Use of the Walnut Digital Signature Algorithm with CBOR Object Signing and Encryption (COSE)
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Security
Internet Engineering Task Force
COSE
WalnutDSA
This document specifies the conventions for using the Walnut Digital
Signature Algorithm (WalnutDSA) for digital signatures with the CBOR
Object Signing and Encryption (COSE) syntax. WalnutDSA is a
lightweight, quantum-resistant signature scheme based on Group Theoretic
Cryptography with implementation and computational efficiency of
signature verification in constrained environments, even on 8- and
16-bit platforms.
The goal of this publication is to document a way to use the
lightweight, quantum-resistant WalnutDSA signature algorithm in
COSE in a way that would allow multiple developers to build
compatible implementations. As of this publication, the
security properties of WalnutDSA have not been evaluated by the
IETF and its use has not been endorsed by the IETF.
WalnutDSA and the Walnut Digital Signature Algorithm are
trademarks of Veridify Security Inc.
Introduction
This document specifies the conventions for using the Walnut Digital
Signature Algorithm (WalnutDSA) for digital signatures with the CBOR Object Signing
and Encryption (COSE) syntax .
WalnutDSA is a Group Theoretic signature scheme where signature validation is both computationally and
space efficient, even on very small processors. Unlike many hash-based
signatures, there is no state required and no limit on the number of
signatures that can be made. WalnutDSA private and public keys are
relatively small; however, the signatures are larger than RSA and
Elliptic Curve Cryptography (ECC), but still smaller than most all other
quantum-resistant schemes (including all hash-based schemes).
COSE provides a lightweight method to encode structured data.
WalnutDSA is a lightweight, quantum-resistant digital
signature algorithm. The goal of this specification is to
document a method to leverage WalnutDSA in COSE in a way that
would allow multiple developers to build compatible
implementations.
As with all cryptosystems, the initial versions of WalnutDSA
underwent significant cryptanalysis, and, in some cases, identified
potential issues. For more discussion on this topic, a summary of all
published cryptanalysis can be found in . Validated issues were addressed by
reparameterization in updated versions of WalnutDSA. Although the IETF
has neither evaluated the security properties of WalnutDSA nor endorsed
WalnutDSA as of this publication, this document provides a method to use
WalnutDSA in conjunction with IETF protocols. As always, users of any
security algorithm are advised to research the security properties of
the algorithm and make their own judgment about the risks involved.
Motivation
Recent advances in cryptanalysis and progress in the development of quantum
computers pose a threat to
widely deployed digital signature algorithms. As a result, there is a
need to prepare for a day that cryptosystems such as RSA and DSA,
which depend on discrete logarithm and factoring, cannot be depended
upon.
If large-scale quantum computers are ever built, these computers
will be able to break many of the public key cryptosystems currently
in use. A post-quantum cryptosystem is a system that is secure against quantum
computers that have more than a trivial number of quantum bits
(qubits). It is open to conjecture when it will be feasible to build
such computers; however, RSA, DSA, the Elliptic Curve Digital
Signature Algorithm (ECDSA), and the Edwards-Curve Digital Signature
Algorithm (EdDSA) are all vulnerable if large-scale quantum computers
come to pass.
WalnutDSA does not depend on the difficulty of discrete
logarithms or factoring. As a result, this algorithm is
considered to be resistant to post-quantum attacks.
Today, RSA and ECDSA are often used to digitally sign
software updates. Unfortunately, implementations of RSA and
ECDSA can be relatively large, and verification can take a
significant amount of time on some very small processors.
Therefore, we desire a digital signature scheme that verifies
faster with less code. Moreover, in preparation for a day
when RSA, DSA, and ECDSA cannot be depended upon, a digital
signature algorithm is needed that will remain secure even if
there are significant cryptanalytic advances or a large-scale
quantum computer is invented. WalnutDSA, specified in , is a quantum-resistant algorithm
that addresses these requirements.
Trademark Notice
WalnutDSA and the Walnut Digital Signature Algorithm are
trademarks of Veridify Security Inc.
Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL
NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED",
"MAY", and "OPTIONAL" in this document are to be interpreted as
described in BCP 14
when, and only when, they appear in all capitals, as shown here.
WalnutDSA Algorithm Overview
This specification makes use of WalnutDSA signatures as
described in and more concretely
specified in . WalnutDSA is a
Group Theoretic cryptographic signature scheme that leverages
infinite group theory as the basis of its security and maps that
to a one-way evaluation of a series of matrices over small
finite fields with permuted multiplicants based on the group
input. WalnutDSA leverages the SHA2-256 and SHA2-512 one-way
hash algorithms in a hash-then-sign
process.
WalnutDSA is based on a one-way function, E-multiplication,
which is an action on the infinite group. A single
E-multiplication step takes as input a matrix and permutation, a
generator in the group, and a set of T-values (entries in the
finite field) and outputs a new matrix and permutation. To
process a long string of generators (like a WalnutDSA
signature), E-multiplication is iterated over each generator.
Due to its structure, E-multiplication is extremely easy to
implement.
In addition to being quantum resistant, the two main benefits
of using WalnutDSA are that the verification implementation is
very small and WalnutDSA signature verification is extremely
fast, even on very small processors (including 16- and even
8-bit microcontrollers). This lends it well to use in constrained and/or
time-sensitive environments.
WalnutDSA has several parameters required to process a signature.
The main parameters are N and q. The parameter N defines the size of
the group by defining the number of strands in use and implies working
in an NxN matrix. The parameter q defines the number of elements in the
finite field. Signature verification also requires a set of T-values,
which is an ordered list of N entries in the finite field F_q.
A WalnutDSA signature is just a string of generators in the
infinite group, packed into a byte string.
WalnutDSA Algorithm Identifiers
The CBOR Object Signing and Encryption (COSE) syntax supports two signature algorithm schemes.
This specification makes use of the signature with appendix scheme for
WalnutDSA signatures.
The signature value is a large byte string. The byte string is
designed for easy parsing, and it includes a length (number of
generators) and type codes that indirectly provide all of the
information that is needed to parse the byte string during
signature validation.
When using a COSE key for this algorithm, the following checks are
made:
- The "kty" field MUST be present, and it
MUST be "WalnutDSA".
- If the "alg" field is present, it MUST be "WalnutDSA".
- If the "key_ops" field is present, it MUST include "sign" when
creating a WalnutDSA signature.
- If the "key_ops" field is present, it MUST include "verify"
when verifying a WalnutDSA signature.
- If the "kid" field is present, it MAY be used to identify the
WalnutDSA Key.

Security Considerations
Implementation Security Considerations
Implementations MUST protect the private keys. Use of a hardware
security module (HSM) is one way to protect the private keys.
Compromising the private keys may result in the ability to forge
signatures. As a result, when a private key
is stored on non-volatile media or stored in a virtual machine
environment, care must be taken to preserve confidentiality and
integrity.
The generation of private keys relies on random numbers. The use of
inadequate pseudorandom number generators (PRNGs) to generate these
values can result in little or no security. An attacker may find it
much easier to reproduce the PRNG environment that produced the keys,
searching the resulting small set of possibilities, rather than brute
force searching the whole key space. The generation of quality
random numbers is difficult, and
offers important guidance in this area.
The generation of WalnutDSA signatures also depends on random
numbers. While the consequences of an inadequate PRNG to generate
these values are much less severe than the generation of private keys,
the guidance in remains
important.
Method Security Considerations
The Walnut Digital Signature Algorithm has undergone
significant cryptanalysis since it was first introduced, and
several weaknesses were found in early versions of the method,
resulting in the description of several attacks with exponential
computational complexity.
A full writeup of all the analysis can be found in
. In summary,
the original suggested parameters (N=8, q=32) were too small, leading to
many of these exponential-growth attacks being practical. However, current
parameters render these attacks impractical. The following
paragraphs summarize the analysis and how the current
parameters defeat all the previous attacks.
First, the team of Hart et al. found a universal forgery attack
based on a group-factoring problem that runs in O(q^{(N-1)/2})
with a memory complexity of log_2(q) N^{2}
q^{(N-1)/2}. With parameters N=10 and q=M31 (the Mersenne
prime 2^{31} - 1), the runtime is 2^{139} and memory
complexity is 2^{151}. W. Beullens found a modification
of this attack but its runtime is even longer.
Next, Beullens and Blackburn found several issues with the
original method and parameters. First, they used a Pollard-Rho
attack and discovered the original public key space was too
small. Specifically, they require that q^{N(N-1)-1} >
2^{2*Security Level}. One can clearly see that (N=10, q=M31)
provides 128-bit security and (N=10, q=M61) provides 256-bit
security.
Beullens and Blackburn also found two issues with the
original message encoder of WalnutDSA. First, the original
encoder was non-injective, which reduced the available
signature space. This was repaired in an update. Second,
they pointed out that the dimension of the vector space
generated by the encoder was too small. Specifically, they
require that q^{dimension} > 2^{(2*Security Level)}. With N=10,
the current encoder produces a dimension of 66, which clearly
provides sufficient security with q=M31 or q=M61.
The final issue discovered by Beullens and Blackburn was a process
to theoretically "reverse" E-multiplication. First, their process
requires knowing the initial matrix and permutation (which are known
for WalnutDSA). But more importantly, their process runs at
O(q^{((N-1)/2)}), which for (N=10, q=M31) is greater than
2^{128}.
A team at Steven's Institute leveraged a length-shortening
attack that enabled them to remove the cloaking elements and
then solve a conjugacy search problem to derive the private
keys. Their attack requires both knowledge of the permutation
being cloaked and also that the cloaking elements themselves
are conjugates. By adding additional concealed cloaking
elements, the attack requires an N! search for each cloaking
element. By inserting k concealed cloaking elements, this
requires the attacker to perform (N!)^{k} work. This allows
k to be set to meet the desired security level.
Finally, Merz and Petit discovered that using a Garside
Normal Form of a WalnutDSA signature enabled them to find
commonalities with the Garside Normal Form of the encoded
message. Using those commonalities, they were able to splice
into a signature and create forgeries. Increasing the number
of cloaking elements, specifically within the encoded message,
sufficiently obscures the commonalities and blocks this
attack.
In summary, most of these attacks are exponential in runtime and it
can be shown that current parameters put the runtime beyond the
desired security level. The final two attacks are also sufficiently
blocked to the desired security level.
IANA Considerations
IANA has added entries for WalnutDSA signatures in the
"COSE Algorithms" registry and WalnutDSA public keys in the "COSE
Key Types" and "COSE Key Type Parameters" registries.
COSE Algorithms Registry Entry
The following new entry has been registered in the "COSE Algorithms" registry:
- Name:
- WalnutDSA
- Value:
- -260
- Description:
- WalnutDSA signature
- Reference:
- RFC 9021
- Recommended:
- No

COSE Key Types Registry Entry
The following new entry has been registered in the "COSE Key Types" registry:
- Name:
- WalnutDSA
- Value:
- 6
- Description:
- WalnutDSA public key
- Reference:
- RFC 9021

COSE Key Type Parameters Registry Entries
The following sections detail the additions to the "COSE Key Type Parameters" registry.
WalnutDSA Parameter: N
The new entry, N, has been registered in the "COSE Key Type Parameters" registry
as follows:
- Key Type:
- 6
- Name:
- N
- Label:
- -1
- CBOR Type:
- uint
- Description:
- Group and Matrix (NxN) size
- Reference:
- RFC 9021

WalnutDSA Parameter: q
The new entry, q, has been registered in the "COSE Key Type Parameters" registry
as follows:
- Key Type:
- 6
- Name:
- q
- Label:
- -2
- CBOR Type:
- uint
- Description:
- Finite field F_q
- Reference:
- RFC 9021

WalnutDSA Parameter: t-values
The new entry, t-values, has been registered in the "COSE Key Type Parameters" registry
as follows:
- Key Type:
- 6
- Name:
- t-values
- Label:
- -3
- CBOR Type:
- array (of uint)
- Description:
- List of T-values, entries in F_q
- Reference:
- RFC 9021

WalnutDSA Parameter: matrix 1
The new entry, matrix 1, has been registered in the "COSE Key Type Parameters" registry
as follows:
- Key Type:
- 6
- Name:
- matrix 1
- Label:
- -4
- CBOR Type:
- array (of array of uint)
- Description:
- NxN Matrix of entries in F_q in column-major form
- Reference:
- RFC 9021

WalnutDSA Parameter: permutation 1
The new entry, permutation 1, has been registered in the "COSE Key Type Parameters" registry
as follows:
- Key Type:
- 6
- Name:
- permutation 1
- Label:
- -5
- CBOR Type:
- array (of uint)
- Description:
- Permutation associated with matrix 1
- Reference:
- RFC 9021

WalnutDSA Parameter: matrix 2
The new entry, matrix 2, has been registered in the "COSE Key Type Parameters" registry
as follows:
- Key Type:
- 6
- Name:
- matrix 2
- Label:
- -6
- CBOR Type:
- array (of array of uint)
- Description:
- NxN Matrix of entries in F_q in column-major form
- Reference:
- RFC 9021

References
Normative References
Secure Hash Standard (SHS)
National Institute of Standards and Technology (NIST)
WalnutDSA(TM): A group theoretic digital signature algorithm
Informative References
The Walnut Digital Signature Algorithm Specification
Post-Quantum Cryptography
Group Theoretic Cryptography
Defeating the Hart et al, Beullens-Blackburn, Kotov-Menshov-Ushakov, and Merz-Petit Attacks on WalnutDSA(TM)
The Factoring Dead: Preparing for the Cryptopocalypse
Quantum Computing: Progress and Prospects
National Academies of Sciences, Engineering, and Medicine
Introduction to post-quantum cryptography
Acknowledgments
A big thank you to for his input
on the concepts and text of this document.