Analysis Of Several Kinds Of Threshold Signature Schemes And Secret Sharing Schemes

In the network environment, we need to store and transfer a large amount of information. Digital signature technology is a new information security technology to ensure the effectiveness of information transmission and solve the contradiction of the communication. Secret sharing is a secret segmentation stored password technology, it is an important means for information security and date security. The master thesis is composed of the following four chapters:In chapter one, we briefly introduce the historical background of digital sig-nature and secret sharing and main tasks of this article.In chapter two, we introduce a threshold group signature scheme based on discrete logarithm.Based on intractability of discrete logarithm, a new threshold group signature scheme is proposed in this chapter with interpolation polynomial. This scheme is unforgeability and can resist conspiracy attack. The analysis from security and correctness shows that the scheme is secure.In chapter three, we introduce a threshold partially blind signature scheme based on bilinear map.In the chapter, the security of the signature scheme is based on discrete logarithm and bilinear map. We introduce a threshold signature scheme in detail, and the analysis from security shows that the scheme is unforgeable.In chapter four, we introduce a threshold secret sharing scheme based on ELGamal deformation.In the chapter, the security of the signature scheme is based on discrete logarithm, but this scheme is different from the general secret sharing scheme. The introduction gives a concrete application example, there is a one-vote veto phenomenon appears in the example, and it is not common in a secret sharing scheme. In this scheme, there is a secret distributor who plays an important role in the generation of secret share and secret recovery, so it is important to select the secret distributor.