The Research Of Several Kinds Of Threshold Digital Sienature Schemes

In recent years, the theory of digital signature technology has been widely used in finance, commerce, military and other fields. By applying the technology of secret sharing to general group signature scheme, we can obtain the threshold digital signature scheme. A (t,n) threshold digital signature scheme means that in a group of n members, it will produce a valid group signature on behalf of the entire group when the users of participant are equal to or more than the threshold value t. This paper first introduces the research background and significance of threshold digital signature, and then proposes three threshold digital signature schemes based on different problems of intractability. The main contributions are as follows:1. In most of the existing threshold digital signature schemes, any t users can cooperate to produce a valid group signature. However, in some specific cases, we need some special users who have the property that we called one-vote veto, such as signing a significant military document, a solely invested enterprise’s contract and so on. We present a directed threshold signature scheme based on the deformation of DSA in chapter2. The scheme not only can solve the above problem, but also have the property that the procedures of verifying the signature can be operated only with the consent of the designated recipient.2. Based on the difficulty of solving the elliptic curve discrete logarithm problem, we present a new threshold signature scheme in chapter3. The proposed scheme overcomes some deficiencies in the most existing schemes:unable to track the signer’s identity, unable to withstand the conspiracy attack and poor stability.3. Based on the difficulty of solving computational Diffe-Hellman problem with respect to bilinear pairing, a proxy threshold ring signature scheme is first proposed in chapter4, which integrates the idea of threshold ring signature scheme and proxy signature scheme. We also give the proof of security in the random oracle model. This scheme has the property of practicability in electronic voting.