A Threshold Group Signature Scheme Based On Mignotte Sequence And A Designated Verifier Signature Scheme Based On Braid Group

Digital signature can be used to authenticate the identity of the signer and ptotect data integrity as the analogue of normal signature. Signer computes the signature according to the algorithm with secret key and the message. Any opponent cannot forge the signature for he doesn't know the secret key of the signer. The verifier can verify the signature with the public information.For example, a couple of people vote on a document in a meeting. It is a valid signature if the signature is created by more than given number of people. A threshold group signature scheme is a solution to this problem. Our threshold signature scheme combines the speciality of Mignotte Sequence with the Chinese Remainder Theorem. Signature is accomplished and get across the verification when no less than tenties are involved in this signature.Another utilization: digital bid. Supposed that a institution initiates a call for tenders, asking some companies to propose their prices for a set of instruments. A company may capture a competitor's signed offer on the transmission line and prepares its offer consequently in order to increase its chance to be selected . To prevent this, the companies may encrypt their offers and signatures in order that they may only be read and verified by the institution. But nothing prevents the latter to reveal them once decrypted. Indeed, since the institution's goal is to obtain a good price (as low as possible). It could show some signed offers to some other companies to influence them in making good offers. Our second scheme is a solution to this problem. With such designated verifier signature, while the institution is convinced about the origin and the authenticity of an offer, it cannot transfer this conviction to others unless it reveal its own secret key used in verification. The security of this scheme based on the difficulty of the mathematical hard problem in braid group. Another superiority is that it can conceal the message to be signed. It is unnecessary to encrypt the message before signing it. Only the institution can recover the message and verify the signature.