Internet DRAFT - draft-ietf-cose-post-quantum-signatures
draft-ietf-cose-post-quantum-signatures
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/.
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Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on 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
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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
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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.
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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)
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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")
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+===========+===============+==============+======+==============+
| 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.
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The public key is represented as x and encoded using base64url
encoding as described in [RFC7517].
Example public key using only required fields:
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=============== NOTE: '\' line wrapping per RFC 8792 ================
{
"kty": "LWE",
"alg": "CRYDI3",
"x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\
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}
Example public key including optional fields:
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=============== NOTE: '\' line wrapping per RFC 8792 ================
{
"kid": "key-0",
"kty": "LWE",
"alg": "CRYDI3",
"key_ops": ["verify"],
"x": "z7u7GwhsjjnfHH3Nkrs2xvvw020Rcw5ymdlTnhRenjDdrOO+nfXRVUZVy9q1\
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/8uzsSQk0AbuhxWFQpSiBP8OZ/U="
}
Prorock, et al. Expires 23 April 2023 [Page 10]
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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]
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oobwJ/EsDi5S7TAl8WrjqIhZ8x6h9eRRXerpaOw/FYk+2MpWByp/98VE12/EwOqAIiPp\
elAvUeMOlRkpG64bJsmyYtHuNWgcv5Qiy7/eGw9ZpvB3J3G3jxvbynExqdFyDc067EKi\
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Gw1V92m6/08Dd6zI1HPqwKbkHx4F567owofKHaM2imin0yVUpwxoRJrulRHMCB3tn8C4\
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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\
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Prorock, et al. Expires 23 April 2023 [Page 12]
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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\
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md42yPFrGw5Na1oefm8vW49EDmevc8AjAtwDirRBDFv9pX3+5S+M6jhteSLYvpKJXQT1\
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elAvUeMOlRkpG64bJsmyYtHuNWgcv5Qiy7/eGw9ZpvB3J3G3jxvbynExqdFyDc067EKi\
5WxDFPuZUjkfKpekNvzQuIrqs49BzcRyMt5ndEVE21TPPfZ/R8B7Rxnb2LiK+hQc+cc9\
pEEaWgwAOiMILcp/1CyY6ImdO6RHsxwflMH7gej+hN41kaoEghIOl9kMGTLZbq5Pc8Pz\
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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\
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gYhzRXByGBgzKGVXJUhoGEY1hgFmZWgmEWYWVoISd4Vlhid4VUMHgSZXhXUSaCgmJ3Eg\
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pPfKPD6D+xXgtJ0FWtYnp1Jy2aIG3HqMiTHoSdVIvccGkf94gpVWTMeJQsQpgq7dAJiJ\
5JOMQjk7JIHcIzxb4T8sQHzA55MFfvM7Hus/8FUX7NfIN1JRmc2zHL/7kdfCFSwG67iW\
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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\
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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\
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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:
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+============+====================+
| "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".
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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\
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}
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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.
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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)
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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
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+=============+===============+==============+======+
| 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.
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+======+============+==============+
| 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].
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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
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* 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
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+==============+=====================================+
| 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.
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* 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.
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+==============+=======+====================+=============+
| 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.
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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:
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* 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:
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* 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
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* 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)
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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)
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* 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\
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\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\
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\pzENPHMi6fTCsv0OtEuvPZJkDvE-osJ_3Ajj9eTdKilJDdIYzSKu2Uodc96vaH3bXJW\
\05iBprV6h-nG6MuQuXIrUNiG9h8nQ7MmaJ_Jdr58_cBChxYZRu1zaJcSwpTecAtktv3\
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\0KZ1CPzbzjqQwQdg9CZ1F02b1Kusl42T2OjUylXsDGg4vaF-_IYucO7js31adyf90GZ\
\sMeoLqrwE1txMYJSk9SWSkjpL0csNDHH_sh5911O1ogQk6QoUIf_lMa-hg7EWKJAkP2\
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\bTEcwboddD_vYorb6HHyv9ciM0qh4g7tgmiphuR5b6LiVyqwxrMAN13cU8TiNIveY9A\
\fbS6qJMshNi61lkux4wnM6fpENDxCvRVCCyLB4NhS57fYddsTPiGZ6w1PeS_2Be8J9h\
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Prorock, et al. Expires 23 April 2023 [Page 37]
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Prorock, et al. Expires 23 April 2023 [Page 38]
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Prorock, et al. Expires 23 April 2023 [Page 39]
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Prorock, et al. Expires 23 April 2023 [Page 40]
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8.1.2. NTRU FALCON512
8.1.2.1. publicKeyJwk
Prorock, et al. Expires 23 April 2023 [Page 41]
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8.1.2.2. privateKeyJwk
{"kty":"NTRU","alg":"FALCON512","x":"CjcORWYeLyAc5OSAR5tLh2bn0KXRcAP\
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Prorock, et al. Expires 23 April 2023 [Page 42]
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Prorock, et al. Expires 23 April 2023 [Page 43]
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8.1.2.3. jws
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8.1.3. 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\
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\FXiDh1s38JjCd-y70y1V2UDBclxU4pQXC43GzzakQjF4s_3NQ"}
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8.1.3.3. jws
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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, <https://doi.org/10.13154/tches.v2018.i1.238-268>.
[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, <https://falcon-sign.info/>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC4648] Josefsson, S., "The Base16, Base32, and Base64 Data
Encodings", RFC 4648, DOI 10.17487/RFC4648, October 2006,
<https://www.rfc-editor.org/info/rfc4648>.
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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, <https://www.rfc-editor.org/info/rfc7515>.
[RFC7517] Jones, M., "JSON Web Key (JWK)", RFC 7517,
DOI 10.17487/RFC7517, May 2015,
<https://www.rfc-editor.org/info/rfc7517>.
[RFC7638] Jones, M. and N. Sakimura, "JSON Web Key (JWK)
Thumbprint", RFC 7638, DOI 10.17487/RFC7638, September
2015, <https://www.rfc-editor.org/info/rfc7638>.
[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,
<https://www.rfc-editor.org/info/rfc8702>.
[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,
<https://www.rfc-editor.org/info/rfc8812>.
[SPHINCS-PLUS]
Hulsing, A., "Sphincs+ Stateless Hash-based Signatures",
2017, <https://sphincs.org>.
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,
<https://www.rfc-editor.org/info/rfc6234>.
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]
