At Auscrypt'92, Harn and Yang first proposed the conception of (t,n) threshold undeniable signature, in which only subsets with at least t members can represent a group to generate, confirm or disavow a signature. Later, several schemes are proposed, but none of them is secure. So up to now, how to design a secure (t,n) threshold undeniable signature scheme is remained an open problem. In this paper, based on discrete logarithm cryptosystem, a secure and efficient (t,n) threshold undeniable signature scheme without a trusted party is presented. This scheme has an attractive property that member's honesty is verifiable because a publicly verifiable secret sharing scheme is used to distribute secrets and two discrete logarithm equality protocols are used to provide necessary proofs of correctness, which are proposed by Schoenmakers at Crypto'99.%在1992年澳大利亚密码会议上, Harn and Yang 第一次提出了(t,n)门限不可否认签名的概念.其中,只有成员个数不少于t的子集才能代表群体产生、确认和否认签名.随后,一些研究者又提出了几个方案,但这些方案都是不安全的.因此,到目前为止,怎样设计一个安全的(t,n)门限不可否认签名方案仍然是个公开问题.提出了一个基于离散对数密码系统的(t,n)门限不可否认签名方案.该方案不仅安全、高效,而且不需要可信任方.另外,方案还具有一个很好的性质,即成员的诚实性是可以验证的.这是由于在分发密钥时,采用了Schoenmakers在1999年美洲密码会议上提出的可公开验证秘密共享方案和两个用来提供正确性证据的离散对数恒等式协议.
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