Some Digital Signature Schemes Based On Cubic Residues

As one of the most important research content, the technology ofdigital signature occupy an important position in the field of informationsecurity by the feature of message integrity, identity authentication,non-repudiation. With the development of the fields of cloud computing,electronic commerce, electronic voting and so on, normal digitalsignature schemes cannot satisfy the particular demands of theseapplication scenes.In this paper, we mainly research some special signature schemesbased on cubic residue theory. Williams and Cao simulate the Rabinscheme and Goldwasser and Micali scheme based on cubic residues at theearliest. Blind signature and group signature are two kinds of specialsignature that are widely used. In a scheme of blind signature, themessage owners can have the message signers to generate a signature forthem, but they won’t disclose the content of the message to the signers. Ina scheme of group signature, any members in the group can sign amessage on the behalf of the entire group, the verifier verifies thesignature with the only group public key.This article first introduces some related mathematical knowledgeand cryptography knowledge. Then we will propose a new blindsignature scheme based on the theory of cubic residue. The security of thescheme is based on the difficult problem of factorization. By acomparison with blind signature scheme based on quadratic residue ofsecurity and efficiency, we can see our scheme is suitable for occasionsthat require high security and own powerful computation.We also propose a group signature scheme based on Xing’sidentity-based signature scheme and the method to transform anidentity-based signature scheme into a group signature scheme. Thescheme achieves the purpose of revoking the specified user through theparticipation of intermediate institutions, and then we analyze the anonymity, unforgeability, exculpability, traceability and other securefeatures of this scheme.