TRIFORS: LINKable Trilinear Forms Ring Signature

Giuseppe D'Alconzo; Andrea Gangemi

Paper 2022/1170

TRIFORS: LINKable Trilinear Forms Ring Signature

Giuseppe D'Alconzo

, Polytechnic University of Turin

Andrea Gangemi

, Polytechnic University of Turin

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 us 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, and taking into account the attack of Beullens from Crypto 2023, we obtain a (linkable) ring signature of competitive length with the state-of-the-art among post-quantum proposals for security level 128.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. Journal of Algebra and Its Applications
DOI: https://doi.org/10.1142/S0219498826502841
Keywords: Tensor Isomorphism Alternating Trilinear Forms Ring Signatures Linkable Ring Signatures
Contact author(s): giuseppe dalconzo @ polito it
andrea gangemi @ polito it
History: 2025-07-15: last of 3 revisions; 2022-09-07: received; See all versions
Short URL: https://ia.cr/2022/1170
License: 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},
      doi = {https://doi.org/10.1142/S0219498826502841},
      url = {https://eprint.iacr.org/2022/1170}
}