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%%% title = "JOSE and COSE Encoding for Falcon" abbrev = "jose-cose-falcon" ipr= "trust200902" area = "Internet" workgroup = "COSE" submissiontype = "IETF" keyword = ["JOSE","COSE","PQC","FALCON"]

[seriesInfo] name = "Internet-Draft" value = "draft-ietf-cose-falcon-latest" stream = "IETF" status = "standard"

[pi] toc = "yes"

[[author]] initials = "M." surname = "Prorock" fullname = "Michael Prorock" organization = "mesur.io" [author.address] email = "[email protected]"

[[author]] initials = "O." surname = "Steele" fullname = "Orie Steele" organization = "Transmute" [author.address] email = "[email protected]"

[[author]] initials = "R." surname = "Misoczki" fullname = "Rafael Misoczki" organization = "Google" [author.address] email = "[email protected]"

[[author]] initials = "M" surname = "Osborne" fullname = "Michael Osborne" organization = "IBM" [author.address] email = "[email protected]"

[[author]] initials = "C" surname = "Cloostermans" fullname = "Christine Cloostermans" organization = "NXP" [author.address] email = "[email protected]"

%%%

.# Abstract

This document describes JSON and CBOR serializations for Falcon, a Post-Quantum Cryptography (PQC) signature suite.

This document does not define any new cryptography, only seralizations of existing cryptographic systems.

This document registers key types for JOSE and COSE, specifically NTRU.

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 FALCON1024 and others as required for use of various parameterizations of the Falcon post-quantum signature scheme.

Note to RFC Editor: FALCON is described and noted as a part of the 2022 PQC Selected Digital Signature Algorithims As a result, this document should not be proceed to AUTH48 until NIST completes paramter tuning and selection as a part of the PQC standardization process.

{mainmatter}

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].

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].

Falcon

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.

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.

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.

Using FALCON with JOSE

This sections is based on CBOR Object Signing and Encryption (COSE) and JSON Object Signing and Encryption (JOSE)

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

  • 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

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

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".

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.

kty alg Paramter Set
NTRU FALCON512 512
NTRU FALCON1024 1024

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 1024 No

The following tables map terms between JOSE and COSE for key types.

Name Value Description Recommended
NTRU TBD kty for NTRU based digital signatures No

Security Considerations

The following considerations SHOULD apply to all parmeter sets 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.

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.

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.

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 Falcon signing algorithm 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 - care should be given in implementations to preserve the property of uniform sampling in implementation.

Randomness considerations

It is recommended that the all nonces are from a trusted source of randomness.

IANA Considerations

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 Parameters" registry:

  • Parameter Name: "pset"
  • Parameter Description: The parameter set of the crypto system
  • Parameter Information Class: Public
  • Used with "kty" Value(s): "NTRU"
  • 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): "NTRU"
  • 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:

  • Parameter Name: "x"
  • Parameter Description: The public key
  • Parameter Information Class: Public
  • Used with "kty" Value(s): "NTRU"
  • 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: "FALCON512"
  • Algorithm Description: FALCON512 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: "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)

Appendix

General References

  • JSON Web Signature (JWS) - RFC7515
  • JSON Web Encryption (JWE) - RFC7516
  • JSON Web Key (JWK) - RFC7517
  • JSON Web Algorithms (JWA) - RFC7518
  • JSON Web Token (JWT) - RFC7519
  • JSON Web Key Thumbprint - RFC7638
  • JWS Unencoded Payload Option - RFC7797
  • CFRG Elliptic Curve ECDH and Signatures - RFC8037

[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.

<title>Fast-Fourier Lattice-based Compact Signatures over NTRU</title>

Appendix A. Acknowledgements

We would like to especially thank David Balenson for careful review of approaches taken in this document. We would also like to thank Michael B. Jones for guidance in authoring.

Appendix B. Document History

-01

  • Added Acknowledgements
  • Added Document History
  • Updated test vectors

-00

  • Created draft-ietf-cose-falcon-00 from draft-ietf-cose-post-quantum-signatures-01 following working group feedback

Appendix C. Test Vectors

NTRU FALCON512

publicKeyJwk

========== NOTE: '\' line wrapping per RFC 8792 ==========
{
  "kty": "NTRU",
  "alg": "FALCON512",
  "x": "TUlJRGp6QUhCZ1Vyemc4REJnT0NBNElBQ1g3ZElvVGR5ajZmN3VmME5vbWJP\
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eG9YMXpsRFZuNzFHMHZkRjBxUGJnV3BKbFZhQ3M1VHlSRlgxR0NZbmJvY2lBR3dKUito\
ekE5SnNKeGJ4TDVBUlNWR3J3Zlg2UEVJM0gvNUpreU1jSEdnNFdoZmJHbzQ4TEdFVlFx\
YVpXUkJHNG96aU00TU9HWGFPTHBZNFJSKzB0TVRnT0lpK0sxUWl1TFBkbjhUK0dJK1c5\
cDFTNTVBU0VHeGRBRFpKZmFSRkZaQll6b1VaeWJtRmt1WmJuUkVGOXh2QzlBbnc3L3Ay\
cG9HUXRwUGpkVlFZc1MxOUVjVWlCQmRhdU1HLzEya1FDTEhZMjlKL0orU2tFR0hKVTFr\
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c1RWMHI5TXJJcjRjTzRNYXBvTTBWbmJZTDA2d25SL2pzTTVPRFhxMVJ5blRMbGFXN29z\
cDA3TUFmQUhDd2V4M1p0bkFNZUFaUVJ4T0Yza1F3QU1reElITE01aThzMmFHTjJtV3FX\
VHR5cGlqMEw4eExtUzBhNXBUR2FWb1lhbnZrV1M1UC9CRjdER3hEUmtxdm1SbERyVXdo\
UjY",
  "use": "sig"
}

privateKeyJwk

========== NOTE: '\' line wrapping per RFC 8792 ==========
{
  "kty": "NTRU",
  "alg": "FALCON512",
  "x": "TUlJRGp6QUhCZ1Vyemc4REJnT0NBNElBQ1g3ZElvVGR5ajZmN3VmME5vbWJP\
ekVtNG84U3JCMytYdWFveTA1cFFjVkpsWUF0VFkzcWsxcUNZcnJOdU9saXI5OC84dHh5\
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{backmatter}