The syzygy distinguisher

Hugues RANDRIAMBOLOLONA

Paper 2024/1193

The syzygy distinguisher

Hugues RANDRIAMBOLOLONA

, ANSSI

Abstract

We present a new distinguisher for alternant and Goppa codes, whose complexity is subexponential in the error-correcting capability, hence better than that of generic decoding algorithms. Moreover it does not suffer from the strong regime limitations of the previous distinguishers or structure recovery algorithms: in particular, it applies to the codes used in the Classic McEliece candidate for postquantum cryptography standardization. The invariants that allow us to distinguish are graded Betti numbers of the homogeneous coordinate ring of a shortening of the dual code. Since its introduction in 1978, this is the first time an analysis of the McEliece cryptosystem breaks the exponential barrier.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Contact author(s): hugues randriam @ ssi gouv fr
History: 2024-07-25: approved; 2024-07-24: received; See all versions
Short URL: https://ia.cr/2024/1193
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1193,
      author = {Hugues RANDRIAMBOLOLONA},
      title = {The syzygy distinguisher},
      howpublished = {Cryptology ePrint Archive, Paper 2024/1193},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/1193}},
      url = {https://eprint.iacr.org/2024/1193}
}