Efficient multiple-collision trapdoor hash family

In this paper, we suggest a Q2 multiple-collision trapdoor hash family under both integer factoring and discrete logarithm problems, and we present their security proofs. In multiple-collision trapdoor hash family, exposing multiple collisions of similar hash functions will not disclose the private key of trapdoor hash value. In the proposed multiple-collision trapdoor hash family, a pair of secret keys is employed for generating digital signature. Under the suggested trapdoor hash family, we present competitive online and off-line signature schemes that can considerably enhance the efficiency of online and off-line signature schemes. Moreover, in the proposed signature scheme, a trapdoor hash function can be employed for signing multiple documents. When a signer embraces this approach in the public-key digital certificate, there is no need to include an ordinary digital signature scheme to sign the hash function in the off-line part. Copyright # 2011 John Wiley & Sons, Ltd.