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Polynomial lattices for the BIKE cryptosystem
1Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, Zurich, 8057 Switzerland.
Cryptography and Communications : Discrete Structures, Boolean Functions and Sequences
|October 10, 2026
Abstract:
In this paper we introduce a rank [Formula: see text] lattice over a polynomial ring arising from the public key of the BIKE cryptosystem (2024). The secret key is a sparse vector in this lattice. We study properties of this lattice and generalize the recovery of weak keys from Bardet, Dragoi, Luque and Otmani (2016). 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.