SEVERAL CRYPTOGRAPHIC APPLICATIONS OF ∑-PROTOCOL

Σ-protocol has been proved to be a very powerful cryptographic tool and widely used innumerous important cryptographic applications.In this paper,the authors make use of Σ-protocol asa main tool to resolve the following difficult problems 1-3 and to construct three efficient cryptographicprotocols 4-6:1) How to construct a protocol for proving a secret integer to be a Blum integer with form PQ,whereP,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 in a (t,n)-threshold secret sharing scheme;3) How to construct witness iudistinguishable and witness hiding protocol not from zero-knowledgeproof;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.