Polynomial Lattices for the BIKE Cryptosystem

Michael Schaller

Paper 2025/1393

Polynomial Lattices for the BIKE Cryptosystem

Michael Schaller, University of Zurich

Abstract

In this paper we introduce a rank $2$ lattice over a polynomial ring arising from the public key of the BIKE cryptosystem. The secret key is a sparse vector in this lattice. We study properties of this lattice and generalize the recovery of weak keys from "Weak keys for the quasi-cyclic MDPC public key encryption scheme". In particular, we show that they implicitly solved a shortest vector problem in the lattice we constructed. Rather than finding only a shortest vector, we obtain a reduced basis of the lattice which makes it possible to check for more weak keys.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Cryptography and Communications
DOI: 10.1007/s12095-026-00875-1
Keywords: Cryptography Coding Theory Polynomials Lattices
Contact author(s): michael schaller @ math uzh ch
History: 2026-02-23: revised; 2025-08-01: received; See all versions
Short URL: https://ia.cr/2025/1393
License: CC BY-SA

BibTeX

@misc{cryptoeprint:2025/1393,
      author = {Michael Schaller},
      title = {Polynomial Lattices for the {BIKE} Cryptosystem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1393},
      year = {2025},
      doi = {10.1007/s12095-026-00875-1},
      url = {https://eprint.iacr.org/2025/1393}
}