Binding BIKE errors to a key pair.

The KEM BIKE is a Round-3 alternative finalist in the NIST Post-Quantum Cryptography project. It uses the FO\(^{\not \bot }\) transformation so that an instantiation with a decoder that has a DFR of \(2^{-128}\) will make it IND-CCA secure. The current BIKE design does not bind the randomness of the ciphertexts (i.e., the error vectors) to a specific public key. We propose to change this design, although currently, there is no attack that leverages this property. This modification can be considered if BIKE is eventually standardized.