigma uniquely
   determines the public key and message for which it is valid.
   Message-bound signatures is the property that a valid signature
   uniquely determines the message for which it is valid, but not
   necessarily the public key.  Non-resignability is the property in
   which one cannot produce a valid signature under another key given a
   signature sigma for some unknown message m.  These properties are not
   provided by classical signature schemes such as DSA or ECDSA, and
   have led to a variety of attacks such as Duplicate-Signature Key
   Selection (DSKS) attacks , and attacks on the protocols for secure
   routing.  A full discussion of these properties in Dilithium can be
   found at [CDFFJ21].  These properties are dependent, in part, on
   unambiguous public key serialization.  It for this reason the public
   key structure defined in Section 4 is intentionally encoded as a
   single OCTET STRING.

9.  References

9.1.  Normative References

   [NIST-PQC] National Institute of Standards and Technology (NIST),
              "Post-Quantum Cryptography", 2016,

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,

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   [RFC5280]  Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
              Housley, R., and W. Polk, "Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,

   [RFC5912]  Hoffman, P. and J. Schaad, "New ASN.1 Modules for the
              Public Key Infrastructure Using X.509 (PKIX)", RFC 5912,
              DOI 10.17487/RFC5912, June 2010,

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <>.

9.2.  Informative References

   [CDFFJ21]  Cremers, Cas., Düzlü, S., Fiedler, R., Fischlin, M., and
              C. Janson, "BUFFing signature schemes beyond
              unforgeability and the case of post-quantum signatures",
              In Proceedings of the 42nd IEEE Symposium on Security and
              Privacy, 2021, <>.

              Bai, S., Ducas, L., Lepoint, T., Lyubashevsky, V.,
              Schwabe, P., Seiler, G., and D. Stehlé, "CRYSTALS-
              Dilithium Algorithm Specifications and Supporting
              Documentation", 2021, <https://pq-

              Lyubashevsky, V., "Fiat-Shamir with aborts: Applications
              to lattice and factoring-based signatures", International
              Conference on the Theory and Application of Cryptology and
              Information Security, 2009, <

   [RFC3279]  Bassham, L., Polk, W., and R. Housley, "Algorithms and
              Identifiers for the Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 3279, DOI 10.17487/RFC3279, April
              2002, <>.

   [RFC5480]  Turner, S., Brown, D., Yiu, K., Housley, R., and T. Polk,
              "Elliptic Curve Cryptography Subject Public Key
              Information", RFC 5480, DOI 10.17487/RFC5480, March 2009,

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Appendix A.  Acknowledgements

   We would like to thank ... for their insightful comments.

Appendix B.  Appendix

   Instead of defining the strength of a quantum algorithm in a
   traditional manner using precise estimates of the number of bits of
   security, NIST has instead elected to define a collection of broad
   security strength categories.  Each category is defined by a
   comparatively easy-to-analyze reference primitive that cover a range
   of security strengths offered by existing NIST standards in symmetric
   cryptography, which NIST expects to offer significant resistance to
   quantum cryptanalysis.  These categories describe any attack that
   breaks the relevant security definition that must require
   computational resources comparable to or greater than those required
   for: Level 1 - key search on a block cipher with a 128-bit key (e.g.,
   AES128), Level 2 - collision search on a 256-bit hash function (e.g.,
   SHA256/ SHA3-256), Level 3 - key search on a block cipher with a
   192-bit key (e.g., AES192), Level 4 - collision search on a 384-bit
   hash function (e.g.  SHA384/ SHA3-384), Level 5 - key search on a
   block cipher with a 256-bit key (e.g., AES 256).

   The parameter sets defined for NIST security levels 2, 3 and 5 are
   listed in the Figure 1, along with the resulting public key and
   private key sizes in bytes.

  | Security |  n  |    q    | (k,l) | eta | gamma1 | Public | Private |
  | Level    |     |         |       |     |        | Key(B) | Key(B)  |
  | 2        | 256 | 8380417 | (4,4) |  2  |  2^17  |  1312  |   2528  |
  | 3        | 256 | 8380417 | (6,5) |  4  |  2^19  |  1952  |   4000  |
  | 5        | 256 | 8380417 | (8,7) |  2  |  2^19  |  2596  |   4864  |

                                 Figure 1

Authors' Addresses

   Jake Massimo
   United States of America

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   Panos Kampanakis
   United States of America

   Sean Turner

   Bas Westerbaan

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