COSE M. Prorock Internet-Draft mesur.io Intended status: Standards Track O. Steele Expires: 23 April 2023 Transmute R. Misoczki Google M. Osborne IBM C. Cloostermans NXP 20 October 2022 JOSE and COSE Encoding for Post-Quantum Signatures draft-ietf-cose-post-quantum-signatures-01 Abstract This document describes JSON and CBOR serializations for several Post-Quantum Cryptography (PQC) based suites including CRYSTALS Dilithium, Falcon, and SPHINCS+. This document does not define any new cryptography, only seralizations of existing cryptographic systems. This document registers key types for JOSE and COSE, specifically LWE, NTRU, and HASH. Key types in this document are specified by the cryptographic algorithm family in use by a particular algorithm as discussed in RFC7517. This document registers signature algorithms types for JOSE and COSE, specifically CRYDI3 and others as required for use of various post- quantum signature schemes. 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 https://datatracker.ietf.org/drafts/current/. Prorock, et al. Expires 23 April 2023 [Page 1] Internet-Draft post-quantum-signatures October 2022 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 23 April 2023. Copyright Notice Copyright (c) 2022 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/ license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License. Table of Contents 1. Notational Conventions . . . . . . . . . . . . . . . . . . . 3 2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. CRYSTALS-Dilithium . . . . . . . . . . . . . . . . . . . . . 3 3.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2. Parameters . . . . . . . . . . . . . . . . . . . . . . . 5 3.2.1. Parameter sets . . . . . . . . . . . . . . . . . . . 5 3.3. Core Operations . . . . . . . . . . . . . . . . . . . . . 5 3.4. Using CRYDI with JOSE . . . . . . . . . . . . . . . . . . 5 3.4.1. CRYDI Key Representations . . . . . . . . . . . . . . 6 3.4.2. CRYDI Algorithms . . . . . . . . . . . . . . . . . . 7 3.4.3. CRYDI Signature Representation . . . . . . . . . . . 16 3.5. Using CRYDI with COSE . . . . . . . . . . . . . . . . . . 20 4. Falcon . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . 20 4.2. Core Operations . . . . . . . . . . . . . . . . . . . . . 21 4.3. Using FALCON with JOSE . . . . . . . . . . . . . . . . . 21 4.3.1. FALCON Key Representations . . . . . . . . . . . . . 22 4.3.2. FALCON Algorithms . . . . . . . . . . . . . . . . . . 23 4.4. Using FALCON with COSE . . . . . . . . . . . . . . . . . 24 5. SPHINCS-PLUS . . . . . . . . . . . . . . . . . . . . . . . . 24 5.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . 25 5.2. Core Operations . . . . . . . . . . . . . . . . . . . . . 26 5.3. Using SPHINCS-PLUS with JOSE . . . . . . . . . . . . . . 26 5.3.1. SPHINCS-PLUS Key Representations . . . . . . . . . . 26 5.3.2. SPHINCS-PLUS Algorithms . . . . . . . . . . . . . . . 28 Prorock, et al. Expires 23 April 2023 [Page 2] Internet-Draft post-quantum-signatures October 2022 5.4. Using SPHINCS-PLUS with COSE . . . . . . . . . . . . . . 28 6. Security Considerations . . . . . . . . . . . . . . . . . . . 29 6.1. Falcon specific Security Considerations . . . . . . . . . 30 6.2. Validating public keys . . . . . . . . . . . . . . . . . 30 6.3. Side channel attacks . . . . . . . . . . . . . . . . . . 30 6.4. Randomness considerations . . . . . . . . . . . . . . . . 30 7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 30 8. Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . 34 8.1. Test Vectors . . . . . . . . . . . . . . . . . . . . . . 35 8.1.1. LWE CRYDI5 . . . . . . . . . . . . . . . . . . . . . 35 8.1.2. NTRU FALCON512 . . . . . . . . . . . . . . . . . . . 41 8.1.3. HASH SPHINCS+-SHAKE-256s-robust . . . . . . . . . . . 45 9. Normative References . . . . . . . . . . . . . . . . . . . . 58 10. Informative References . . . . . . . . . . . . . . . . . . . 59 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 59 1. Notational Conventions The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119]. 2. Terminology The following terminology is used throughout this document: PK : The public key for the signature scheme. SK : The secret key for the signature scheme. signature : The digital signature output. message : The input to be signed by the signature scheme. sha256 : The SHA-256 hash function defined in [RFC6234]. shake256 : The SHAKE256 hash function defined in [RFC8702]. 3. CRYSTALS-Dilithium 3.1. Overview This section of the document describes the lattice signature scheme CRYSTALS-Dilithium (CRYDI). The scheme is based on "Fiat-Shamir with Aborts"[Lyu09, Lyu12] utlizing a matrix of polynomials for key material, and a vector of polynomials for signatures. The parameter set is strategically chosen such that the signing algorithm is large enough to maintain zero-knowledge properties but small enough to Prorock, et al. Expires 23 April 2023 [Page 3] Internet-Draft post-quantum-signatures October 2022 prevent forgery of signatures. An example implementation and test vectors are provided. CRYSTALS-Dilithium is a post-quantum approach to digital signatures that is an algorithmic apprach that seeks to ensure key pair and signing properties that is a strong implementation meeting Existential Unforgeability under Chosen Message Attack (EUF-CMA) properties, while ensuring that the security levels reached meet security needs for resistance to both classical and quantum attacks. The algoritm itself is based on hard problems over module lattices, specifically Ring Learning with Errors (Ring-LWE). For all security levels the only operations required are variants of Keccak and number theoretic transforms (NTT) for the ring Zq[X]/(X256+1). This ensures that to increase or decrease the security level involves only the change of parameters rather than re-implementation of a related algorithm. While based on Ring-LWE, CRYSTALS-Dilithium has less algebraic structure than direct Ring-LWE implementations and more closely resembles the unstructured lattices used in Learning with Errors (LWE). This brings a theorectical protection against future algebraic attacks on Ring-LWE that may be developed. CRYSTALS-Dilithium, brings several advantages over other approaches to signature suites: * Post-quantum in nature - use of lattices and other approaches that should remain hard problems even when under attack utilizing quantum approaches * Simple implementation while maintaining security - a danger in many possible approaches to cryptography is that it may be possible inadvertently introduce errors in code that lead to weakness or decreases in security level * Signature and public key size - compared to other post-quantum approaches a reasonable key size has been achieved that also preserves desired security properties * Conservative parameter space - parameterization is utilized for the purposes of defining the sizes of matrices in use, and thereby the number of polynomials described by the key material. * Parameter set adjustment for greater security - increasing this matrix size increases the number of polynomials, and thereby the security level * Performance and optimization - the approach makes use of well known transforms that can be highly optimized, especially with use of hardware optimizations without being so large that it cannot be deployed in embedded or IoT environments without some degree of optimization. Prorock, et al. Expires 23 April 2023 [Page 4] Internet-Draft post-quantum-signatures October 2022 The primary known disadvantage to CRYSTALS-Dilithium is the size of keys and signatures, especially as compared to classical approaches for digital signing. 3.2. Parameters Unlike certain other approaches such as Ed25519 that have a large set of parameters, CRYSTALS-Dilithium uses distinct numbers of paramters to increase or decrease the security level according to the required level for a particular scenario. Under CRYSTALS-Dilithium, the key parameter specification determines the size of the matrix and thereby the number of polynomials that describe the lattice. For use according to this specification we do not recommend a parameter set of less than 3, which should be sufficient to maintain 128 bits of security for all known classical and quantum attacks. Under a parameter set at NIST level 3, a 6x5 matrix is utilized that thereby consists of 30 polynomials. 3.2.1. Parameter sets Parameter sets are identified by the corresponding NIST level per the table below +============+=============+================+ | NIST Level | Matrix Size | memory in bits | +============+=============+================+ | 2 | 4x4 | 97.8 | +------------+-------------+----------------+ | 3 | 6x5 | 138.7 | +------------+-------------+----------------+ | 5 | 8x7 | 187.4 | +------------+-------------+----------------+ Table 1 3.3. Core Operations Core operations used by the signature scheme should be implemented according to the details in [CRYSTALS-Dilithium]. Core operations include key generation, sign, and verify. 3.4. Using CRYDI with JOSE This sections is based on CBOR Object Signing and Encryption (COSE) and JSON Object Signing and Encryption (JOSE) (https://datatracker.ietf.org/doc/html/rfc8812#section-3) Prorock, et al. Expires 23 April 2023 [Page 5] Internet-Draft post-quantum-signatures October 2022 3.4.1. CRYDI Key Representations A new key type (kty) value "LWE" (for keys related to the family of algorithms that utilize Learning With Errors approaches to Post- quantum lattice based cryptography) is defined for public key algorithms that use base 64 encoded strings of the underlying binary material as private and public keys and that support cryptographic sponge functions. It has the following parameters: * The parameter "kty" MUST be "LWE". * The parameter "alg" MUST be specified, and its value MUST be one of the values specified in the table below +========+===================================+ | alg | Description | +========+===================================+ | CRYDI5 | CRYSTALS-Dilithium paramter set 5 | +--------+-----------------------------------+ | CRYDI3 | CRYSTALS-Dilithium paramter set 3 | +--------+-----------------------------------+ | CRYDI2 | CRYSTALS-Dilithium paramter set 2 | +--------+-----------------------------------+ Table 2 * The parameter "pset" MAY be specfied to indicate the not only paramter set in use for the algorithm, but SHOULD also reflect the targeted NIST level for the algorithm in combination with the specified paramter set. For "alg" "CRYDI" one of the described parameter sets "2", "3", or "5" MUST be specified. Parameter set "3" or above SHOULD be used with "CRYDI" for any situation requiring at least 128bits of security against both quantum and classical attacks * The parameter "x" MUST be present and contain the public key encoded using the base64url [RFC4648] encoding. * The parameter "d" MUST be present for private keys and contain the private key encoded using the base64url encoding. This parameter MUST NOT be present for public keys. Sizes of various key and signature material is as follows (for "pset" value "2") Prorock, et al. Expires 23 April 2023 [Page 6] Internet-Draft post-quantum-signatures October 2022 +===========+===============+==============+======+==============+ | Variable | Paramter Name | Paramter Set | Size | base64url | | | | | | encoded size | +===========+===============+==============+======+==============+ | Signature | sig | 2 | 3293 | 4393 | +-----------+---------------+--------------+------+--------------+ | Public | x | 2 | 1952 | 2605 | | Key | | | | | +-----------+---------------+--------------+------+--------------+ | Private | d | 2 | 4000 | 5337 | | Key | | | | | +-----------+---------------+--------------+------+--------------+ Table 3 When calculating JWK Thumbprints [RFC7638], the four public key fields are included in the hash input in lexicographic order: "kty", "alg", and "x". 3.4.2. CRYDI Algorithms In order to reduce the complexity of the key representation and signature representations we register a unique algorithm name per pset. This allows us to omit registering the pset term, and reduced the likelyhood that it will be misused. These alg values are used in both key representations and signatures. +=====+========+==============+ | kty | alg | Paramter Set | +=====+========+==============+ | LWE | CRYDI5 | 5 | +-----+--------+--------------+ | LWE | CRYDI3 | 3 | +-----+--------+--------------+ | LWE | CRYDI2 | 2 | +-----+--------+--------------+ Table 4 3.4.2.1. Public Key Per section 5.1 of [CRYSTALS-Dilithium]: | The public key, containing p and t1, is stored as the | concatenation of the bit-packed representations of p and t1 in | this order. Therefore, it has a size of 32 + 288 kbytes. Prorock, et al. Expires 23 April 2023 [Page 7] Internet-Draft post-quantum-signatures October 2022 The public key is represented as x and encoded using base64url encoding as described in [RFC7517]. Example public key using only required fields: Prorock, et al. Expires 23 April 2023 [Page 8] Internet-Draft post-quantum-signatures October 2022 =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kty": "LWE", "alg": "CRYDI3", "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ zoGXgq43odFFthboEdKNT/enyu+VvUGoIJ6cN8C/1B6o1WlYHEaL0BEIFFbAiAhZ/vnf\ cUYMaVPqsDJuETsjetcE32kGCD7Jkume2tO68DlIhB/2Z2JX8mkcbxFI6KrmXiRxXQj9\ 9LVn1fEzdf3Vfpcs/C3omsFGqmTpLDK+AvW/SWVkDi2NKq7hL/AyxlW2u2cqVErQZUTS\ Z+ic6V8kZfxr3gRMnH0KuF5BtjleZ/yVvqqPjwPOZegCKEl2Gd8duhcUde7CR55pil1o\ UXy5AwgCcZTdEcJn1OPObGoots9T19gw1x4vnZCQUKVDPZuZ1gIkGqDUYXS0lcNTjCMs\ miFEmnOZvB88jxULpb1vl9HoQ3ocM2oZu4AZRt9G/L07Mwcui0uFCWtAIau+2gqNAn/Z\ AS10l0j2N0LLtAaOxoF+Ctzscrt0ZMyGHmoQ9daHkpUvEq0cO8hDtLplnq3lQIIIfROQ\ jcNs9vNKBu87COBjukZD+L8vV4zy8FNO59MCSb9UCLwz2xvfdI1js9/J7hTGaVec8VPx\ md42yPFrGw5Na1oefm8vW49EDmevc8AjAtwDirRBDFv9pX3+5S+M6jhteSLYvpKJXQT1\ zs1379KvIHwkn9VHpA+PiUUw9TgF6xF8xWEGSNlOo1Vn1xtM3givehjYxJ5p5/kBEFZI\ DCyFzstAirJ2GadNhae+P1JFZzJWnX5jaLwzldquZwF3yTzNho4sgBA+fKqiXcgn2nw1\ vz0Dkbxr6cMaUool0eFScU1nAz1Z39W64LtT2nEuYsORx/ht2RzJxxFc21X3nLeEDFCe\ NkNDxQFBSfpZjKKgJtXEx23mp+CbBVMrbagsLnzsAGLYbnroVmATU5Iqr6LgYBpuFs+N\ Rkq7ZXh6CZPukMGQbcOGuNwO6NBuuMNhir5ayGk1ZBiW82C7Nu0hs2pLcgNqWMtt1+LW\ 8R96KyoSc784ZYAZ40QqvoySwmxQPBRTRJ+wB0sVpGBLTxdY9Gw3pXeXN5nao340d2ZA\ 7YEMlqcTHCAv3F8B9ewl7OfQlmg6bvdMuoVdVE+p0er7IAmWMRgviIzYv9sKEEQrCmua\ 2qL5xPSbD05KRf8ZAZ2B8lSCDR1nzXrQXZbXBKJivsCVQDuzxrwGE0gqRMpbk4f5GYCG\ 4i/O8Knoru+jjf6wVQDYKfyz1QUGRlXHkGUGlXfv03r7UbJugycjVO5kbGxhoZkqOq8z\ ZEpkefvrrNoxeotw/z4QpjI8JlY97GDb0mGVHbmdHugjMtVTGhVJFBbPIinmR+emt7O+\ 4qOr7ywRxCvt2lziWtpPBwaf/1XDnN5Gesex1gR1YrcTRNmB808b01sxLQmxcTt4eQ0/\ LUkas7qTJ3AQThOfDdtIpkqsthsBFy+WjSQuoXCYMRcPi6MlpxJndDF32lCnL1ranV6e\ F2ST0SYT+NwNDesMzTRmNbHUW5KAhu0k9WABTvcM5ba0Uq6iOa1NsFrcLag+KhxN6HPn\ oobwJ/EsDi5S7TAl8WrjqIhZ8x6h9eRRXerpaOw/FYk+2MpWByp/98VE12/EwOqAIiPp\ elAvUeMOlRkpG64bJsmyYtHuNWgcv5Qiy7/eGw9ZpvB3J3G3jxvbynExqdFyDc067EKi\ 5WxDFPuZUjkfKpekNvzQuIrqs49BzcRyMt5ndEVE21TPPfZ/R8B7Rxnb2LiK+hQc+cc9\ pEEaWgwAOiMILcp/1CyY6ImdO6RHsxwflMH7gej+hN41kaoEghIOl9kMGTLZbq5Pc8Pz\ 6F2LKTBMJWg9o/0blvilMH9EPblcLeF/bR1AZTUD6ZFdi2TxN6Epn3QVqeG/qPm1EBTF\ Gw1V92m6/08Dd6zI1HPqwKbkHx4F567owofKHaM2imin0yVUpwxoRJrulRHMCB3tn8C4\ ZpFl+sGV3Gip3tKlS7PKQkTqI6DMwxEbdrvtdY1sHZagpclLDisA/yFT4RR2m3VNJR9P\ 6Nx3teqN1eg6RXmD/MlKCdWrlcjZ/6yeIQYwbr9CjItY/tLQX2gtAR1SXOh99UUBVv+Z\ E03VOZ+Ecsc78lSB9G/6n6CFzlbk/HgAF+cu0yMbGnEM8W3mTUspS4JBACwk5w0XWNNQ\ DWVEdgzuLGhPq+hYExDjVZrLELhkH8YgZA+7RXXUZHM/joNOGHUhpUG/bFo3ktnaILCu\ xsOXMUbDC3VcitFFHsGK1svtcERDFxk1HA8pGa59jT0do6n3wEbnBDU1soKNFtpmcVkE\ Ul3XpvuoW3BgCwJzBUCWvPs47DJRgGxO11bSaEYYlhTVaaShcvzgz46AkqO+Q7TjckDP\ /8uzsSQk0AbuhxWFQpSiBP8OZ/U=" } Example public key including optional fields: Prorock, et al. Expires 23 April 2023 [Page 9] Internet-Draft post-quantum-signatures October 2022 =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kid": "key-0", "kty": "LWE", "alg": "CRYDI3", "key_ops": ["verify"], "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ zoGXgq43odFFthboEdKNT/enyu+VvUGoIJ6cN8C/1B6o1WlYHEaL0BEIFFbAiAhZ/vnf\ cUYMaVPqsDJuETsjetcE32kGCD7Jkume2tO68DlIhB/2Z2JX8mkcbxFI6KrmXiRxXQj9\ 9LVn1fEzdf3Vfpcs/C3omsFGqmTpLDK+AvW/SWVkDi2NKq7hL/AyxlW2u2cqVErQZUTS\ Z+ic6V8kZfxr3gRMnH0KuF5BtjleZ/yVvqqPjwPOZegCKEl2Gd8duhcUde7CR55pil1o\ UXy5AwgCcZTdEcJn1OPObGoots9T19gw1x4vnZCQUKVDPZuZ1gIkGqDUYXS0lcNTjCMs\ miFEmnOZvB88jxULpb1vl9HoQ3ocM2oZu4AZRt9G/L07Mwcui0uFCWtAIau+2gqNAn/Z\ AS10l0j2N0LLtAaOxoF+Ctzscrt0ZMyGHmoQ9daHkpUvEq0cO8hDtLplnq3lQIIIfROQ\ jcNs9vNKBu87COBjukZD+L8vV4zy8FNO59MCSb9UCLwz2xvfdI1js9/J7hTGaVec8VPx\ md42yPFrGw5Na1oefm8vW49EDmevc8AjAtwDirRBDFv9pX3+5S+M6jhteSLYvpKJXQT1\ zs1379KvIHwkn9VHpA+PiUUw9TgF6xF8xWEGSNlOo1Vn1xtM3givehjYxJ5p5/kBEFZI\ DCyFzstAirJ2GadNhae+P1JFZzJWnX5jaLwzldquZwF3yTzNho4sgBA+fKqiXcgn2nw1\ vz0Dkbxr6cMaUool0eFScU1nAz1Z39W64LtT2nEuYsORx/ht2RzJxxFc21X3nLeEDFCe\ NkNDxQFBSfpZjKKgJtXEx23mp+CbBVMrbagsLnzsAGLYbnroVmATU5Iqr6LgYBpuFs+N\ Rkq7ZXh6CZPukMGQbcOGuNwO6NBuuMNhir5ayGk1ZBiW82C7Nu0hs2pLcgNqWMtt1+LW\ 8R96KyoSc784ZYAZ40QqvoySwmxQPBRTRJ+wB0sVpGBLTxdY9Gw3pXeXN5nao340d2ZA\ 7YEMlqcTHCAv3F8B9ewl7OfQlmg6bvdMuoVdVE+p0er7IAmWMRgviIzYv9sKEEQrCmua\ 2qL5xPSbD05KRf8ZAZ2B8lSCDR1nzXrQXZbXBKJivsCVQDuzxrwGE0gqRMpbk4f5GYCG\ 4i/O8Knoru+jjf6wVQDYKfyz1QUGRlXHkGUGlXfv03r7UbJugycjVO5kbGxhoZkqOq8z\ ZEpkefvrrNoxeotw/z4QpjI8JlY97GDb0mGVHbmdHugjMtVTGhVJFBbPIinmR+emt7O+\ 4qOr7ywRxCvt2lziWtpPBwaf/1XDnN5Gesex1gR1YrcTRNmB808b01sxLQmxcTt4eQ0/\ LUkas7qTJ3AQThOfDdtIpkqsthsBFy+WjSQuoXCYMRcPi6MlpxJndDF32lCnL1ranV6e\ F2ST0SYT+NwNDesMzTRmNbHUW5KAhu0k9WABTvcM5ba0Uq6iOa1NsFrcLag+KhxN6HPn\ oobwJ/EsDi5S7TAl8WrjqIhZ8x6h9eRRXerpaOw/FYk+2MpWByp/98VE12/EwOqAIiPp\ elAvUeMOlRkpG64bJsmyYtHuNWgcv5Qiy7/eGw9ZpvB3J3G3jxvbynExqdFyDc067EKi\ 5WxDFPuZUjkfKpekNvzQuIrqs49BzcRyMt5ndEVE21TPPfZ/R8B7Rxnb2LiK+hQc+cc9\ pEEaWgwAOiMILcp/1CyY6ImdO6RHsxwflMH7gej+hN41kaoEghIOl9kMGTLZbq5Pc8Pz\ 6F2LKTBMJWg9o/0blvilMH9EPblcLeF/bR1AZTUD6ZFdi2TxN6Epn3QVqeG/qPm1EBTF\ Gw1V92m6/08Dd6zI1HPqwKbkHx4F567owofKHaM2imin0yVUpwxoRJrulRHMCB3tn8C4\ ZpFl+sGV3Gip3tKlS7PKQkTqI6DMwxEbdrvtdY1sHZagpclLDisA/yFT4RR2m3VNJR9P\ 6Nx3teqN1eg6RXmD/MlKCdWrlcjZ/6yeIQYwbr9CjItY/tLQX2gtAR1SXOh99UUBVv+Z\ E03VOZ+Ecsc78lSB9G/6n6CFzlbk/HgAF+cu0yMbGnEM8W3mTUspS4JBACwk5w0XWNNQ\ DWVEdgzuLGhPq+hYExDjVZrLELhkH8YgZA+7RXXUZHM/joNOGHUhpUG/bFo3ktnaILCu\ xsOXMUbDC3VcitFFHsGK1svtcERDFxk1HA8pGa59jT0do6n3wEbnBDU1soKNFtpmcVkE\ Ul3XpvuoW3BgCwJzBUCWvPs47DJRgGxO11bSaEYYlhTVaaShcvzgz46AkqO+Q7TjckDP\ /8uzsSQk0AbuhxWFQpSiBP8OZ/U=" } Prorock, et al. Expires 23 April 2023 [Page 10] Internet-Draft post-quantum-signatures October 2022 3.4.2.2. Private Key Per section 5.1 of [CRYSTALS-Dilithium]: | The secret key contains p,K,tr,s1,s2 and t0 and is also stored as | a bit-packed representation of these quantities in the given | order. Consequently, a secret key requires 64 + 48 + 32((k+l) * | dlog (2n+ 1)e + 14k) bytes. For the weak, medium and high | security level this is equal to 112 + 576k+ 128l bytes. With the | very high security parameters one needs 112 + 544k + 96l = 3856 | bytes. The private key is represented as d and encoded using base64url encoding as described in [RFC7517]. Example private key using only required fields: =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kty": "LWE", "alg": "CRYDI3", "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ zoGXgq43odFFthboEdKNT/enyu+VvUGoIJ6cN8C/1B6o1WlYHEaL0BEIFFbAiAhZ/vnf\ cUYMaVPqsDJuETsjetcE32kGCD7Jkume2tO68DlIhB/2Z2JX8mkcbxFI6KrmXiRxXQj9\ 9LVn1fEzdf3Vfpcs/C3omsFGqmTpLDK+AvW/SWVkDi2NKq7hL/AyxlW2u2cqVErQZUTS\ Z+ic6V8kZfxr3gRMnH0KuF5BtjleZ/yVvqqPjwPOZegCKEl2Gd8duhcUde7CR55pil1o\ UXy5AwgCcZTdEcJn1OPObGoots9T19gw1x4vnZCQUKVDPZuZ1gIkGqDUYXS0lcNTjCMs\ miFEmnOZvB88jxULpb1vl9HoQ3ocM2oZu4AZRt9G/L07Mwcui0uFCWtAIau+2gqNAn/Z\ AS10l0j2N0LLtAaOxoF+Ctzscrt0ZMyGHmoQ9daHkpUvEq0cO8hDtLplnq3lQIIIfROQ\ jcNs9vNKBu87COBjukZD+L8vV4zy8FNO59MCSb9UCLwz2xvfdI1js9/J7hTGaVec8VPx\ md42yPFrGw5Na1oefm8vW49EDmevc8AjAtwDirRBDFv9pX3+5S+M6jhteSLYvpKJXQT1\ zs1379KvIHwkn9VHpA+PiUUw9TgF6xF8xWEGSNlOo1Vn1xtM3givehjYxJ5p5/kBEFZI\ DCyFzstAirJ2GadNhae+P1JFZzJWnX5jaLwzldquZwF3yTzNho4sgBA+fKqiXcgn2nw1\ vz0Dkbxr6cMaUool0eFScU1nAz1Z39W64LtT2nEuYsORx/ht2RzJxxFc21X3nLeEDFCe\ NkNDxQFBSfpZjKKgJtXEx23mp+CbBVMrbagsLnzsAGLYbnroVmATU5Iqr6LgYBpuFs+N\ Rkq7ZXh6CZPukMGQbcOGuNwO6NBuuMNhir5ayGk1ZBiW82C7Nu0hs2pLcgNqWMtt1+LW\ 8R96KyoSc784ZYAZ40QqvoySwmxQPBRTRJ+wB0sVpGBLTxdY9Gw3pXeXN5nao340d2ZA\ 7YEMlqcTHCAv3F8B9ewl7OfQlmg6bvdMuoVdVE+p0er7IAmWMRgviIzYv9sKEEQrCmua\ 2qL5xPSbD05KRf8ZAZ2B8lSCDR1nzXrQXZbXBKJivsCVQDuzxrwGE0gqRMpbk4f5GYCG\ 4i/O8Knoru+jjf6wVQDYKfyz1QUGRlXHkGUGlXfv03r7UbJugycjVO5kbGxhoZkqOq8z\ ZEpkefvrrNoxeotw/z4QpjI8JlY97GDb0mGVHbmdHugjMtVTGhVJFBbPIinmR+emt7O+\ 4qOr7ywRxCvt2lziWtpPBwaf/1XDnN5Gesex1gR1YrcTRNmB808b01sxLQmxcTt4eQ0/\ LUkas7qTJ3AQThOfDdtIpkqsthsBFy+WjSQuoXCYMRcPi6MlpxJndDF32lCnL1ranV6e\ F2ST0SYT+NwNDesMzTRmNbHUW5KAhu0k9WABTvcM5ba0Uq6iOa1NsFrcLag+KhxN6HPn\ Prorock, et al. Expires 23 April 2023 [Page 11] Internet-Draft post-quantum-signatures October 2022 oobwJ/EsDi5S7TAl8WrjqIhZ8x6h9eRRXerpaOw/FYk+2MpWByp/98VE12/EwOqAIiPp\ elAvUeMOlRkpG64bJsmyYtHuNWgcv5Qiy7/eGw9ZpvB3J3G3jxvbynExqdFyDc067EKi\ 5WxDFPuZUjkfKpekNvzQuIrqs49BzcRyMt5ndEVE21TPPfZ/R8B7Rxnb2LiK+hQc+cc9\ pEEaWgwAOiMILcp/1CyY6ImdO6RHsxwflMH7gej+hN41kaoEghIOl9kMGTLZbq5Pc8Pz\ 6F2LKTBMJWg9o/0blvilMH9EPblcLeF/bR1AZTUD6ZFdi2TxN6Epn3QVqeG/qPm1EBTF\ Gw1V92m6/08Dd6zI1HPqwKbkHx4F567owofKHaM2imin0yVUpwxoRJrulRHMCB3tn8C4\ ZpFl+sGV3Gip3tKlS7PKQkTqI6DMwxEbdrvtdY1sHZagpclLDisA/yFT4RR2m3VNJR9P\ 6Nx3teqN1eg6RXmD/MlKCdWrlcjZ/6yeIQYwbr9CjItY/tLQX2gtAR1SXOh99UUBVv+Z\ E03VOZ+Ecsc78lSB9G/6n6CFzlbk/HgAF+cu0yMbGnEM8W3mTUspS4JBACwk5w0XWNNQ\ DWVEdgzuLGhPq+hYExDjVZrLELhkH8YgZA+7RXXUZHM/joNOGHUhpUG/bFo3ktnaILCu\ xsOXMUbDC3VcitFFHsGK1svtcERDFxk1HA8pGa59jT0do6n3wEbnBDU1soKNFtpmcVkE\ Ul3XpvuoW3BgCwJzBUCWvPs47DJRgGxO11bSaEYYlhTVaaShcvzgz46AkqO+Q7TjckDP\ /8uzsSQk0AbuhxWFQpSiBP8OZ/U=", "d": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDUBgL6FklHURz5btM5\ yrI5FQdWk+U2srVuSmfDV7EYG897mUFY35Z0WQ0mZ9XvIOKCh+GFFOk56b5FOFq6xnV8\ UDQnFyY2JREUOHdiUjcUNxA1YxR3QiQ0BkE1AUBmFEOAUHZGBzQAU2dxVIgTQRV3U3g4\ GGiISEYQhHRSWDIBQ2Z3UIIWdSV1EWhwBTYiWGI3VmJVI1UIU2REdUhHBoJ2gRhFUThy\ BSQnhBIGI1AoMVB2MCNhUXQiNUGCKHgzUmQxU3dEgBhmQyIQgmFjdxY1dCJgGBSEB4Ij\ CEJ0MBGIQWRRN3QjRmRSQWQIJgNjcjdnMlJhJIU1MlJRd1NmF4dwhHIIdEYYcAhEclBQ\ JjESAiBwBQYzYlAIIocBcoZFcGVkA2SDMCVTBjgzCAAzNnQGYHI1VwJzYxQRckBIZBV4\ VxZmZiVlYXgHFRNjdEFIYVOFIVdhcnIINEhhIURjg0cxJ0SCIWYUUVcHJzdDUTASciAW\ UiJAglIoQkIwNjMlcwACZxcHZVJAh4EnNnWAZVVoBjNnNEcicTdyEEUHBVFjETETNjd0\ YUFmFDVXNUcHFVJoE2AlVwFhMzc0dQckMYJUaBJ0JkUBdyd1AnZiJ3hYYkWAgyR1VziD\ BERVh1NQAFIGWIhUZXCEQxIThyR1FIGGNTKAcwdRNBGDYEd2RVEwUDMzWAAhNQEEMYAS\ hUSCgTJ3VIdXUlFBFxFkhVCCZEABJjQCAxFGNkhHQzM1YSSHNlEBEmJkgWZCVwZHRSVD\ GDZzRCQiNhE3IghDhSFoBYCHNFVHMxZAZTSGAVMUQkhBKIFRQEVBB0cHNGEiJVVScQQh\ hzQiBzKBYRY4Q0R2MVUldwVCIkQYEEgFYEREY2NERyFVdHJzdAZHBmhmdSCFIgh1IwGB\ AxNzFjEoUWFCF4AhZRJSEROEEThxAGYBJTgUcUdFJBOFRmcVYnZUUFCAY1AnZEZBVThS\ ECBQYBNGeAdzQ3KGhIE3ZiFxQoVCgQBjEFdFcIV0IAaFcgI0iAgAUVQAhEInQWECY1I4\ E2U0MkAXQSZkdSRRc2I4BjEiSGd4hgQEEDcTRmhFd3MBMmY2gERxNwiISAVkFVETGCcI\ gYhzRXByGBgzKGVXJUhoGEY1hgFmZWgmEWYWVoISd4Vlhid4VUMHgSZXhXUSaCgmJ3Eg\ MQIzIDIThwRSARQhBFB2QQBjEgIoEHN1BhMCiIIBUlZWCHdBMyZFQoQ2UUJXJCFnZyFD\ RTFUUTQoQmUjB0aHJXJHeDZlJGBCExATEUEDg3BTAChWImN0AWcFB3IUgBEARxVUREdX\ QzhVBEBBF4UgcRhCg4gUcoRkdYCAIUQBRUJUYjFjEBYUhSBjIyV2cXBYckEiMic1N4ED\ gDUGVSCHhCYURXcQB1ODg4hDJFJ3Jld2gyYnQYclRjE3VWcQNXJBYnOGhYFoU2dHATAw\ OEeBUGQjJHcDgUJTRXBXJ3IAEjEXhXeEEmghIAAGdjUVBndnI2FCAVcyV4cxIyZ2dYE1\ ZEiHcYJYaCcXQXJCaER1coIDRWJkcSNhEVF3JGOCQkYWYkcndRA1QTh0MFgzIyVocYJY\ cwIAFRNiE1VAUECBI3MzQiZkUhR1cid1NSAXFXN0gUNnRCV0ISNmYnB3NIZyMIQWEVVz\ ElEohnQyKBNoY1cCdmdjVYiGhVUlA0CHMTZIURBgR4aIJwJQJlIDMYhwNGNwiGcIBUdA\ NXMBETUgICJyMkMIN1BAIAB4gEMDUwhndFJkQDEgRRMld4EzhRM0ZhGAYHMgZ4NhEEhn\ U2I2VicBBXZUFUNoczcmBzBnUEBxUWcDg4RHUXZSOEZogABHRAISVEAzdoQhRmBgEWYE\ Z4U1dgQ2gjgQUjMScgIIFQR3YFczhTYoB1IiVCYGBAVmVAFIdhRmZ1InhwdTRjJjNhVx\ IzcWgjFlFCaChlIWUySIaDFwAWV3RAIxg2QWYgAYMUjP7wmwOwPp7Ukl3L1KalY/6dN4\ dBr1AYS8JnkVq6pPeBfO7ccX95SrVfAO7EX7RVEYyhVR9QOQyEpLBUMcfcfnHCZWKM0o\ OBF7BXiWMR9BQo4ybtpJGKQ+IZyCKUJVRhZ+uae182qYcBKFMdOOzXiO8kAa98eUy6SR\ pPfKPD6D+xXgtJ0FWtYnp1Jy2aIG3HqMiTHoSdVIvccGkf94gpVWTMeJQsQpgq7dAJiJ\ 5JOMQjk7JIHcIzxb4T8sQHzA55MFfvM7Hus/8FUX7NfIN1JRmc2zHL/7kdfCFSwG67iW\ U4ob2kTwdKzPvOL+d3e+AOE0PihJ4vVJAOjhWmO2fIFNvFhNqPh0MSiSkatPGbSVdqQ1\ Prorock, et al. Expires 23 April 2023 [Page 12] Internet-Draft post-quantum-signatures October 2022 PsG6C+1YqMrTM7KFr4hTQM8a3+tAOsImMjXSSPDkVeuJFq1rw642SJJx8yZTXVe8g75D\ ZTYghbeX5LLzaVkt9mZS7cW16Zy+C3MwnWDrGQ6hUDxYaYJp7SOGJHepcmVV214oD6nw\ 5QprgpGIxVcdXQUO0fhKwerYDkoOIj+uqk7NYDvOt8zANphYcE3v+6yVFyYh3eg7DYRJ\ rIzIcbaG91ySv2iRRC+cWaymH6xuqaHRwZu/p962/u8/c3rITJzCoVc+ObnZ5oItZFBe\ AYFhLBx7PvPdBULXyCqmtkOtnT/jnaCUVxtGeaIeQmmeM4yPq3d5uWBfOvIyuPmfBSKd\ Y0NETGlsaoQuqFpOkCmQdMVZKh3UZ8AOjw22LlqaZlrUf0akb0fs7le2HT47KV9yOJHC\ tec9tjHUeBVmma5O4AofGcVXLbkqKv+Soax9GooHVOv+uxa8iwjAdTZKtqwKnKDx4jaR\ +zotCsYi4BuB2JbkjnHG6NL7ubN+aNKnwnzZnMKQZIh2Q7vSRYKTM8j9OGLq7IP8q2NS\ oc7iT//eAvb4oF6LaY7qebxQ6ROXCSRrrXgpo+pw3ltfuUCuGzAxD4+wMZU3dlXsivhJ\ PnTEjI/V6GmkRlfZ9XnYfj8SILETWk03dMFJh3LmUwkbRV+C3mL2GzjgQVTkvP82KDBL\ DAR9iKyPkJnMnK9Ix/StVyJbGAtGp4jHnp+PSjz9ja4qI9jVRjGgIUQhw0DnI0fnplUn\ Qhz3F9MQXMPLSPvFw8M0xkUKsAcxQvxZGb5LkYByZ0ZrO/ipphwnE6zQuOva+8uTyBX/\ B9VR24tUItvlhy7SS6JrULrvTA+D/ZCiqKRx61iF6pU3BoC8fgA9D/AifiQnPz0SI5kx\ FJfDTz1LWMjUlQKBHFvRFLE9eFD0rnwAGx7Pgpyc/KrLqVmcmj/96TYtoedp/iW4asfY\ C2vs+GVyxVoumIdFPHJpencWbE/niZnVDaJCih1iqgXzDsI8bENh2B9cutDWX+bsHZSC\ jSQb9YkGN+MoNiJlXmQHSJDyfPhzWPibdS/lpS90ppPWIY+PpLOfzDSGFFWswQ4q5Phc\ pLWHx5lw9KSye+T86p6kadnBBTLTyfn0dG7NpO9QKQObMN60MnybkVGx5nH9yLJlFlmV\ 0H+K0VZIKm4UzYV+RYfqqXYtMqTQxeQ1U7L7o0H+6viErxuKj5rS3i+r1rdfECAGgCoq\ 0mixATHISAHi2eSV5fk3r5xMkKSwwPIRuMt50+kklRPUoLohTj7G1CnL6O2xwBdQMTUx\ 4Jq5JBWnfB+U4D9n0si1DwikIhpaUyOoBeaWo4iFQiWVLwjeeQvY6zj66l7OXsPHjZXg\ uCitsWfp5MYV3cLTkb80uCM/xhp4Y0Edobt6x3k1FD8vbh8g3YAG0Xe/U+Iz3klnpCt2\ ROQ2lGQa0JMl4nbQr3tqTLoXv4szaErfP/Xw05Cnt9DsBzN5DNrmfF6EDcfVf/hn8v9a\ wrg6Rfv8Jpys1YFpwLanhb3Wz+x1yaDsa54IdlFOFnyBxv8GppbFrMpVFx/nLAXGIocc\ WjcRKs0tBJUW/IoXeKOMPUd1wHR4dqUCEXsoexHJiNe5sH+akr6UIDObF70hhupBoiY9\ AzVXi5zXf2VdafyQrkGfKz4BEUkiqcaajHr1CF9ZJ+Mjdmfr3z0xyCmCAWir5ZLOBXDj\ T7sYCV3QjCz4a2mGvee9IxC9kSLapCq90UMAxnTLjJGQM/dlpgjDsjsCZX5wKdsnMs79\ 60Z75BGDOC1dDINj4f5kHZmwwcmw/04mi/1RPBUABXse3Up3eJQOX2haZPqmY0+2PZTF\ exku9pETHtKcfSdRe1oJLmlB34JSogRmNp1eBxakcIL09huiFVtGVZng/pC/ryoJ/T9q\ 9w4aV5H+4u2dHc29Vb77SasxCdRH0sDaLaPpesRXsrdJwjbizOgzRlIx+83oO7NuhE+C\ kKfO7cZMrFm8r8g1MlzDiFrTf3RTusMtiW6CVlVuTROPZFngqaR5yeYPprpSELtQHSwz\ U5AaY5Qd8tbky5ec+2/QkXO+cdyWhQUuBRpibwpRpD3x1yTgT4E91cwTFpvSLk54ZHf+\ D3EsZf0PYMN6d4jVdh9iv+0tCebnfMqP65wY26YBopSLtCXXb1anUlRPlzPzRq99yKnt\ FM7gK1XnBAZoZBBqCyZw9OHWmttIFWcml4Wd5BxF9uZh2Y8gtcN8UKWHv43tsNBa7j/T\ ikIBSkIVI/6EQvyPW4YTdyz2V8RKHN5XcdpdWFaVhgSJMC4I6Bm0Lwenhkmal7Sd247q\ uCtEow8qh+w7Jk4SxrmvJxd5sBnvz15OKEaHPeWNNJW00bWEDT+0ZzzD8vMN1/GkbbB3\ s7UfcJXZbRu7HtQ+wHIblBKVstX3hMonra+k6wS9KPhcAaC3IjZ7ZApSedKk1sW1SuDg\ l48YW2/cyS3LvmISQn9KPWK7yEpNQnV0vurn3ZFOGO0eDjSXUjI+xIrRia5GQ1yb31ma\ nJnf2PdHcMmVr0wu4lMGno7a14nMRdnXkBU8bVOp8wF6Toz59hBJ3a/F+mP4/a19Ixra\ wiVVeEPgoi9QQ9NcLgQEFCoskA+EpcLK0FxV2rYI9JFNF/nDxP5nmGtnkmlFaLo+pleH\ CJYS0OTGKQr6X+Y65NOllx5nNwsnWkIUkCodoSt4Givdoe/S9JNIu8tW+jTBae2hNr9c\ glErCNKDYe1+T+Ldyr9rfOKm9LKNyTBsodgF4KI/hFh9Iv/i55DTWtqjpN0eQnPTB3/6\ +7KzTfSE9il5UMcP3zKKC2mAQvtyYxF3k0m24ZTwPs2LAPJkr/xtPH3BnGE/UfUDmvDS\ TBp9m049Nh9oDZvI4HKsY8auiyENk0ys67F9GTHhOYM0FgHyP5qk4/IR5YC3lnq7xx6i\ owebEJAy63htMytq+xd3cJyZR0lWBUOqvSpd/A==" } Example private key using optional fields: Prorock, et al. Expires 23 April 2023 [Page 13] Internet-Draft post-quantum-signatures October 2022 =============== NOTE: '\' line wrapping per RFC 8792 ================ { "kid": "key-0", "kty": "LWE", "alg": "CRYDI3", "key_ops": ["sign"], "x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\ 5zDn77zTgrIskM3WX8bqslc+B1fq12iA/wxD2jc1d6j+YjKCtkGH26OR7vc0YC2ZiMzW\ zGl7yebt7JkmjRbN1N+u/2fAKFLuziMcLNP6WLoWbMqxoC2XOOVNAWX3QjXrCcGU23Nr\ imtdmWz5NrP43E592Sctt5M+SVlfgQeYv8pHmtkQknE8/jr7TrgNpuiV7nXmhWHTMJ4I\ zoGXgq43odFFthboEdKNT/enyu+VvUGoIJ6cN8C/1B6o1WlYHEaL0BEIFFbAiAhZ/vnf\ cUYMaVPqsDJuETsjetcE32kGCD7Jkume2tO68DlIhB/2Z2JX8mkcbxFI6KrmXiRxXQj9\ 9LVn1fEzdf3Vfpcs/C3omsFGqmTpLDK+AvW/SWVkDi2NKq7hL/AyxlW2u2cqVErQZUTS\ Z+ic6V8kZfxr3gRMnH0KuF5BtjleZ/yVvqqPjwPOZegCKEl2Gd8duhcUde7CR55pil1o\ UXy5AwgCcZTdEcJn1OPObGoots9T19gw1x4vnZCQUKVDPZuZ1gIkGqDUYXS0lcNTjCMs\ miFEmnOZvB88jxULpb1vl9HoQ3ocM2oZu4AZRt9G/L07Mwcui0uFCWtAIau+2gqNAn/Z\ AS10l0j2N0LLtAaOxoF+Ctzscrt0ZMyGHmoQ9daHkpUvEq0cO8hDtLplnq3lQIIIfROQ\ jcNs9vNKBu87COBjukZD+L8vV4zy8FNO59MCSb9UCLwz2xvfdI1js9/J7hTGaVec8VPx\ md42yPFrGw5Na1oefm8vW49EDmevc8AjAtwDirRBDFv9pX3+5S+M6jhteSLYvpKJXQT1\ zs1379KvIHwkn9VHpA+PiUUw9TgF6xF8xWEGSNlOo1Vn1xtM3givehjYxJ5p5/kBEFZI\ DCyFzstAirJ2GadNhae+P1JFZzJWnX5jaLwzldquZwF3yTzNho4sgBA+fKqiXcgn2nw1\ vz0Dkbxr6cMaUool0eFScU1nAz1Z39W64LtT2nEuYsORx/ht2RzJxxFc21X3nLeEDFCe\ NkNDxQFBSfpZjKKgJtXEx23mp+CbBVMrbagsLnzsAGLYbnroVmATU5Iqr6LgYBpuFs+N\ Rkq7ZXh6CZPukMGQbcOGuNwO6NBuuMNhir5ayGk1ZBiW82C7Nu0hs2pLcgNqWMtt1+LW\ 8R96KyoSc784ZYAZ40QqvoySwmxQPBRTRJ+wB0sVpGBLTxdY9Gw3pXeXN5nao340d2ZA\ 7YEMlqcTHCAv3F8B9ewl7OfQlmg6bvdMuoVdVE+p0er7IAmWMRgviIzYv9sKEEQrCmua\ 2qL5xPSbD05KRf8ZAZ2B8lSCDR1nzXrQXZbXBKJivsCVQDuzxrwGE0gqRMpbk4f5GYCG\ 4i/O8Knoru+jjf6wVQDYKfyz1QUGRlXHkGUGlXfv03r7UbJugycjVO5kbGxhoZkqOq8z\ ZEpkefvrrNoxeotw/z4QpjI8JlY97GDb0mGVHbmdHugjMtVTGhVJFBbPIinmR+emt7O+\ 4qOr7ywRxCvt2lziWtpPBwaf/1XDnN5Gesex1gR1YrcTRNmB808b01sxLQmxcTt4eQ0/\ LUkas7qTJ3AQThOfDdtIpkqsthsBFy+WjSQuoXCYMRcPi6MlpxJndDF32lCnL1ranV6e\ F2ST0SYT+NwNDesMzTRmNbHUW5KAhu0k9WABTvcM5ba0Uq6iOa1NsFrcLag+KhxN6HPn\ oobwJ/EsDi5S7TAl8WrjqIhZ8x6h9eRRXerpaOw/FYk+2MpWByp/98VE12/EwOqAIiPp\ elAvUeMOlRkpG64bJsmyYtHuNWgcv5Qiy7/eGw9ZpvB3J3G3jxvbynExqdFyDc067EKi\ 5WxDFPuZUjkfKpekNvzQuIrqs49BzcRyMt5ndEVE21TPPfZ/R8B7Rxnb2LiK+hQc+cc9\ pEEaWgwAOiMILcp/1CyY6ImdO6RHsxwflMH7gej+hN41kaoEghIOl9kMGTLZbq5Pc8Pz\ 6F2LKTBMJWg9o/0blvilMH9EPblcLeF/bR1AZTUD6ZFdi2TxN6Epn3QVqeG/qPm1EBTF\ Gw1V92m6/08Dd6zI1HPqwKbkHx4F567owofKHaM2imin0yVUpwxoRJrulRHMCB3tn8C4\ ZpFl+sGV3Gip3tKlS7PKQkTqI6DMwxEbdrvtdY1sHZagpclLDisA/yFT4RR2m3VNJR9P\ 6Nx3teqN1eg6RXmD/MlKCdWrlcjZ/6yeIQYwbr9CjItY/tLQX2gtAR1SXOh99UUBVv+Z\ E03VOZ+Ecsc78lSB9G/6n6CFzlbk/HgAF+cu0yMbGnEM8W3mTUspS4JBACwk5w0XWNNQ\ DWVEdgzuLGhPq+hYExDjVZrLELhkH8YgZA+7RXXUZHM/joNOGHUhpUG/bFo3ktnaILCu\ xsOXMUbDC3VcitFFHsGK1svtcERDFxk1HA8pGa59jT0do6n3wEbnBDU1soKNFtpmcVkE\ Ul3XpvuoW3BgCwJzBUCWvPs47DJRgGxO11bSaEYYlhTVaaShcvzgz46AkqO+Q7TjckDP\ /8uzsSQk0AbuhxWFQpSiBP8OZ/U=", "d": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDUBgL6FklHURz5btM5\ yrI5FQdWk+U2srVuSmfDV7EYG897mUFY35Z0WQ0mZ9XvIOKCh+GFFOk56b5FOFq6xnV8\ Prorock, et al. Expires 23 April 2023 [Page 14] Internet-Draft post-quantum-signatures October 2022 UDQnFyY2JREUOHdiUjcUNxA1YxR3QiQ0BkE1AUBmFEOAUHZGBzQAU2dxVIgTQRV3U3g4\ GGiISEYQhHRSWDIBQ2Z3UIIWdSV1EWhwBTYiWGI3VmJVI1UIU2REdUhHBoJ2gRhFUThy\ BSQnhBIGI1AoMVB2MCNhUXQiNUGCKHgzUmQxU3dEgBhmQyIQgmFjdxY1dCJgGBSEB4Ij\ CEJ0MBGIQWRRN3QjRmRSQWQIJgNjcjdnMlJhJIU1MlJRd1NmF4dwhHIIdEYYcAhEclBQ\ JjESAiBwBQYzYlAIIocBcoZFcGVkA2SDMCVTBjgzCAAzNnQGYHI1VwJzYxQRckBIZBV4\ VxZmZiVlYXgHFRNjdEFIYVOFIVdhcnIINEhhIURjg0cxJ0SCIWYUUVcHJzdDUTASciAW\ UiJAglIoQkIwNjMlcwACZxcHZVJAh4EnNnWAZVVoBjNnNEcicTdyEEUHBVFjETETNjd0\ YUFmFDVXNUcHFVJoE2AlVwFhMzc0dQckMYJUaBJ0JkUBdyd1AnZiJ3hYYkWAgyR1VziD\ BERVh1NQAFIGWIhUZXCEQxIThyR1FIGGNTKAcwdRNBGDYEd2RVEwUDMzWAAhNQEEMYAS\ hUSCgTJ3VIdXUlFBFxFkhVCCZEABJjQCAxFGNkhHQzM1YSSHNlEBEmJkgWZCVwZHRSVD\ GDZzRCQiNhE3IghDhSFoBYCHNFVHMxZAZTSGAVMUQkhBKIFRQEVBB0cHNGEiJVVScQQh\ hzQiBzKBYRY4Q0R2MVUldwVCIkQYEEgFYEREY2NERyFVdHJzdAZHBmhmdSCFIgh1IwGB\ AxNzFjEoUWFCF4AhZRJSEROEEThxAGYBJTgUcUdFJBOFRmcVYnZUUFCAY1AnZEZBVThS\ ECBQYBNGeAdzQ3KGhIE3ZiFxQoVCgQBjEFdFcIV0IAaFcgI0iAgAUVQAhEInQWECY1I4\ E2U0MkAXQSZkdSRRc2I4BjEiSGd4hgQEEDcTRmhFd3MBMmY2gERxNwiISAVkFVETGCcI\ gYhzRXByGBgzKGVXJUhoGEY1hgFmZWgmEWYWVoISd4Vlhid4VUMHgSZXhXUSaCgmJ3Eg\ MQIzIDIThwRSARQhBFB2QQBjEgIoEHN1BhMCiIIBUlZWCHdBMyZFQoQ2UUJXJCFnZyFD\ RTFUUTQoQmUjB0aHJXJHeDZlJGBCExATEUEDg3BTAChWImN0AWcFB3IUgBEARxVUREdX\ QzhVBEBBF4UgcRhCg4gUcoRkdYCAIUQBRUJUYjFjEBYUhSBjIyV2cXBYckEiMic1N4ED\ gDUGVSCHhCYURXcQB1ODg4hDJFJ3Jld2gyYnQYclRjE3VWcQNXJBYnOGhYFoU2dHATAw\ OEeBUGQjJHcDgUJTRXBXJ3IAEjEXhXeEEmghIAAGdjUVBndnI2FCAVcyV4cxIyZ2dYE1\ ZEiHcYJYaCcXQXJCaER1coIDRWJkcSNhEVF3JGOCQkYWYkcndRA1QTh0MFgzIyVocYJY\ cwIAFRNiE1VAUECBI3MzQiZkUhR1cid1NSAXFXN0gUNnRCV0ISNmYnB3NIZyMIQWEVVz\ ElEohnQyKBNoY1cCdmdjVYiGhVUlA0CHMTZIURBgR4aIJwJQJlIDMYhwNGNwiGcIBUdA\ NXMBETUgICJyMkMIN1BAIAB4gEMDUwhndFJkQDEgRRMld4EzhRM0ZhGAYHMgZ4NhEEhn\ U2I2VicBBXZUFUNoczcmBzBnUEBxUWcDg4RHUXZSOEZogABHRAISVEAzdoQhRmBgEWYE\ Z4U1dgQ2gjgQUjMScgIIFQR3YFczhTYoB1IiVCYGBAVmVAFIdhRmZ1InhwdTRjJjNhVx\ IzcWgjFlFCaChlIWUySIaDFwAWV3RAIxg2QWYgAYMUjP7wmwOwPp7Ukl3L1KalY/6dN4\ dBr1AYS8JnkVq6pPeBfO7ccX95SrVfAO7EX7RVEYyhVR9QOQyEpLBUMcfcfnHCZWKM0o\ OBF7BXiWMR9BQo4ybtpJGKQ+IZyCKUJVRhZ+uae182qYcBKFMdOOzXiO8kAa98eUy6SR\ pPfKPD6D+xXgtJ0FWtYnp1Jy2aIG3HqMiTHoSdVIvccGkf94gpVWTMeJQsQpgq7dAJiJ\ 5JOMQjk7JIHcIzxb4T8sQHzA55MFfvM7Hus/8FUX7NfIN1JRmc2zHL/7kdfCFSwG67iW\ U4ob2kTwdKzPvOL+d3e+AOE0PihJ4vVJAOjhWmO2fIFNvFhNqPh0MSiSkatPGbSVdqQ1\ PsG6C+1YqMrTM7KFr4hTQM8a3+tAOsImMjXSSPDkVeuJFq1rw642SJJx8yZTXVe8g75D\ ZTYghbeX5LLzaVkt9mZS7cW16Zy+C3MwnWDrGQ6hUDxYaYJp7SOGJHepcmVV214oD6nw\ 5QprgpGIxVcdXQUO0fhKwerYDkoOIj+uqk7NYDvOt8zANphYcE3v+6yVFyYh3eg7DYRJ\ rIzIcbaG91ySv2iRRC+cWaymH6xuqaHRwZu/p962/u8/c3rITJzCoVc+ObnZ5oItZFBe\ AYFhLBx7PvPdBULXyCqmtkOtnT/jnaCUVxtGeaIeQmmeM4yPq3d5uWBfOvIyuPmfBSKd\ Y0NETGlsaoQuqFpOkCmQdMVZKh3UZ8AOjw22LlqaZlrUf0akb0fs7le2HT47KV9yOJHC\ tec9tjHUeBVmma5O4AofGcVXLbkqKv+Soax9GooHVOv+uxa8iwjAdTZKtqwKnKDx4jaR\ +zotCsYi4BuB2JbkjnHG6NL7ubN+aNKnwnzZnMKQZIh2Q7vSRYKTM8j9OGLq7IP8q2NS\ oc7iT//eAvb4oF6LaY7qebxQ6ROXCSRrrXgpo+pw3ltfuUCuGzAxD4+wMZU3dlXsivhJ\ PnTEjI/V6GmkRlfZ9XnYfj8SILETWk03dMFJh3LmUwkbRV+C3mL2GzjgQVTkvP82KDBL\ DAR9iKyPkJnMnK9Ix/StVyJbGAtGp4jHnp+PSjz9ja4qI9jVRjGgIUQhw0DnI0fnplUn\ Qhz3F9MQXMPLSPvFw8M0xkUKsAcxQvxZGb5LkYByZ0ZrO/ipphwnE6zQuOva+8uTyBX/\ B9VR24tUItvlhy7SS6JrULrvTA+D/ZCiqKRx61iF6pU3BoC8fgA9D/AifiQnPz0SI5kx\ FJfDTz1LWMjUlQKBHFvRFLE9eFD0rnwAGx7Pgpyc/KrLqVmcmj/96TYtoedp/iW4asfY\ C2vs+GVyxVoumIdFPHJpencWbE/niZnVDaJCih1iqgXzDsI8bENh2B9cutDWX+bsHZSC\ Prorock, et al. Expires 23 April 2023 [Page 15] Internet-Draft post-quantum-signatures October 2022 jSQb9YkGN+MoNiJlXmQHSJDyfPhzWPibdS/lpS90ppPWIY+PpLOfzDSGFFWswQ4q5Phc\ pLWHx5lw9KSye+T86p6kadnBBTLTyfn0dG7NpO9QKQObMN60MnybkVGx5nH9yLJlFlmV\ 0H+K0VZIKm4UzYV+RYfqqXYtMqTQxeQ1U7L7o0H+6viErxuKj5rS3i+r1rdfECAGgCoq\ 0mixATHISAHi2eSV5fk3r5xMkKSwwPIRuMt50+kklRPUoLohTj7G1CnL6O2xwBdQMTUx\ 4Jq5JBWnfB+U4D9n0si1DwikIhpaUyOoBeaWo4iFQiWVLwjeeQvY6zj66l7OXsPHjZXg\ uCitsWfp5MYV3cLTkb80uCM/xhp4Y0Edobt6x3k1FD8vbh8g3YAG0Xe/U+Iz3klnpCt2\ ROQ2lGQa0JMl4nbQr3tqTLoXv4szaErfP/Xw05Cnt9DsBzN5DNrmfF6EDcfVf/hn8v9a\ wrg6Rfv8Jpys1YFpwLanhb3Wz+x1yaDsa54IdlFOFnyBxv8GppbFrMpVFx/nLAXGIocc\ WjcRKs0tBJUW/IoXeKOMPUd1wHR4dqUCEXsoexHJiNe5sH+akr6UIDObF70hhupBoiY9\ AzVXi5zXf2VdafyQrkGfKz4BEUkiqcaajHr1CF9ZJ+Mjdmfr3z0xyCmCAWir5ZLOBXDj\ T7sYCV3QjCz4a2mGvee9IxC9kSLapCq90UMAxnTLjJGQM/dlpgjDsjsCZX5wKdsnMs79\ 60Z75BGDOC1dDINj4f5kHZmwwcmw/04mi/1RPBUABXse3Up3eJQOX2haZPqmY0+2PZTF\ exku9pETHtKcfSdRe1oJLmlB34JSogRmNp1eBxakcIL09huiFVtGVZng/pC/ryoJ/T9q\ 9w4aV5H+4u2dHc29Vb77SasxCdRH0sDaLaPpesRXsrdJwjbizOgzRlIx+83oO7NuhE+C\ kKfO7cZMrFm8r8g1MlzDiFrTf3RTusMtiW6CVlVuTROPZFngqaR5yeYPprpSELtQHSwz\ U5AaY5Qd8tbky5ec+2/QkXO+cdyWhQUuBRpibwpRpD3x1yTgT4E91cwTFpvSLk54ZHf+\ D3EsZf0PYMN6d4jVdh9iv+0tCebnfMqP65wY26YBopSLtCXXb1anUlRPlzPzRq99yKnt\ FM7gK1XnBAZoZBBqCyZw9OHWmttIFWcml4Wd5BxF9uZh2Y8gtcN8UKWHv43tsNBa7j/T\ ikIBSkIVI/6EQvyPW4YTdyz2V8RKHN5XcdpdWFaVhgSJMC4I6Bm0Lwenhkmal7Sd247q\ uCtEow8qh+w7Jk4SxrmvJxd5sBnvz15OKEaHPeWNNJW00bWEDT+0ZzzD8vMN1/GkbbB3\ s7UfcJXZbRu7HtQ+wHIblBKVstX3hMonra+k6wS9KPhcAaC3IjZ7ZApSedKk1sW1SuDg\ l48YW2/cyS3LvmISQn9KPWK7yEpNQnV0vurn3ZFOGO0eDjSXUjI+xIrRia5GQ1yb31ma\ nJnf2PdHcMmVr0wu4lMGno7a14nMRdnXkBU8bVOp8wF6Toz59hBJ3a/F+mP4/a19Ixra\ wiVVeEPgoi9QQ9NcLgQEFCoskA+EpcLK0FxV2rYI9JFNF/nDxP5nmGtnkmlFaLo+pleH\ CJYS0OTGKQr6X+Y65NOllx5nNwsnWkIUkCodoSt4Givdoe/S9JNIu8tW+jTBae2hNr9c\ glErCNKDYe1+T+Ldyr9rfOKm9LKNyTBsodgF4KI/hFh9Iv/i55DTWtqjpN0eQnPTB3/6\ +7KzTfSE9il5UMcP3zKKC2mAQvtyYxF3k0m24ZTwPs2LAPJkr/xtPH3BnGE/UfUDmvDS\ TBp9m049Nh9oDZvI4HKsY8auiyENk0ys67F9GTHhOYM0FgHyP5qk4/IR5YC3lnq7xx6i\ owebEJAy63htMytq+xd3cJyZR0lWBUOqvSpd/A==" } 3.4.3. CRYDI Signature Representation For the purpose of using the CRYSTALS-Dilithium Signature Algorithm (CRYDI) for signing data using "JSON Web Signature (JWS)" [RFC7515], algorithm "CRYDI" is defined here, to be applied as the value of the "alg" parameter. The following key subtypes are defined here for use with CRYDI: Prorock, et al. Expires 23 April 2023 [Page 16] Internet-Draft post-quantum-signatures October 2022 +============+====================+ | "paramter" | CRYDI Paramter Set | +============+====================+ | 5 | CRYDI5 | +------------+--------------------+ | 3 | CRYDI3 | +------------+--------------------+ | 2 | CRYDI2 | +------------+--------------------+ Table 5 The key type used with these keys is "LWE" and the algorithm used for signing is "CRYDI". These subtypes MUST NOT be used for key agreement. The CRYDI variant used is determined by the subtype of the key (CRYDI3 for "pset 3" and CRYDI2 for "pset 2"). Implementations need to check that the key type is "LWE" for JOSE and that the pset of the key is a valid subtype when creating a signature. The CRYDI digital signature is generated as follows: 1. Generate a digital signature of the JWS Signing Input using CRYDI with the desired private key, as described in Section 3.2 (#name- sign). The signature bit string is the concatenation of a bit packed representation of z and encodings of h and c in this order. 2. The resulting octet sequence is the JWS Signature. When using a JWK for this algorithm, the following checks are made: * The "kty" field MUST be present, and it MUST be "LWE" for JOSE. * The "alg" field MUST be present, and it MUST represent the algorith and parameter set. * If the "key_ops" field is present, it MUST include "sign" when creating an CRYDI signature. * If the "key_ops" field is present, it MUST include "verify" when verifying an CRYDI signature. * If the JWK "use" field is present, its value MUST be "sig". Prorock, et al. Expires 23 April 2023 [Page 17] Internet-Draft post-quantum-signatures October 2022 Example signature using only required fields, represented in compact form: eyJhbGciOiJQUzM4NCIsImtpZCI6ImJpbGJvLmJhZ2dpbnNAaG9iYml0b24uZX hhbXBsZSJ9 . SXTigJlzIGEgZGFuZ2Vyb3VzIGJ1c2luZXNzLCBGcm9kbywgZ29pbmcgb3V0IH lvdXIgZG9vci4gWW91IHN0ZXAgb250byB0aGUgcm9hZCwgYW5kIGlmIHlvdSBk b24ndCBrZWVwIHlvdXIgZmVldCwgdGhlcmXigJlzIG5vIGtub3dpbmcgd2hlcm UgeW91IG1pZ2h0IGJlIHN3ZXB0IG9mZiB0by4 . cu22eBqkYDKgIlTpzDXGvaFfz6WGoz7fUDcfT0kkOy42miAh2qyBzk1xEsnk2I pN6-tPid6VrklHkqsGqDqHCdP6O8TTB5dDDItllVo6_1OLPpcbUrhiUSMxbbXU vdvWXzg-UD8biiReQFlfz28zGWVsdiNAUf8ZnyPEgVFn442ZdNqiVJRmBqrYRX e8P_ijQ7p8Vdz0TTrxUeT3lm8d9shnr2lfJT8ImUjvAA2Xez2Mlp8cBE5awDzT 0qI0n6uiP1aCN_2_jLAeQTlqRHtfa64QQSUmFAAjVKPbByi7xho0uTOcbH510a 6GYmJUAfmWjwZ6oD4ifKo8DYM-X72Eaw The same example decoded for readability: =============== NOTE: '\\' line wrapping per RFC 8792 =============== { "header": { "alg": "CRYDI3", "kid": "did:example:123#key-0" }, "payload": "It's a dangerous business, Frodo, going out your door.\ \ You step onto the road, and if you don't keep your feet, there's\ \ no knowing where you might be swept off to.", "signature": "2As8T1AHenWzLuTojcAYFDnT05n4bmDGIWenHqoXVizL7311HtVg\ \7PEJHYmpc1fIvFNrm0xJt0asD5bQk3ZY8WuEQDUjsn4j+zbyob8MPQI5u3p5ZkqlLhG\ \6Q8p1q0Hd5voY4a78vNxFJpYsETc0bECAft196z5hml2VjuDBqI7W4ju/iDKambJIDz\ \NLYgYinNyPcHjlfBP7aCfOqGBAOQrWuVgrAkdeM+uH6djaXW25+FeUl4Lg1uOIBPrcj\ \ZJO4MO7j7BmiuHJDB74QG/ifVqnvr4z2alMWHjjR7nPPr2CIKpuRthSpNWYVTRSN3mM\ \v0GjVLyaqhJpmUmewhjaQCi3iP7c59yKatGYjLPPEapsbN7ypIo1Bod/R2PZR0zeool\ \d9k30VmGsVLkJ4OEIFnlA8epv+bJISApZWrGuU6NBP8vr4UB2D9DRd8zwvd/vI0BWdq\ \nfglX4x18lWe8Tnd+21UC9n4zUb+KQlo9RR14VfXEOt9g5aOIzCWjAN+Oz8vqJ/ZwgH\ \zZotZNF+nZehtFPcPLM3dpoUkEI391VH3QQ6VTYfbMW9wGJ6UnylxZFEzNCnMFF9Qhs\ \7Xehy4yEDgJBFYIvbTRCfD+EbZbWQAnLKsm7UXXBR7HdUsJMhTkwdffGziWJBTf1UsG\ \tqaCF1bvXgbcCSe0XGhc0QkQKwwj3kNWY9/hnhH1bn7kyySqaI+W4Ph3pKwRb38sCS/\ \Gb3ryptI8zez0JR+lClWnu18noJjGincZq7jCGMiMCRFpzUV6rpY/FiM26IpZ8M9ShF\ \BHsTN7KGpyIqG6Yc3GzOJ/4ir7V3I3wYguK7iBUiuTM+OKwxtM75carZJPX/2lkn2Hh\ \TC+JVb2/yaHS2oDrlCwQosNhA/cB/cm+YmYgHc3KQwrZ/3Axr6weUSrWJ8qV+vJ5QKK\ \a1+CLrkVGJX6vh+ps1NB5EV9yyMhBXAbbJZ3K+dGed3G7Vj/qF2kbnIUlSIeP1f6LsH\ \XASuVLTU6qG0rTaCMYKwaAc5ROwAgyZmPXuOUwyCtNFb0+S73uX5/N2drrUPdXiURW+\ \luFKCtaNimU8myoz6YkoY234kz8pedST8eqBZAioe8HeYEKtZSAyYov4YfLgkqHqJG6\ \ycD2uA33kwnMim+jg/hIrWAIYYP9R90KECTvFR877RtfFgfn3+tZjWlmsxHZ5pNsTIA\ \dNR+VmNpoUZkQ0dgHuFLztyAnCaumL38LHYHFHj2boa0zYsMGw8WtpEQ3+BNgoanNax\ \dJ5THRRmhvMS3EDwanERimsZ6ZjdK8uchuVhytNiiKvBwEFWYIyoK9uUMBoEfDje4DX\ \wIAefXYCqPK8eXhL+9qDLxADlDQbCu+Ey3whX/r4r2Q6l+34HpRrn3g5ok+GtO/3ni9\ Prorock, et al. Expires 23 April 2023 [Page 18] Internet-Draft post-quantum-signatures October 2022 \dYiIYpcXYfhMGDoXJLZ3IMkK7L6e5u4/Wye7lot2B5ekSGRrkLkjv+bTIkppxbTU4Pi\ \n40qbD91sRzw2/GzZmJsfcFaKbj5dhoNWyh5cZr1PqsxMI5EdXSxJ69VWf8e+h4iPoB\ \YS1JnUjhicVWslpA1rdAvTkAsVY8rC22e09Hxzbkb/E7bt3iLDpekbbQAghZ31AwDv5\ \KEG72bBbXIYHzPvhJzrlS2LR0XKTJVd8tAxOSdxQDOt8tE2eKpmWZ38MJfRIxt2Rzol\ \p+bpKrR++pMLRrpViekVpZl/tlEojImNO5rLqxZhLxvZOyDfcT37jc1oqire527/Y9L\ \3k894eHNYcXxjb0LGGPDeLuTSEX+afHZLNbd93Qa5VTmLwsPxEW/Erua6nXUrAR/87P\ \0gIyce3h3sl5jzCXsQm/iODgyn7PTEo5ksQCFRPiyXq5xgiXGKGGkqTGg28Ohdby+lN\ \DPnNHU2J0F6GLTqwK3qGbBLzDGIMR2sePGpxZ/pecoX7yn5bTOf4iY1OCyLo5nEgSeb\ \JdBJh0ZU+QodLRN0cnenLmP1oNK2yCuT9uIAlWH9C1CLhBiEOfoIs9/r1W1XHPiPsX7\ \c21w+B1IPfzUX1cVdndnNo4XdHl9CH1tYJDLr8LfeuYnz+bnaFlqEUryTc8zUl4A+qB\ \SIDDDjefCbmDsTrdqzGT2J89MKViOogy3qJzyt3jo04xq+Q3OGjbOFJikyJEqUm8BmX\ \d3ctGfzsEr+5w7fDRco40/tDQUSH0qOWOsPkhuelLqKDziJXwhPQI42miVN2A4+OAS4\ \f2uTgpDNn1gIfH2+dOCkBjlhZeA1Tgrp8FHQxcaO5kut6cTLrL7CSBqINa7Khe1zyXa\ \PZG/tXUk+iv0BYT92b7CRNmg1qhE0G8V3q3QrB6EePYa1WxRQ7ij4rRcQWcj66A1hZ5\ \KjDUVJh+02cZTFrv97wM/im3vb3dbiSxAiQExSa2KATfLI2oS+y7RlRNJ+9nF/vTaFc\ \0HOdKfmuJAUkAcyk/h0Quvdaf9jxEcstj95mva+HkIqPuFifidlvGiafKr4fHZryp1h\ \g7QUtDRU2a4BRfzcLz6PKOBFV3xVI7qoQbKEqQyldv8mZRd0LBRKprxHW7PdUqutH2V\ \GEmZ4UuCYXT11UweBx2W9lHrQX+xaKAjTu6oLYIOvmFVCUr4mCrYRcLZnzwORcsqIl4\ \G88x8r5aeilL4lsQZO3kNotR4n0qzFVRU2+EXO7QJFm+NKxB7aRZ5oH+dSy+Ye6aMeG\ \Epv491LU0LVnZNMBP2eUhoEoOgimmZGtUobjRdLuYyNiJfJzVkjwF3gYQtY59zb+46N\ \SzvWUqpFUG80Vswns8GNAQ5hfLoH8OGGohT+UvoqvpTEXhiAAFstT/EQrHLZrYpXHJI\ \YaICW+6uo9ixL0oWkfI0HlYaXyNkaFKHQ5ZbPaP45dbWq/dqXdrRe2YU8AqdjCxyyzO\ \lyZR6zH9wHj0k1AIOHvnKZ/B2v4bS8YAtNZ1zgKbOvM4qqSIFETfr8N4yIteumHEznP\ \prD7Gr6W2VCS/0FXnQt5y0QC8z4ffrnggwPjcZfsCRSknktQB1q6Cx8KUOipf+RhOvs\ \HnNN3qJZmxz6YCvo2M7fxJtyRvm34UEVaj8QKXrmzX70Y9rDl6wEhhvSThaeq4dcfAC\ \vczGXWgCLB10gl+Iz6hVDTgCx7bC2BQ2oHtzSDc+v/UuJewvVaIL9tn4CtMZU86f3Zc\ \fTN2zke5alNpoJP9A+mkbcfy0aD6yFcn3nw2ueFDsssRg1ZcS5CujNeylAwxRYaNSmU\ \zDzMygHu0CTxfGEG2c63J32HkG4Ds58KSk7HSD58jgScBv+QjBUAGSJozFG9y7yIF5R\ \kD74aSJMYmuzow2UnGayR9yM5ONbW1brD4wNyJHqDIroCUvrL8zu24ErFWDKy6VaZ0m\ \ggPvX38IoxIPnE+PmOtRGr+ua9r9zO47TtEoADjIEtwQuNem0S1fqeVx2Fd1TmKc5+v\ \cxMsmuEKQiewTbviLdIWHTz4snU/dt77cxQEFWkS3pu31kCLyLbpiCKMrn1nELafNBg\ \RbzwEqGTT0i24Kz/kvC5RYr2USuHKksZxPfgx7Y0OpY3IbemFO11EmnG9odSwnVcww+\ \9/IIevZHUw1qqTxZu1re/AMfqhKgaD8XiwuKxPZQQo7Z6jj3yOugAVWYOw/88bAXO2k\ \deVc0mG53sKH9ChLg35LdPrpLgHeFjIHJ27L9ucqUw70Pu58vRJUnYDey997y57k1vh\ \9RwPkNvIs269v6s/xfg9VM9N4aY4X25EWCxchMWlH9LMamYF6JTP0v7v00cdHycmX5D\ \EnwqspYYNomVpJlOOxgMAO9oy1E4dhg3IJo+fJgL9rgOxJ4INTJOg/9tUz21LPI3c1c\ \D5pPs/y0zy0cF9f6ahaYxMDk/nfout2FGmoesMCaTN11JngYYC5H95cDeMwErm6ppSU\ \woCqut45noJq0VS4V3PKfASIfuUwP3vgFKo+82Wy3dqEr+sBAsve44CKQ8Tq1GLYjet\ \L3xugCkl0uaGh6TFqj2X/vJlXOW0Ouyvzt62fxeQ4esOrs4LdRxkJbKT2I2p6rQAlBi\ \GaZLvOuccQh7NSt7BEJBy8QUrPV10vPmCNGQrKS6alC/JNFLaxmsP4CPQqwRQ3fg2ia\ \qQRol0htD+UFjWUBXrQdrs48b9TdLHmbPHPbG6+ZeuCi87kJ/zJyjHA0SYUP6awkfga\ \ckiLUppo0oNIc9/qsVr2lFIWIO9+UWnIFR9nNFPzgbqw/cMOC/uWAOOsGS8ADQ/rePO\ \fTXx0mfkvI2YeTdiIayy+uwUxoLdz90DGhUysP+JGU9kZTqYNJYsjC4OgLXS+qKCYai\ \oW/leFs1fdP6SH+E24pOOJARU/f/ZajcMMXAwQdIVeOo7jvDhMydne90/18fcwpNVN0\ \tswhRsnW4uMCSAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIEBMZHyE=" } Prorock, et al. Expires 23 April 2023 [Page 19] Internet-Draft post-quantum-signatures October 2022 3.5. Using CRYDI with COSE The approach taken here matches the work done to support secp256k1 in JOSE and COSE in [RFC8812]. The following tables map terms between JOSE and COSE for signatures. +========+=======+======================+=============+ | Name | Value | Description | Recommended | +========+=======+======================+=============+ | CRYDI5 | TBD | CRYSTALS-Dilithium | No | | | | with parameter set 5 | | +--------+-------+----------------------+-------------+ | CRYDI3 | TBD | CRYSTALS-Dilithium | No | | | | with parameter set 3 | | +--------+-------+----------------------+-------------+ | CRYDI2 | TBD | CRYSTALS-Dilithium | No | | | | with parameter set 2 | | +--------+-------+----------------------+-------------+ Table 6 The following tables map terms between JOSE and COSE for key types. +======+=======+=========================+=============+ | Name | Value | Description | Recommended | +======+=======+=========================+=============+ | LWE | TBD | kty for Learning with | No | | | | Errors based Signatures | | +------+-------+-------------------------+-------------+ Table 7 4. Falcon 4.1. Overview This section of the document describes the lattice signature scheme [Falcon], the "Fast Fourier lattice-based compact signatures over NTRU". Falcon is based on the GPV hash-and-sign lattice-based signature framework introduced by Gentry, Peikert and Vaikuntanathan [GPV08], which is a framework that requires a class of lattices and a trapdoor sampler technique. For the class of lattices, Falcon uses the well-known NTRU lattices, while for the trapdoor sampler, it uses a new fast Fourier sampling technique [DP16]. The underlying hard problem is the short integer solution problem (SIS) over NTRU lattices, for which no efficient solving algorithm is currently known for both classical as well as quantum settings. Prorock, et al. Expires 23 April 2023 [Page 20] Internet-Draft post-quantum-signatures October 2022 The main design principle of Falcon is compactness, i.e. it was designed in a way that achieves minimal total memory bandwidth requirement (the sum of the signature size plus the public key size). This is possible due to the compactness of NTRU lattices. Falcon also offers very efficient signing and verification procedures. The main potential downsides of Falcon refer to the non-triviality of its algorithms and the need for floating point arithmetic support. The GPV framework, which underpins the Falcon design, is proven to be secure in the (quantum) random oracle model as long as the SIS problem remains intractable. Falcon requires an adaption of this prove to account for the fact it uses NTRU lattices. Falcon brings several advantages over other approaches to signature suites: * Post-quantum secure as long as the NTRU-SIS problem remains intractable. * Compactness: Falcon aims at minimum signature plus public key sizes. This should be contrasted with hash-based signature schemes (e.g. SPHINCS+), which minimizes public key sizes but suffer from long signatures, and multivariate quadratic schemes, which minimizes signatures sizes but suffers from long public keys. It also offers substantially shorter signatures than other lattice schemes while public keys are about the same size. * Efficiency: Falcon can produce thousands of signatures per second on a common computer, while verification is up to ten times faster. The operations in Falcon have O(n log n) complexity for degree n. * Side-channel resistance: Falcon may still have an important limitation regarding side-channel attacks due to the hardness of implementing discrete Gaussian sampling over the integers in constant-time. This gap that may have recently filled, but is under active investigation. 4.2. Core Operations Core operations used by the signature scheme should be implemented according to the details in [Falcon]. Core operations include key generation, sign, and verify. 4.3. Using FALCON with JOSE This sections is based on CBOR Object Signing and Encryption (COSE) and JSON Object Signing and Encryption (JOSE) (https://datatracker.ietf.org/doc/html/rfc8812#section-3) Prorock, et al. Expires 23 April 2023 [Page 21] Internet-Draft post-quantum-signatures October 2022 4.3.1. FALCON Key Representations A new key type (kty) value "NTRU" (for keys related to the family of algorithms that utilize NTRU based approaches to Post-quantum lattice based cryptography) is defined for public key algorithms that use base 64 encoded strings of the underlying binary material as private and public keys and that support cryptographic sponge functions. It has the following parameters: * The parameter "kty" MUST be "NTRU". * The parameter "alg" MUST be specified, and its value MUST be one of the values specified the below table +============+================================+ | alg | Description | +============+================================+ | FALCON512 | Falcon with parameter set 512 | +------------+--------------------------------+ | FALCON1024 | Falcon with parameter set 1024 | +------------+--------------------------------+ Table 8 * The parameter "pset" MAY be specfied to indicate the parameter set in use for the algorithm, but SHOULD also reflect the targeted NIST level for the algorithm in combination with the specified parameter set. For "alg" "FALCON" one of the described parameter sets "512" or "1024" MUST be specified. Parameter set "512" or above SHOULD be used with "FALCON" for any situation requiring at least 128bits of security against both quantum and classical attacks * The parameter "x" MUST be present and contain the public key encoded using the base64url [RFC4648] encoding. * The parameter "d" MUST be present for private keys and contain the private key encoded using the base64url encoding. This parameter MUST NOT be present for public keys. Sizes of various key and signature material is as follows Prorock, et al. Expires 23 April 2023 [Page 22] Internet-Draft post-quantum-signatures October 2022 +=============+===============+==============+======+ | Variable | Paramter Name | Paramter Set | Size | +=============+===============+==============+======+ | Signature | sig | 512 | 666 | +-------------+---------------+--------------+------+ | Public Key | x | 512 | 897 | +-------------+---------------+--------------+------+ | Private Key | d | 512 | 1281 | +-------------+---------------+--------------+------+ | Signature | sig | 1024 | 1280 | +-------------+---------------+--------------+------+ | Public Key | x | 1024 | 1793 | +-------------+---------------+--------------+------+ | Private Key | d | 1024 | 2305 | +-------------+---------------+--------------+------+ Table 9 When calculating JWK Thumbprints [RFC7638], the four public key fields are included in the hash input in lexicographic order: "kty", "alg", and "x". When using a JWK for this algorithm, the following checks are made: * The "kty" field MUST be present, and it MUST be "NTRU" for JOSE. * The "alg" field MUST be present, and it MUST represent the algorith and parameter set. * If the "key_ops" field is present, it MUST include "sign" when creating an NTRU signature. * If the "key_ops" field is present, it MUST include "verify" when verifying an NTRU signature. * If the JWK "use" field is present, its value MUST be "sig". 4.3.2. FALCON Algorithms In order to reduce the complexity of the key representation and signature representations we register a unique algorithm name per pset. This allows us to omit registering the pset term, and reduced the likelyhood that it will be misused. These alg values are used in both key representations and signatures. Prorock, et al. Expires 23 April 2023 [Page 23] Internet-Draft post-quantum-signatures October 2022 +======+============+==============+ | kty | alg | Paramter Set | +======+============+==============+ | NTRU | FALCON512 | 512 | +------+------------+--------------+ | NTRU | FALCON1024 | 1024 | +------+------------+--------------+ Table 10 4.4. Using FALCON with COSE The approach taken here matches the work done to support secp256k1 in JOSE and COSE in [RFC8812]. The following tables map terms between JOSE and COSE for signatures. +============+=======+================================+=============+ | Name | Value | Description | Recommended | +============+=======+================================+=============+ | FALCON512 | TBD | Falcon with parameter set 512 | No | +------------+-------+--------------------------------+-------------+ | FALCON1024 | TBD | Falcon with parameter set | No | | | | 1024 | | +------------+-------+--------------------------------+-------------+ Table 11 The following tables map terms between JOSE and COSE for key types. +======+=======+====================+=============+ | Name | Value | Description | Recommended | +======+=======+====================+=============+ | NTRU | TBD | kty for NTRU based | No | | | | digital signatures | | +------+-------+--------------------+-------------+ Table 12 5. SPHINCS-PLUS This section defines core operations used by the signature scheme, as proposed in [SPHINCS-PLUS]. Prorock, et al. Expires 23 April 2023 [Page 24] Internet-Draft post-quantum-signatures October 2022 5.1. Overview This section of the document describes the hash-based signature scheme SPHINCS+. The scheme is based on the concept of authenticating a large number or few-time signatures keypair using a combination of Merkle-tree signatures, a so-called hypertree. For each message to be signed a (pseudo-)random FTS keypair is selected with which the message can be signed. Combining this signature along with an authentication path through the hyper-tree consisting of hash-based many-time signatures then gives the SPHINC+ signature. The parameter set is strategically chosen such that the probability of signing too many messages with a specific FTS keypair to impact security is small enough to prevent forgery attacks. A trade-off in parameter set can be made on security guarantees, performance and signature size. SPHINCS+ is a post-quantum approach to digital signatures that is promises Post-Quantum Existential Unforgeability under Chosen Message Attack (PQ-EU-CMA), while ensuring that the security levels reached meet security needs for resistance to both classical and quantum attacks. The algoritm itself is based on the hardness assumptions of its underlying hash functions, which can be chosen from the set Haraka, SHA-256 or SHAKE256. For all security levels the only operations required are calls to these hash functions on various combinations of parameters and internal states. Contrary to CRYSTALS-Dilithium and Falcon, SPHINCS+ is not based on any algebraic structure. This reduces the possible attack surface of the algorithm. SPHINCS+ brings several advantages over other approaches to signature suites: * Post-quantum in nature - use of cryptographically secure hash functions and other approaches that should remain hard problems even when under an attack utilizing quantum approaches * Minimal security assumptions - compared to other schemes does not base its security on a new paradigm. The security is solely based on the security of the assumptions of the underlying hash function. * Performance and Optimization - based on combining a great many hash function calls of SHA-256, SHAKE256 or Haraka means existing (secure) SW and HW implementations of those hash functions can be re-used for increased performance * Private and Public Key Size - compared to other post-quantum approaches a very small key size is the form of hash inputs- outputs. This then has the drawback that either a large signature or low signing speed has to be accepted Prorock, et al. Expires 23 April 2023 [Page 25] Internet-Draft post-quantum-signatures October 2022 * Cryptanalysis assuarance - attacks (both pre-quantum and quantum) are easy to relate to existing attacks on hash functions. This allows for precise quantification of the security levels * Overlap with stateful hash-based algorithms - means there are possibilities to combine implementions with those of XMSS and LMS. For example, both have the same underlying hash functions and utilize existing HW acceleration. Furthermore, an API to a XMSS implementation can be directly used by the subroutines of Sphincs+ * Inherent resistance against side-channel attacks - since its core primitive is a hash function, it thereby is hard to attack with side-channels. The primary known disadvantage to SPHINCS+ is the size signatures, or the speed of signing, depending on the chosen parameter set. Especially in IoT applications this might pose a problem. Additionally hash-based schemes are also vulnerable to differential and fault attacks. 5.2. Core Operations Core operations used by the signature scheme should be implemented according to the details in [SPHINCS-PLUS]. Core operations include key generation, sign, and verify. 5.3. Using SPHINCS-PLUS with JOSE This sections is based on CBOR Object Signing and Encryption (COSE) and JSON Object Signing and Encryption (JOSE) (https://datatracker.ietf.org/doc/html/rfc8812#section-3) 5.3.1. SPHINCS-PLUS Key Representations A new key type (kty) value "HASH" (for keys related to the family of algorithms that utilize hash based approaches to post-quantum cryptography) is defined for public key algorithms that use base 64 encoded strings of the underlying binary material as private and public keys and that support cryptographic sponge functions. It has the following parameters: * The parameter "kty" MUST be "HASH". * The parameter "alg" MUST be specified, and its value MUST be one of the values specified the below table Prorock, et al. Expires 23 April 2023 [Page 26] Internet-Draft post-quantum-signatures October 2022 +==============+=====================================+ | alg | Description | +==============+=====================================+ | SPHINCS+128s | SPHINCS+ with parameter set of 128s | +--------------+-------------------------------------+ | SPHINCS+128f | SPHINCS+ with parameter set of 128f | +--------------+-------------------------------------+ | SPHINCS+192s | SPHINCS+ with parameter set of 192s | +--------------+-------------------------------------+ | SPHINCS+192f | SPHINCS+ with parameter set of 192f | +--------------+-------------------------------------+ | SPHINCS+256s | SPHINCS+ with parameter set of 256s | +--------------+-------------------------------------+ | SPHINCS+256f | SPHINCS+ with parameter set of 256f | +--------------+-------------------------------------+ Table 13 * The parameter "pset" MAY be specfied to indicate the paramter set in use for the algorithm, but SHOULD also reflect the targeted NIST level for the algorithm in combination with the specified paramter set. For "alg" "HAS" one of the described parameter sets as listed in the section SPHINCS+ Algorithms MUST be specified. * The parameter "x" MUST be present and contain the public key encoded using the base64url [RFC4648] encoding. * The parameter "d" MUST be present for private keys and contain the private key encoded using the base64url encoding. This parameter MUST NOT be present for public keys. When calculating JWK Thumbprints [RFC7638], the four public key fields are included in the hash input in lexicographic order: "kty", "alg", and "x". When using a JWK for this algorithm, the following checks are made: * The "kty" field MUST be present, and it MUST be "HASH" for JOSE. * The "alg" field MUST be present, and it MUST represent the algorith and parameter set. * If the "key_ops" field is present, it MUST include "sign" when creating a HASH signature. * If the "key_ops" field is present, it MUST include "verify" when verifying a HASH signature. Prorock, et al. Expires 23 April 2023 [Page 27] Internet-Draft post-quantum-signatures October 2022 * If the JWK "use" field is present, its value MUST be "sig". 5.3.2. SPHINCS-PLUS Algorithms In order to reduce the complexity of the key representation and signature representations we register a unique algorithm name per pset. This allows us to omit registering the pset term, and reduced the likelyhood that it will be misused. These alg values are used in both key representations and signatures. Sphincs+ targets different security levels (128-, 192- and 256-bit security) and tradeoffs between size and speed. For each security level a small (s) and fast (f) parameter set is provided. +======+==============+==============+ | kty | alg | Paramter Set | +======+==============+==============+ | HASH | SPHINCS+128s | 128s | +------+--------------+--------------+ | HASH | SPHINCS+128f | 128f | +------+--------------+--------------+ | HASH | SPHINCS+192s | 192s | +------+--------------+--------------+ | HASH | SPHINCS+192f | 192f | +------+--------------+--------------+ | HASH | SPHINCS+256s | 256s | +------+--------------+--------------+ | HASH | SPHINCS+256f | 256f | +------+--------------+--------------+ Table 14 5.4. Using SPHINCS-PLUS with COSE The approach taken here matches the work done to support secp256k1 in JOSE and COSE in [RFC8812]. The following tables map terms between JOSE and COSE for signatures. Prorock, et al. Expires 23 April 2023 [Page 28] Internet-Draft post-quantum-signatures October 2022 +==============+=======+====================+=============+ | Name | Value | Description | Recommended | +==============+=======+====================+=============+ | SPHINCS+128s | TBD | SPHINCS+ with | No | | | | parameter set 128s | | +--------------+-------+--------------------+-------------+ | SPHINCS+128f | TBD | SPHINCS+ with | No | | | | parameter set 128f | | +--------------+-------+--------------------+-------------+ | SPHINCS+192s | TBD | SPHINCS+ with | No | | | | parameter set 192s | | +--------------+-------+--------------------+-------------+ | SPHINCS+192f | TBD | SPHINCS+ with | No | | | | parameter set 192f | | +--------------+-------+--------------------+-------------+ | SPHINCS+256s | TBD | SPHINCS+ with | No | | | | parameter set 256s | | +--------------+-------+--------------------+-------------+ | SPHINCS+256f | TBD | SPHINCS+ with | No | | | | parameter set 256f | | +--------------+-------+--------------------+-------------+ Table 15 The following tables map terms between JOSE and COSE for key types. +======+=======+======================================+=============+ | Name | Value | Description | Recommended | +======+=======+======================================+=============+ | HASH | TBD | kty for hash based | No | | | | digital signature | | +------+-------+--------------------------------------+-------------+ Table 16 6. Security Considerations The following considerations SHOULD apply to all signature schemes described in this specification, unless otherwise noted. Care should be taken to ensure "kty" and intended use match, the algorithms described in this document share many properties with other cryptographic approaches from related families that are used for purposes other than digital signatures. Prorock, et al. Expires 23 April 2023 [Page 29] Internet-Draft post-quantum-signatures October 2022 6.1. Falcon specific Security Considerations Falcon utilizes floating point multiplications as part of fast Fourier transforms in its internal operations. This is somewhat novel and care should be taken to ensure consistent implementation across hardware platforms. Well tested underlying implementations should be selected for use with JOSE and COSE implementations. 6.2. Validating public keys All algorithms in that operate on public keys require first validating those keys. For the sign, verify and proof schemes, the use of KeyValidate is REQUIRED. 6.3. Side channel attacks Implementations of the signing algorithm SHOULD protect the secret key from side-channel attacks. Multiple best practices exist to protect against side-channel attacks. Any implementation of the the CRYSTALS-Dilithium, Falcon or Sphincs+ signing algorithms SHOULD utilize the following best practices at a minimum: * Constant timing - the implementation should ensure that constant time is utilized in operations * Sequence and memory access persistance - the implemention SHOULD execute the exact same sequence of instructions (at a machine level) with the exact same memory access independent of which polynomial is being operated on. * Uniform sampling - uniform sampling is the default in CRYSTALS- Dilithium to prevent information leakage, however care should be given in implementations to preserve the property of uniform sampling in implementation. * Secrecy of S1 - utmost care must be given to protection of S1 and to prevent information or power leakage. As is the case with most proposed lattice based approaches to date, fogery and other attacks may succeed, for example, with Dilithium through leakage of S1 (https://eprint.iacr.org/2018/821.pdf) through side channel mechanisms. 6.4. Randomness considerations It is recommended that the all nonces are from a trusted source of randomness. 7. IANA Considerations The following has NOT YET been added to the "JSON Web Key Types" registry: Prorock, et al. Expires 23 April 2023 [Page 30] Internet-Draft post-quantum-signatures October 2022 * Name: "LWE" * Description: LWE family post-quantum signature algorithm key pairs * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 3.1 of this document (TBD) The following has NOT YET been added to the "JSON Web Key Types" registry: * Name: "NTRU" * Description: NTRU family post-quantum signature algorithm key pairs * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 3.1 of this document (TBD) The following has NOT YET been added to the "JSON Web Key Types" registry: * Name: "HASH" * Description: Hash based post-quantum signature algorithm key pairs * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 3.1 of this document (TBD) The following has NOT YET been added to the "JSON Web Key Parameters" registry: * Parameter Name: "pset" * Parameter Description: The parameter set of the crypto system * Parameter Information Class: Public * Used with "kty" Value(s): "LWE", "NTRU", "HASH" * Change Controller: IESG * Specification Document(s): Section 2 of this document (TBD) The following has NOT YET been added to the "JSON Web Key Parameters" registry: * Parameter Name: "d" * Parameter Description: The private key * Parameter Information Class: Private * Used with "kty" Value(s): "LWE", "NTRU", "HASH" * Change Controller: IESG * Specification Document(s): Section 2 of RFC 8037 The following has NOT YET been added to the "JSON Web Key Parameters" registry: Prorock, et al. Expires 23 April 2023 [Page 31] Internet-Draft post-quantum-signatures October 2022 * Parameter Name: "x" * Parameter Description: The public key * Parameter Information Class: Public * Used with "kty" Value(s): "LWE", "NTRU", "HASH" * Change Controller: IESG * Specification Document(s): Section 2 of RFC 8037 The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "CRYDI2" * Algorithm Description: CRYDI2 signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 3.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "CRYDI3" * Algorithm Description: CRYDI3 signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 3.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "CRYDI5" * Algorithm Description: CRYDI5 signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 3.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "FALCON512" * Algorithm Description: FALCON512 signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG Prorock, et al. Expires 23 April 2023 [Page 32] Internet-Draft post-quantum-signatures October 2022 * Specification Document(s): Section 4.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "FALCON1024" * Algorithm Description: FALCON1024 signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 4.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "SPHINCS+128s" * Algorithm Description: SPHINCS+128s signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 5.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "SPHINCS+128f" * Algorithm Description: SPHINCS+128f signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 5.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "SPHINCS+192s" * Algorithm Description: SPHINCS+192s signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 5.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) Prorock, et al. Expires 23 April 2023 [Page 33] Internet-Draft post-quantum-signatures October 2022 The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "SPHINCS+192f" * Algorithm Description: SPHINCS+192f signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 5.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "SPHINCS+256s" * Algorithm Description: SPHINCS+256s signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 5.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) The following has NOT YET been added to the "JSON Web Signature and Encryption Algorithms" registry: * Algorithm Name: "SPHINCS+256f" * Algorithm Description: SPHINCS+256f signature algorithms * Algorithm Usage Location(s): "alg" * JOSE Implementation Requirements: Optional * Change Controller: IESG * Specification Document(s): Section 5.1 of this document (TBD) * Algorithm Analysis Documents(s): (TBD) 8. Appendix * JSON Web Signature (JWS) - RFC7515 (https://tools.ietf.org/html/ rfc7515) * JSON Web Encryption (JWE) - RFC7516 (https://tools.ietf.org/html/ rfc7516) * JSON Web Key (JWK) - RFC7517 (https://tools.ietf.org/html/rfc7517) * JSON Web Algorithms (JWA) - RFC7518 (https://tools.ietf.org/html/ rfc7518) * JSON Web Token (JWT) - RFC7519 (https://tools.ietf.org/html/ rfc7519) * JSON Web Key Thumbprint - RFC7638 (https://tools.ietf.org/html/ rfc7638) * JWS Unencoded Payload Option - RFC7797 (https://tools.ietf.org/html/rfc7797) Prorock, et al. Expires 23 April 2023 [Page 34] Internet-Draft post-quantum-signatures October 2022 * CFRG Elliptic Curve ECDH and Signatures - RFC8037 (https://tools.ietf.org/html/rfc8037) * CRYSTALS-Dilithium - Dilithium (https://www.pq- crystals.org/dilithium/data/dilithium-specification- round3-20210208.pdf) * SPHINCS+ - SPHINCS-PLUS (https://sphincs.org/data/sphincs+- round3-specification.pdf) [DP16]: Leo Ducas and Thomas Prest. Fast fourier orthogonalization. In Sergei A. Abramov, Eugene V. Zima, and Xiao-Shan Gao, editors, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC 2016, Waterloo, ON, Canada, July 19-22, 2016, pages 191-198. ACM, 2016. [GPV08]: Craig Gentry, Chris Peikert, and Vinod Vaikuntanathan. Trapdoors for hard lattices and new cryptographic constructions. In Richard E. Ladner and Cynthia Dwork, editors, 40th ACM STOC, pages 197-206, Victoria, BC, Canada, May 17-20, 2008. ACM Press. 8.1. Test Vectors 8.1.1. LWE CRYDI5 8.1.1.1. publicKeyJwk {"kty":"LWE","alg":"CRYDI5","x":"lgNFI62eq4YKxuvpMl2V9SVtGV5z_vQQZei\ \iCziAVcFMuUUzjpbwrd7uKHRbtxNPWsLIlfYKmM5SM-OLeoDII-GNQYJfm3QRt9l33P\ \AOyJpbeLidJg6e4UAIZJQx-KbKrIVqK6F42P8WmhDWxgc5xJZXUabUtMHV-irm9pMP8\ \kjrlRFuIenHS_YYj3RrX9yeAZKmD6YJsROVMEprjR1B7uOQxJYX1WNNRD5AEiGL8TKF\ \oxbOg-qDIP-M6ubjuKZqlhd3_-z1bLJDVkN_uh9hSIlqpghWD7niDldxKBAUldyELqn\ \WzvadJyhKTt3KevLOWGuPJGc927VgDnTVSvaiOW0bZu3wHEup5PxsqymxGEuJGkiY6Q\ \zL15KWzr4jdhq-_HpknGUjg2LbC0Q-f5raUm27vkT8EI7A3i-ar5Jhd9lhfXpGJ4Ui6\ \amgeTedhqJCKOzTrEF12ecwQ9ERhjdsksC8XMDe2lQS1W-AyHfntg2oPeC7O2q0E46J\ \MG_OUcLtMo3ShprY1VF93ObswsozfX6mmwqinQvYSpDAC7HHd39mp6CwJu10auoPi7H\ \DEAb0aSO-qUgdh8WOPgyCEe0GJ_Hpl7sokVq5dXtbV4458_zDtc-pUcX7C8J3OUgLfN\ \KsZzeOxQhgqkk0nG56CTleN_9u4rfWQzQZBH5ofr_biWHgr05HZ-UdjL4ezxPUIGW7M\ \_HvwktpowTnXfV4-6HTF16jqmH-AmO5XJlwjP44IbRMNk5m-vHOBJj6ELGiDuNQoiat\ \hKHS_-L0AO-7d2IxcpVuNWZfz1SvHzC4XPHt2lp0l_Rp9vu7obwGlFRrnLx1IrWcK6n\ \R3ux8oDJTM3H8J4cdRgzKaPM9_lBMhamWnpCXFThwRWshaTapgnLEfEXpMjikdho-SP\ \8DH6yddFrV-Sl_1Z8re1vD5CUXh50EcOepvnDYK5deW-Jqh6e_wGGlrwD7d9XZK9hKQ\ \oX1cYPsfkdgRIBywrD1bMIs7pyu5PVNSR39HD5woExp1y5bKgCaJDF-tBSl1tGQVl1U\ \pzENPHMi6fTCsv0OtEuvPZJkDvE-osJ_3Ajj9eTdKilJDdIYzSKu2Uodc96vaH3bXJW\ \05iBprV6h-nG6MuQuXIrUNiG9h8nQ7MmaJ_Jdr58_cBChxYZRu1zaJcSwpTecAtktv3\ \R-Yp2Lc7LxebwbEa19598X7CQtyS4RoUKorLOX4FkuXplJZduQbM2QftVqA6ufBkFH2\ \3Axy_fZooaz0oBM8YYBAIqJAs2Ya1iLfrdqo42rDL0K_VXmVGqctqKhM0etvM2nfx_8\ \VbsdoSmionB4d2Ur3no0AvzZbHcmIdHFg-EgJzfoIAhgKdHIzsN_AWEC9CFAp0dPwdi\ \MUs0sPhkWNAfs9hmnEX-IzxO57IyxE_iLkI9smuR6f2NkU23279NaZHBmIpmPU1tryg\ \SZ0i8yssFqKCDpRZwVV83F1Wcg3pnGsh9HXHC7rqI3-TB0_KxbTEmgKVspoido3Tl2Z\ \9Dx-9Jawe6rd7g1lheMOzlBWEfHFWwDTr5TxhEOo59zATIaJu4DxWkKfFQj4iXMYP-R\ Prorock, et al. Expires 23 April 2023 [Page 35] Internet-Draft post-quantum-signatures October 2022 \hA8QxNe82yUXoJGJo04f-C7N1xXJ64dOPoW0JNeDyM7liqtAQQgR6TNzVJvOb97E4Wl\ \AAC2gYfXGS8kOawcTyeWdytjXs8fqwOPJ3or2HZK1jnXZloGeSJILxHOQtl2PDM2k-W\ \0KZ1CPzbzjqQwQdg9CZ1F02b1Kusl42T2OjUylXsDGg4vaF-_IYucO7js31adyf90GZ\ \sMeoLqrwE1txMYJSk9SWSkjpL0csNDHH_sh5911O1ogQk6QoUIf_lMa-hg7EWKJAkP2\ \w2NsxPqr8vIAcdyCO_t5b6XpYCp7gkZiVxFn8tSrlofZbyW-zT1gp1gVEMhrWK5tIBZ\ \gE2ftMnG-AGekLYFD3aMzF3YZIDa3-Fs-_-YBOjx4ptOLCa8mXMUTj9s0KTXyB3BhYA\ \V7n8MDBRYITV17KMkLrY9vU1uhkxzSrNnBtSewEXf8Q4sGv2wEJjRJZyNPQzGtXRHNr\ \FKwCG3TVklCwc1d5C2Ttwh5HBtMtCBxTkAchRgRZshMWyVjnUiPn4rcGA-5XP6n8EZM\ \XOPo9vYkFuvb83GSB1g56jNCKGNStA-ZP33KKw_U8zdGz1fKX5xGvWrTU1MkhTST-aX\ \DHqpKjFTPU2M3wfraj37lfYK42rUYR-viKHyRXVH221DI6Ke-s1rKQxzSSHjSUBl3ID\ \eHtFb-pklL_JqIabpAKh_LkSthBvsiM1M8PUkiw30zzKQqScYiMxl_Ns3yvoahiWDh0\ \xO38smAiws9FjgI71mRywWBGJj4z21HTWfMAwWbzbld0MqZ4AW4zN6e-pMSfnPl-jF9\ \2C-FcXG58UQuBociY7Jwpg1XvWrVsTo3I8Qedzp1RYVV8qu3TQCCiCLom-UOwehbPdE\ \hp3ugI2nYjVygbk2QwseoRISKEylUlJ_vveItZCkinsK5Cy5g9OD59Ym4WzpdXjtRIP\ \k1ilfyLYcFwgdnNVLSNk1hb1iHgde9rghymzaUkEDdQwjfjXu8BsjKABdVyJwqF2r3g\ \V5UlK300F8Etd7n36y3RBxIx1fqkpCD-G-tePQ0zkbYwRouMC5P7Ws_Qj1WPAq9vIVF\ \WYDmRcXN4PKLb94qOQu8Ev2MfffDKDTvuPWU33UvOd3KbzKd3Jyfpq62WbeXEr_JgJ6\ \o442fEaWx4gh9tq1XZFQ4Wb9GzTuGz_hLkpCdOQd7snxiHPSxYqOjd9g8lYcsQKOhw_\ \dHCuSKyxxIAmI2MwLmGp6YnhY_JrfuUpZ1jfwcSCUqrzEvAS7CDvwzJ6-PAi2XO43ou\ \SP1-CGg9JS5hIiiIR5hpW3-Fqg2tOeqv7fFn_fAGyEtpHWDxkLJDTDcIzL2eU2umYUr\ \dbPynO9J99cEW3MU956D6LbmgRWK6lxQ5m539KMP7D4KQPPDt6CRA3YqAzZw-Vga8zd\ \2UxphCkORsaAs8pBihHwwe4ZhQl5qolmFKtQT2chnqVkn6nmpQmH3Th13XGf0RlByq-\ \bTEcwboddD_vYorb6HHyv9ciM0qh4g7tgmiphuR5b6LiVyqwxrMAN13cU8TiNIveY9A\ \fbS6qJMshNi61lkux4wnM6fpENDxCvRVCCyLB4NhS57fYddsTPiGZ6w1PeS_2Be8J9h\ \IN1g_yLmN8C1-9dgSx3yYYJZ4MGBNzxtbQIYcdH0_1mraXouf7hkhHAvbDPEcpCfUxt\ \mAI8hlYy-Pq1fjQTHoaEm9XaVe0SQfN6EsrbcXF2zjrG2uJuglRRM-IoWhleeMc1lv8\ \WCi33fB2KJhNo-iTKlhFYQmsO6qJyxusPu5Bmcl1EzONbBuHOeIHxzWBFoz5o4ziz3A\ \C1sD7eTc5-bF9enC-6J7OzRTx6mft5GwF8-FkQFJdqulPfgnr-_TYQZScKHW0Iki8kp\ \TUTr"} 8.1.1.2. privateKeyJwk {"kty":"LWE","alg":"CRYDI5","x":"lgNFI62eq4YKxuvpMl2V9SVtGV5z_vQQZei\ \iCziAVcFMuUUzjpbwrd7uKHRbtxNPWsLIlfYKmM5SM-OLeoDII-GNQYJfm3QRt9l33P\ \AOyJpbeLidJg6e4UAIZJQx-KbKrIVqK6F42P8WmhDWxgc5xJZXUabUtMHV-irm9pMP8\ \kjrlRFuIenHS_YYj3RrX9yeAZKmD6YJsROVMEprjR1B7uOQxJYX1WNNRD5AEiGL8TKF\ \oxbOg-qDIP-M6ubjuKZqlhd3_-z1bLJDVkN_uh9hSIlqpghWD7niDldxKBAUldyELqn\ \WzvadJyhKTt3KevLOWGuPJGc927VgDnTVSvaiOW0bZu3wHEup5PxsqymxGEuJGkiY6Q\ \zL15KWzr4jdhq-_HpknGUjg2LbC0Q-f5raUm27vkT8EI7A3i-ar5Jhd9lhfXpGJ4Ui6\ \amgeTedhqJCKOzTrEF12ecwQ9ERhjdsksC8XMDe2lQS1W-AyHfntg2oPeC7O2q0E46J\ \MG_OUcLtMo3ShprY1VF93ObswsozfX6mmwqinQvYSpDAC7HHd39mp6CwJu10auoPi7H\ \DEAb0aSO-qUgdh8WOPgyCEe0GJ_Hpl7sokVq5dXtbV4458_zDtc-pUcX7C8J3OUgLfN\ \KsZzeOxQhgqkk0nG56CTleN_9u4rfWQzQZBH5ofr_biWHgr05HZ-UdjL4ezxPUIGW7M\ \_HvwktpowTnXfV4-6HTF16jqmH-AmO5XJlwjP44IbRMNk5m-vHOBJj6ELGiDuNQoiat\ \hKHS_-L0AO-7d2IxcpVuNWZfz1SvHzC4XPHt2lp0l_Rp9vu7obwGlFRrnLx1IrWcK6n\ \R3ux8oDJTM3H8J4cdRgzKaPM9_lBMhamWnpCXFThwRWshaTapgnLEfEXpMjikdho-SP\ \8DH6yddFrV-Sl_1Z8re1vD5CUXh50EcOepvnDYK5deW-Jqh6e_wGGlrwD7d9XZK9hKQ\ \oX1cYPsfkdgRIBywrD1bMIs7pyu5PVNSR39HD5woExp1y5bKgCaJDF-tBSl1tGQVl1U\ Prorock, et al. 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Expires 23 April 2023 [Page 37] Internet-Draft post-quantum-signatures October 2022 \LQAIrZI0iAImygl5MRpUpSF2aAJokYAwgRQIJBtAyhRkhhuQhZGEieKSIAsEbUwwjCE\ \0iQgVBBCCZRJWJRwC0ZG0SZl2rBBGKgo5CJEArFwSzBAG0hlkJQMGgclwgQm2AIqETE\ \kSYgtCLQpELFBGAIEwBhEysRQ2UgCkwgJgbhg2IYtFCZqEBZxoBJOpJIBjERpSahAwb\ \iMTKKIyihqwJKFGhCMwkBSUTaRiLSNjAKJoihwGchAy7JgAoYtSShyg8YNIEKI2hYhI\ \hdyCUVJ3CCSVIJgSDINgsKMkJCEoEYFACURwYBxQagJoIIIAZFBRMZxmCguIjMxo6KJ\ \U0AB07aN0qQQgzhtHKglCwYKCCZsUAhhlDYOgUYMSZaBlERBDEkpw7YtGgNOUqYFC6J\ \h2ZQNCQaBWCIhozIKDDhpZChuRIKA5AaFIhiREUlQJMAN1AZRlKhQYUJyGiFgGUdqQw\ \BS3IJhlCiGyoiFI7MApJKFWkANCzYSygQlkSgpnKSBikIqYiIFBLAkIcGMwrQJYCAkI\ \acEiSACyoJkCBQKQkIg4xZMECBgkphtBBgtmDQpCqWJIgAwCAWGIpEBIhaEXDYIUwRl\ \gAKBIaeQEoUglMgMgCZCGpcwwpQp2YKMyqaRCkhQowQB0YBBhBghC7lQRDYpFAghS8C\ \IAYclGDmSFCEQ2aaNgEBsygRBpBaFIRMs4xgMCUJgArVk3AJoEbkxCSBI4haCI5VJlJ\ \RQYyAFgSYJAUdJjAAqSyZRCgIQYiZJywYkUIaEAzYJWahBSwZOiTYgk4YpECcmCyFhE\ \wIxEjFy4jYQwTJwkAQEUqJMxChuDIkhCiBJiAhGmCBOgxQJTBJukzYkm4JomUZtHDeG\ \CAhpS6QkABUswMIFS6QgShgpmKYpwASE2hYIiwBIAzVgkERNZAYlGAlFg0BMQQRRWyi\ \OkohJERItyJhEE0NwkbREmJBFGgWIk0BhRBBOSgBNYRZJFKOITAJghARtIwVxmZaQCh\ \RpXBAMijJMYYAhkTQwibIxwTRCA8dNIJJgW5KNDJYAELiMoSCIGqZBVKAgSURtYDgMx\ \Dgk4IYgFCCEwhaG45IwY5CNzKJQIAUKBEQEoARmHCBJWDggm4YsyUAkUMQlXKAtwiJS\ \FKIMUjBpYgAJA8BFwzgIG0aRVBCIAsBBYIhkFLMgGCMqI0WCEjgAAJBtCZhBCSUQiyR\ \uUEItYkaK2agNAEQm4ESREhNmIreMAxYuETZpEyJBUAJuJBRu7kh_85-NnVU1ybdxVd\ \53EQwXd5rJr3r9DUZ9en2KzzPDgzcTPEBfQk6JsroofVPkTLuv91Qj4vyeB31IohvBL\ \bh8fqaYioveZBPNbp2I_J9RfRRCxdSXau28NFfYfc5aeDMHfOM_UKqIIu-hUZNtGUNR\ \NxS58X2hiJPFORu5EjJDMagA9tjYrRggbZuWkcpf67BUt2NMG68zIj27rB3tb3NwPzf\ \zr1PJ0uVn0q17uZr5HozPSJMHqUjfJFxeMLxLNpYfIyxkMjlKT_WsvQiWacudZKFWk6\ \IJhi8Pwp7wBXeF2zzDfZkpMtRKNeQxLGeJ5RCWqcW40FIOFzkVI1p-fckThXER0UXJL\ \j_5Od5_KhaZPO22eM3MM0AvDhg3ZcoKKGIOxtL9WGS3Cg5xMrtiJOwN42YyehXxGUN8\ \NYZL3nufSS0zslDq3SmQ6dM-SzsAB1oYw9g-DB07Y2xcPsNzH6QvcOc6oa9t0JK9RYF\ \BySCyH9ZSCwfij1FFD81Zgd8ociINcPU8BFV0WpnOcYdRWmzX6czabmaVWCdGcBfCIB\ \8kNw28PZhYmrzkgF3Ti8qDTCrZFMay1knaS0qRX3NDWIEs4fU_rYiMKsYi9dIEmXqPj\ \zknXYi-Sj21mjxliPWZkT1Iqbh7d14i-1C4c9WA5HCXPSPNa8VRb-dmVjdZ9ZBvlYzU\ \BiaRLfxwx6pbdslldHxDgFFBc8J9eDsH_-9dQgDmgGrgQgNI9ItlZwpvrTLb-n3YZmo\ \ZhCd0mWgTZnuMRSCmWPTj_2iHgtqX-EHj0hOjqXXfu7t54FMSgyKYMiu8q1_xm_Xztg\ \CPjE8tkCq1bAXZ-Vw4MXTf0ks9tiiUMExVLzT7hEgTVreYOqB_oToZVd_BVJqvbCNDe\ \GBp3Sd8q2VdWr_X3ISmr1SBacl7loRwsVElEEa6a_unR2Cpk9M_j9wMXAR_-0pnY0sO\ \GJKv9_1mWEMc8393npbg5P7I7cTS6bJOpcopRX2mlwof_QB65633bf51FBpmJ7qI-9e\ \iEz0EJ4o46RNo990ZEEJ6z7HLCE_IJJwnnRQbaNUPymZhoJ7ALMTxU-TODBL1jotS-_\ \2ZJPbS_yIOnx7sD1Gk4IqF39TDWUhqEdDbXR3laEJHTfeCezn32UBDuz_Jp3yl6nSrW\ \htiFk-gZPfHf-6cz8C1QCV7ezl_HiwIflF2RSVT3ZNkkisfkvRnwJpK_RS5H8jvvMR3\ \uVUE3MLVKznPg7Y5cbUERoCL_6DE6FHpZqPa6H0WKg7SE3bZpXbQiTnfo17kZqpYBCo\ \KBjDkHzQgMNnA-l1Z2Pdzkumgz_volZO8WuK2pNg47c44Yenm2RBxvag1KsI8ZWSK_n\ \Xia9yzygQHVh2h89MV2z1bynRinC5VysJ5KG1Zya_0jgLOmX0D1MG2m6mwmQ5OzHeJe\ \ymk87uzKJDfdCAcrUSRRlVyBFO4Fxe2fdl58q1ofIrI6S1juh0gb0wPryCy5Izh4aaP\ \gSpGYG7O6Eddi_8pdmIluXr7eSkwIqsQCT0eLYtXDmOWMmh5W4QDBZHrV_iA7nNM1PW\ \fynapnsoyiCewwqIeForRRbYEnMHUd5ksFYHlLtAbsqvB9oIm98crCkN3V0eWg8Tzti\ \f11S8JqD5G5QY8CdvxXzh5AeOIUziedqZd0trBhswRDpaM7n61vPt3wurgDgHktFJn1\ \VVQtgIEqjMFP_lWfrDWaVSCgd5ekSvuPmYdjatIp3v0N5uyj_GqkCU0O98X7NcyWfBA\ \gGtbTmn5yl25HFqPsLyGND0suzXjOeNX9N4e01u7d-Z57-9baO4sEJ1sHQ3PGTwc6Sa\ \Y1BR-EF79WZBES9VI0AElkSkdMHIAVAQ9-JJxxJgNbdcWLbmrdH5-fWtEKRYRoA9LOO\ \pe6ry1kBv3uOMqAKn7uneUrvADZmHxrVgAP1TV4OlYBdqOiz5QfauvgCM-V4S16D3Rd\ Prorock, et al. 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NTRU FALCON512 8.1.2.1. publicKeyJwk Prorock, et al. Expires 23 April 2023 [Page 41] Internet-Draft post-quantum-signatures October 2022 {"kty":"NTRU","alg":"FALCON512","x":"CjcORWYeLyAc5OSAR5tLh2bn0KXRcAP\ \cAssTZu2nYLIatsrnlb2j23yBKQNdC_ak2axFDLyj8QeWtIyNphAjVTqC8Nfz6cuoHA\ \GIPMV7rwWxd0WYYJTWUZUHJbJGIo75KV7-eQGQ2KUDcyQgjhcBWCxOwPxyYUN1EC138\ \onR_xvcakAhjagU1GNowliiWVwEoVvK8oPtE-m8Wz8u4TfQ6wRorRZ1MsQENBHesWEt\ \5H5UIGYhyck7hXVF4FHpLFEIvxSTjDUm3OZQXEmRM_4WARVQQnya7MM3Z6FIzJvoPV7\ \IXGBqsaLrqwCpH9PBkECjzK4YIilVDA5iUR9gdbjAmjJqSgpHfmFWi9OGlhARYI-j12\ \t8f3KykkFlyqHUuhulI7Y7Az3nAwXgePqsise7fSMIssXmtaFUag4g0k1QBklpwUiY4\ \h9aNN4SjYKZQO7m1ZU9YJK7bVG3hmlaAKDiUXmas0tUTkh8Kld_oFS9BtOX15Q2oOEq\ \Yd6YAJhY5lebavuaVtWTO9U4uzhPQtljcoRZkITdB8igKbrjxgxFdJ6mU1IuvFpE6eQ\ \qAZ4M6U6jRVmzWZRScP0C0WXSPnlxrfJ1bEvhXNIepUmLsjjWKFuMbYcEjo2e4g85KA\ \2bBsgfmqoUVE7M7KHrqUKdMZjkXd0nOaEg41gRmSUC3ASK2oqlWhV1H1KlrzDF01hBp\ \L3yErDiT_Ng4Q6yrcE9rjAv2qSdigBwK3Jujeh50GFr5eKZR1570OlApp_Bs5v17CqJ\ \8Q3VSUbKu0WT2HybcjOKpgnm0WM8Zn6IxeA9AOTfc8CRNwUMwZYWoLVSmvkBTYAAUSK\ \EGmmRy6cCXZJ9zv580TOQ5Bm-bMSnydrY4ZOlaWthXDElEWMFK23zQyYHkPzG1JvIuf\ \AUagNCQGQUy1_iWdpNOZ5DlDSJ1CIpWHASdrvnJ5gqUeYh-_1Bt7wVV9rknBQHQKe6c\ \9rxgJhLq0erQ4BkyaDwWF6EDMUDJ9gLE2oDcnYJK6KuBsTjzZRIPWi5TANMQQWgZlgC\ \mVeZQ_Zt6wB46mHKFxMzkQgIwPLVmVLt5dWJS1Cf8Bn13yYqc0R59cifsW61GTnmiqk\ \LLKeU6Iu3eWo2OLhHXIUSLeGJWwYV2HzjNirrV12LdRzo9oqkb_EiLagseRL6s4vaPq\ \BB9uIvQYuRDXRJxJUNSj2yNREPNDCICOAiJYRx1ZHCS_46kGKkDs04t4Z1SAdGXWAEw\ \Ns4o-GWwjKyok6EYT1pa5mc6CEdp5N3A2h6kvxRPSZcD8EfKB3cWzQsbWkGbvoNXaxa\ \HWkbEa0kZIDgKiRiInC-iVoRzqqXRBKFBMLG6QPJm61pK2VLxrJCjP9qw193OOyUKif\ \QzgswOnYwDamsekYHOAmfL2b_kciRZl6EaVSlbnCYBkLVyiU0uTrcigrWLRtG1OJUkN\ \iYCVF2AGx8TihI86WV3BZFCrVNjsyqucRhmOxxd6RqEZTge7i4bzWx4zAKzRZKJyovV\ \1VtoX8Ct36hVtXVKsFn9vxqz6OdZtaWV12PG7CFCLGVnYKCONsX2s9YHo2AhxXRE74s\ \hAUaD2APOKPXT0laA_BvgcssHJ3Jqsdy72JTImu24-mYpFLn8PIAk0Y8AGGnYmFNXdI\ \z6ONvSxnH6T-oapAGJ8EYaTtsXDy25cJkaUyBanxiIW20CuoDVzu7jiPjwUuGLMUc27\ \EpJAr2fGT3A5okzEdXN-Iiof3iwm5GfBUNRkLiD_kbIve4nOb_RkEVkRDY2i51fRKwk\ \BxTptO3Po6rlZRKyr4SDgaNNwVljxc-Rcy7V9RDWkjqesoR_SkNy_e-lBev8DexEAHX\ \crqhqifuLCa0fzn5GC6t-ai0my_tvMTKVsMBfW11SRfYKtw3vILELOLGJirsl1zGyZp\ \wYHmHK9Fk0TPLnystG67flhWb0RM4awAyh4UZUK1QYWyEk-okmRtSmbJCCkoXFcRX5J\ \BlElSMgWGaKGLt9AYA0fMoRNMStBXHU9dTJ0V2oLvITAfgS3K0aHEW7kI0shtPP6SPh\ \XyYql-ijPQ3aPBBldkhfi21WiDBmhLA-yxUxcrVlZ2NkZtj34Qch0rzQoNLLVDpqLsm\ \Z9yRNiXzEMxEaKmY5rXhngKhBcXuRP2p7SUZN5L6pEqaYncYWqUi4XAD1iYHxngDBdL\ \kKyUhqWDcRZacAKLuK5NWjcNXce5RNDVMti5WfguGRNZ5Qu8xsK6X1Ez9k0lNKVTUnV\ \SQtBbFbGYwIFNl3KYcgHEbMpSS5p6oYQhHl_8eqqIrWCvrC413ENMeFnHRsqrErnlZw\ \SmSz4BDFA0GcuyNvVWt5_BUKx94IqY2ra_LQ-Lz8j5JDSzNxWJORBAA2S8o3m1teTEg\ \KANewDdZTcvsVA0"} 8.1.2.2. privateKeyJwk {"kty":"NTRU","alg":"FALCON512","x":"CjcORWYeLyAc5OSAR5tLh2bn0KXRcAP\ \cAssTZu2nYLIatsrnlb2j23yBKQNdC_ak2axFDLyj8QeWtIyNphAjVTqC8Nfz6cuoHA\ \GIPMV7rwWxd0WYYJTWUZUHJbJGIo75KV7-eQGQ2KUDcyQgjhcBWCxOwPxyYUN1EC138\ \onR_xvcakAhjagU1GNowliiWVwEoVvK8oPtE-m8Wz8u4TfQ6wRorRZ1MsQENBHesWEt\ \5H5UIGYhyck7hXVF4FHpLFEIvxSTjDUm3OZQXEmRM_4WARVQQnya7MM3Z6FIzJvoPV7\ \IXGBqsaLrqwCpH9PBkECjzK4YIilVDA5iUR9gdbjAmjJqSgpHfmFWi9OGlhARYI-j12\ \t8f3KykkFlyqHUuhulI7Y7Az3nAwXgePqsise7fSMIssXmtaFUag4g0k1QBklpwUiY4\ \h9aNN4SjYKZQO7m1ZU9YJK7bVG3hmlaAKDiUXmas0tUTkh8Kld_oFS9BtOX15Q2oOEq\ Prorock, et al. 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Expires 23 April 2023 [Page 43] Internet-Draft post-quantum-signatures October 2022 \AEY-9AAHjd_zXhjELpfdAToAn-cvwi8YYAfEUg_FH_v_gJ4Hw9AAQgCGHgej93wO-D8\ \ohg-EXh_EMH-7GL4Q-4EAOi5sQ-hBkQAlHsBgg2P4x_IA397ED2xcAMWxA5sPBX9vvf\ \ACX3heCDwR_AEQ-g6P4gBwHn-94AIBi8MXff4EHPCDwey8H_4x95_gBe-IPxaAEYxeG\ \HgwgCHw99J3YNgJ83wDJ4ARjJ4Oh-18exez_wRgEAIBeAf3vjGDoffAMH_a6P_P9GP4\ \Ph8EgwZGAofk5wfiB_3fAeMAGwi8MAOHD8HgfF8AehCDo_A4LYA_MHvyi_74BE70v_7\ \AEIS_D_oAED0gPi-Mv-eCEJBhB3pC_94wMiB8ARF6AAOh4TwCB__RO-LDH1_h_05_8O\ \19gT8-QaAPLq7xvz5gop5Qf--Of-JBQKDxP_8eXU-Qwl2Q_uzO7lAObM-evnKd7lQPc\ \CFQfsLOb-4dI0-Q0SEhPs0hsBQxTh1uwRA-QS9QYBFv8KAwIU4er8HAAOHOALBvTnDv\ \gK9-P3yiA48gcOCxYs2vAG9OgnGiTMEysU29r9-uIS8dX5--0E9P71_gI2IDUK7-HZF\ \_UE3fL80uEK7vX_1BfbASAK6QPpAwP5B-nsQOcJ7QH_MgH2ycgrQSX1CVgn9QwAuvwi\ \7BLdGR4f70DS-gAQ7-MQGygSJAYMAu3y8CUGDywPBSwl-xEXG_vYDv3PEQj8FgX60xP\ \_9ifi1O34Dvv5CPvVEhDY-gYHEwTC7P8R6-HJENojDBMMGuks_cvoIQgP9_cA4wYWF_\ \T3FwbX3hznHOgpFiL03-sF7uYi-g3g6vAT59z5GAET_BzpCN0GAwkHHtgTIPr55d0LE\ \AwD7iME__khGQYYK93c0Cza9OEN2fHt8vM0_wT88ukP7Ov8AfU8GgjtFQPh8Qbu6gjv\ \8_AISA8m6iz3_w00Aesb5O8HFQ4zAegODxIMBPcCHuzm-yfbBvvr5vP0A9fewOkRAuU\ \HBssYFrkjERIZ9h3r8CPo3dso9gUK9ecJ8toQ2CEe2f3hEBLz7wASDwMbBvYCFPsl-w\ \r49tvp9CgE-xQT8PUQGdviBxnY1xwWBdX-CAvxJu4MLgP07x7oKOzW8REIORUM-vsQE\ \PLi9Qj94u_3CezpABPk1AwZBAXbKOcn4O76F-4W5w4uzPfqJw4qAfcm-vLVIu3FF_H4\ \9N7CHvIJ6AzwAPkA-w_UCiz4FT4D5-IBAukSEAIR-vDr8wPpBsgKA_3_5v4LDxMX4fk\ \bBw7wBvYNBAAC4_UU7Q7uKM3x_g0BD_3m5xn86wQH4e786O8hAfQR4_0DDg717N_0Fd\ \73E-sBIAP1ABH99BcgAyfH_-vS7uLcB-3u5fjvIfAyERbtB_8g_SEu__zvNRzrAA798\ \TLu9RLU-BP7DRbnC-kmxAcAQRDsFwvuGxf5A_QA3BTnAtXuFNv48ePawvi_GfHwGfHT\ \NPL7--nj_Rzu3AnsCuoTJAX07Q_q-fH7BCcXHOzzHOcs-eDYE-A1J_H39t3-zPgUBx0\ \I30oSMAUH9vMS1BAC9vob_vMRATHmBfv48R_ZAu7k39spBvUU5xX5ACwB-fv-Hu8JHQ\ \DoJecN7eAzJuDuDhkTE_YT-dS7-gYaFCLg9fcO5RT-6h0WISJBAOtY5BkLsvoX4gThG\ \TEEOPQQ-v_gA_sP9BYk_AsI_N8EGxUIHAny5A4J6k769_MB6-8Z5wb6BSkp8vn4FBQK\ \9_XZ9-YUCP4AJA"} 8.1.2.3. jws Prorock, et al. 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HASH SPHINCS+-SHAKE-256s-robust 8.1.3.1. publicKeyJwk {"kty":"HASH","alg":"SPHINCS+-SHAKE-256s-robust","x":"C_NSiMVMN6kpAv\ \1O21izzVkl7cN0ls-tX3xL8VeIOHWzfwmMJ37LvTLVXZQMFyXFTilBcLjcbPNqRCMXi\ \z_c1A"} 8.1.3.2. privateKeyJwk {"kty":"HASH","alg":"SPHINCS+-SHAKE-256s-robust","x":"C_NSiMVMN6kpAv\ \1O21izzVkl7cN0ls-tX3xL8VeIOHWzfwmMJ37LvTLVXZQMFyXFTilBcLjcbPNqRCMXi\ \z_c1A","d":"-gEaHimlK26FRDpf33I6BKsfT3muN8xdOyonuYSgHtEoDxDBsTe30nU\ \O8OWZrfwJxvKyVxo6HCThjbMJX9LqSQvzUojFTDepKQL9TttYs81ZJe3DdJbPrV98S_\ \FXiDh1s38JjCd-y70y1V2UDBclxU4pQXC43GzzakQjF4s_3NQ"} Prorock, et al. 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Expires 23 April 2023 [Page 57] Internet-Draft post-quantum-signatures October 2022 \PRFhkodNhviOffaj8px5KpxMAI4qgxdSrL27C4pmlZ56NWMvuBA6So0BkOzGeXyNKyh\ \p9ehEDcyKVgIToZcdy09EA4nOUl6CnVATCX9G13tfELJqcOx530SMQMLj0KX9jdYC-i\ \YPBpBhMfbjFp5h7zFg7lP5agqXAqxOB5enrD1uIHfgjaoKMptEBIPb2vP7q21_pJkPY\ \UJBAa_bsXyNjlJrU2ds6VL42aqzBd9fwk6gLJLTxXzz_w5vJAbI4laktZLu337e0tSt\ \6zviSwdJ-z7az18F46Q1l2H6nUi3Mcpv0dU9A-6WokWHZB7Tm8v6xmImfShdvpZzZDl\ \2_p3mwxiK8j0GuMiS6kD8Lognv-wwSvX7w6NCC2spzTofbbeDh6h_-AGXr0sxq__XCZ\ \rqQebAqo2w6KiUimp6HOPD19yOzuDj187W3_pE39TZyQgRu4OKXrph6hURGevqf2udj\ \9Vk4aPtk3sm-bGLD65z-qMfDvUwKqve1utKi8le0oTqDiVT92KgG4uTdbLdNZAOyCoN\ \YVLNCm-IBGAmS4pHqdbsz-p77MNdanXVQgPyLRZzxy5CKPQvgTUoi8Y9CcBa9dhxN9_\ \M88jIlJs1282BB05dYJVnYupsEhx_HBENzOpCEF2coLEZPEmy6CFLEtEgtq9k4Soq3h\ \AEpFlN_nd3RBqv0M4Q4Uve5egNMr3RHghbJsovrs1bHdNDHjZ7xsacW_aSlyEuIyvDa\ \jCLsl-GTDqb1rbarlV55zamBekyFYZzP6Demcoi7jWSlZmvvlThpZCCXtJF2n_7ozxx\ \f-L9Boi29Cx0fsiJ5z36xhOReXVpyWw4xkMJ2ybt_zt9XqsmVZ4v3RunJ025PjWcd80\ \hND6H1w2O0GqsUrQ8kFwwEIVS95oFXQ2ZTtaTp-XO7Dz9pTmF1pnHnefFTK4tC6SUF7\ \dvpFiUsYU8bwI-Zwix9S7Boeksx43NOBtGxBr3l-1WBr4qx4JLxcXptoT-vqaeRnix4\ \0kpBgxBfWvkr5w9pZ5AbL4wl42nLnTw33K6mqdW1DxVQNDTTmBuX6CjI1tTlxw8QdF9\ \KnESRSNp-d-2O0AvDcYgDCHSr7flegjQqQIQ7Nk9CJWXzFXp6vC7-bYAAGjhkabSFev\ \P97o-eIzfVDZZd3hp9IgnF2heMtZb9BAzy0R_XJ5W0H7tK_B9VWfrghJ9wGhQ51e77-\ \o67okVQ8iwSkiSrs0_njVroSrvb563wy5N-SGnbA0-V4AYeDyteZ2RTdr7ouzihoU7j\ \OHERvWFGpegIDyUOKJ4rj9_W9XznUlnzHjmIX47Wfybdn0fU3N-j9f9ZsT9YYfBSudX\ \Woa12F8ngJc8QT6zBmnCysBwRTlcjfZdWJTaLDC0gMRXezq59U1ahXKvYwlnXiWV5Sm\ \hiR2NpT2lKVFVFaEpUa05US3kxVFNFRkxSUzB5TlRaekxYSnZZblZ6ZENKOS5PVEE0T\ \ldReVltVm1Oamt5T0RaaE5tTmlZalV4TmpJell6aG1ZVEkxT0RZeU9UazBOV05rTlRW\ \allUY3dOV05qTkdVMk5qY3dNRE01TmpnNU5HVXdZdw 9. Normative References [CRYSTALS-Dilithium] Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schwabe, P., Seiler, G., and D. Stehle, "CRYSTALS- Dilithium: A Lattice-Based Digital Signature Scheme", 2018, . [Falcon] Fouque, P., Hoffstein, J., Kirchner, P., Lyubashevsky, V., Pornin, T., Prest, T., Ricosset, T., Seiler, G., Whyte, W., and Z. Zhang, "Fast-Fourier Lattice-based Compact Signatures over NTRU", 2017, . [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, . [RFC4648] Josefsson, S., "The Base16, Base32, and Base64 Data Encodings", RFC 4648, DOI 10.17487/RFC4648, October 2006, . Prorock, et al. Expires 23 April 2023 [Page 58] Internet-Draft post-quantum-signatures October 2022 [RFC7515] Jones, M., Bradley, J., and N. Sakimura, "JSON Web Signature (JWS)", RFC 7515, DOI 10.17487/RFC7515, May 2015, . [RFC7517] Jones, M., "JSON Web Key (JWK)", RFC 7517, DOI 10.17487/RFC7517, May 2015, . [RFC7638] Jones, M. and N. Sakimura, "JSON Web Key (JWK) Thumbprint", RFC 7638, DOI 10.17487/RFC7638, September 2015, . [RFC8702] Kampanakis, P. and Q. Dang, "Use of the SHAKE One-Way Hash Functions in the Cryptographic Message Syntax (CMS)", RFC 8702, DOI 10.17487/RFC8702, January 2020, . [RFC8812] Jones, M., "CBOR Object Signing and Encryption (COSE) and JSON Object Signing and Encryption (JOSE) Registrations for Web Authentication (WebAuthn) Algorithms", RFC 8812, DOI 10.17487/RFC8812, August 2020, . [SPHINCS-PLUS] Hulsing, A., "Sphincs+ Stateless Hash-based Signatures", 2017, . 10. Informative References [RFC6234] Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, DOI 10.17487/RFC6234, May 2011, . Authors' Addresses Michael Prorock mesur.io Email: mprorock@mesur.io Orie Steele Transmute Email: orie@transmute.industries Rafael Misoczki Google Prorock, et al. Expires 23 April 2023 [Page 59] Internet-Draft post-quantum-signatures October 2022 Email: rafaelmisoczki@google.com Michael Osborne IBM Email: osb@zurich.ibm.com Christine Cloostermans NXP Email: christine.cloostermans@nxp.com Prorock, et al. Expires 23 April 2023 [Page 60]