In this talk we study the BIKE cryptosystem. We will introduce a lattice
over a polynomial ring which we construct from the public key. The
private key is a vector in this lattice with special properties (being
sparse). We study the properties of this lattice.
Furthermore, using this framework we will reformulate a previous work
about weak keys for BIKE in terms of this lattice and show that their
weak keys correspond to shortest vectors in this rank 2 lattice. Instead
of only finding the shortest vector, we are able to construct a reduced
basis and generalize their attack.
We also propose new problems which arise from the reformulation of their
attack in terms of lattices.
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