{"ID":2888425,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.23641","arxiv_id":"2507.23641","title":"Polynomial Lattices for the BIKE Cryptosystem","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.","short_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 schem...","url_abs":"https://arxiv.org/abs/2507.23641","url_pdf":"https://arxiv.org/pdf/2507.23641v2","authors":"[\"Michael Schaller\"]","published":"2025-07-31T15:18:52Z","proceeding":"cs.CR","tasks":"[\"cs.CR\"]","methods":"[]","has_code":false}