Applications Of Chinese Remainder Theorem In Digital Signature

With the development of computer technology and the widespread improvement of electronic communications technology, the information security is more and more focused on. The digital signature is a basic core technology used widely in many fields, such as military affairs, telecommunications, e-commerce and so on. Instead of the traditional handwritten signature, the use of e-signatures can solve the problems of failing to transmit rapidly and remotely, so that the integrity and non-repudiation of data can be achieved. According to different application requirements, traditional digital signature can not meet the needs of diversity of electronic signatures. Therefore, it is important for the direction of the research on statistics identification to develop some digital signatures with special characters to meet special needs. Such as, the proxy signature, group signature, blind signature, group blind signature and so on.The Chinese remainder theorem is a basic mathematical theorem, but plays a very important role in the study of modern cryptography, especially in the appearance of various kinds of encryption and signature algorithm under the public key cryptosystems.Mathematical properties of the Chinese remainder theorem has been used in digital signature, not only ensure calculation simplification of integration of some important secret information, but also can better ensure the privacy of the private key and identity, which increase the security of the program. At the same time, simplify the calculation by controlling the length of the data during the process.Major study includes:Firstly, in order to better achieve the implementation of adding group members or revoking group members, which proposes a group signature scheme using Chinese remainder theorem without changing the secret key of other legal group members.Secondly, the design of group blind signature scheme using Chinese remainder theorem, which based on the new structure of group signature scheme and the characters of blind signature.Thirdly, constructing an efficient and secure group multi-signature scheme based on the Chinese remainder theorem, which can achieve that several groups sign a message together in a safe situation.