On the length of cryptographic hash-values used in identification schemes

Many interactive identification schemes based on the zero-knowledge concept use cryptographic hash-values, either in their basic design or in specific variants. In this paper, we first show that 64-bit hash-values, a length often suggested, definitely decrease the level of the security of all these schemes. (Of course, this does not compromise the security of the schemes by themselves). Then we prove that collision-resistance is a sufficient condition to achieve the claimed level of security. Finally, by using a weaker notion of collision-resistance, we present interesting variants of some of these schemes (in particular the Schnorr and the Guillou-Quisquater schemes) which minimize the number of communication bits for a given level of security.