Solving the Tensor Isomorphism Problem for special orbits with low rank points:  Cryptanalysis and repair of an Asiacrypt 2023 commitment scheme

Valerie Gilchrist; Laurane Marco; Christophe Petit; Gang Tang

Paper 2024/337

Solving the Tensor Isomorphism Problem for special orbits with low rank points: Cryptanalysis and repair of an Asiacrypt 2023 commitment scheme

Valerie Gilchrist, Université Libre de Bruxelles

Laurane Marco, École Polytechnique Fédérale de Lausanne

Christophe Petit, Université Libre de Bruxelles

Gang Tang, University of Technology Sydney

Abstract

The Tensor Isomorphism Problem (TIP) has been shown to be equivalent to the matrix code equivalence problem, making it an interesting candidate on which to build post-quantum cryptographic primitives. These hard problems have already been used in protocol development. One of these, MEDS, is currently in Round 1 of NIST's call for additional post-quantum digital signatures. In this work, we consider the TIP for a special class of tensors. The hardness of the decisional version of this problem is the foundation of a commitment scheme proposed by D'Alconzo, Flamini, and Gangemi (Asiacrypt 2023). We present polynomial-time algorithms for the decisional and computational versions of TIP for special orbits, which implies that the commitment scheme is not secure. The key observations of these algorithms are that these special tensors contain some low-rank points, and their stabilizer groups are not trivial. With these new developments in the security of TIP in mind, we give a new commitment scheme based on the general TIP that is non-interactive, post-quantum, and statistically binding, making no new assumptions. Such a commitment scheme does not currently exist in the literature.

Note: Updated proofs and small corrections.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: tensor rank matrix equivalence commitment scheme stabilizer
Contact author(s): valerie gilchrist @ ulb be
laurane marco @ epfl ch
christophe petit @ ulb be
gang tang-1 @ student uts edu au
History: 2024-04-30: revised; 2024-02-26: received; See all versions
Short URL: https://ia.cr/2024/337
License: CC BY

BibTeX

@misc{cryptoeprint:2024/337,
      author = {Valerie Gilchrist and Laurane Marco and Christophe Petit and Gang Tang},
      title = {Solving the Tensor Isomorphism Problem for special orbits with low rank points:  Cryptanalysis and repair of an Asiacrypt 2023 commitment scheme},
      howpublished = {Cryptology ePrint Archive, Paper 2024/337},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/337}},
      url = {https://eprint.iacr.org/2024/337}
}