Security Analysis of the Gennaro-Halevi-Rabin Signature Scheme

We exhibit an attack against a signature scheme recently proposed by Gennaro, Halevi and Rabin [9]. The scheme’s security is based on two assumptions namely the strong RSA assumption and the existence of a division-intractable hash-function. For the latter, the authors conjectured a security level exponential in the hash-function’s digest size whereas our attack is sub-exponential with respect to the digest size. Moreover, since the new attack is optimal, the length of the hash function can now be rigorously fixed. In particular, to get a security level equivalent to 1024-bit RSA, one should use a digest size of approximately 1024 bits instead of the 512 bits suggested in [9].