### TRIFORS: LINKable Trilinear Forms Ring Signature

##### Abstract

We present TRIFORS (TRIlinear FOrms Ring Signature), a logarithmic post-quantum (linkable) ring signature based on a novel assumption regarding the equivalence of alternating trilinear forms. The basis of this work is the construction by Beullens, Katsumata and Pintore from Asiacrypt 2020 to obtain a linkable ring signature from a cryptographic group action. The group action on trilinear forms used here is the same employed in the signature presented by Tang et al. at Eurocrypt 2022. We first define a sigma protocol that, given a set of public keys, the ring, allows to prove the knowledge of a secret key corresponding to a public one in the ring. Furthermore, some optimisations are used to reduce the size of the signature: among others, we use a novel application of the combinatorial number system to the space of the challenges. Using the Fiat-Shamir transform, we obtain a (linkable) ring signature of competitive length with the state-of-the-art among post-quantum proposals for security levels 128 and 192.

Note: Revision: minor fixes and new set of parameters

Available format(s)
Category
Public-key cryptography
Publication info
Preprint.
Keywords
Tensor Isomorphism Alternating Trilinear Forms Ring Signatures Linkable Ring Signatures
Contact author(s)
giuseppe dalconzo @ polito it
andrea gangemi @ polito it
History
2022-11-24: last of 2 revisions
See all versions
Short URL
https://ia.cr/2022/1170

CC BY

BibTeX

@misc{cryptoeprint:2022/1170,
author = {Giuseppe D'Alconzo and Andrea Gangemi},
title = {TRIFORS: LINKable Trilinear Forms Ring Signature},
howpublished = {Cryptology ePrint Archive, Paper 2022/1170},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1170}},
url = {https://eprint.iacr.org/2022/1170}
}

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