摘要
∑-protocol has been proved to be a very powerful cryptographic tool and widely used in nnmerous important cryptographic applications. In this paper, the authors make use of ∑-protocol as a main tool to resolve the following difficult problems 1-3 and to construct three ettlcient cryptographic protocols 4 6：1） How to construct a protocol for proving a secret integer to be a Blum integer with form PQ, where P, Q are two different primes and both -- 3（mod 4）;2） How to construct a protocol for proving a secret polynomial with exact degree t - 1 iil a （t, n）- threshold secret sharing scheme：3） How to construct witness indistinguishable and witness hiding protocol not from zero-knowledge proof;4） A publicly verifiable secret sharing scheme with information-theoretic security;5） A delegateable signature scheme under the existence of one-way permutations;6） Non-interactive universal designated verifier signature schemes.
基金
supported by the Foundation of tihe National Natural Science of China under Grant Nos 90604034 (Key Project), 10726012, 10871222, 10531040,and 10471156
