Signature And Signcryption On Conic Curve

Public key cryptography is an important reform in the history of modern cryptography science. It solved two most difficult problems in symmetric cryptography, key distribution and digital signature. The main feature of public key cryptography algorithm is the use of two related keys to separate the function of encryption and decryption compared with symmetric cryptography, and it is too hard to compute decryption key with knowing the encryption algorithm and the encryption key.The role of message authentication is to protect the communication parties to prevent the attacks from the third-party, but it can’t protect the fraud from the other party in communication. As there are many fraudulence forms in communication, and if it doesn’t establish the trust relationship and exists much conflict in both sides, single message authentication becomes insufficient. Signature can resolve this problem.Digital signature is a cryptography which can achieve the authentication for a message or document. Its main purpose is to ensure the authenticity and reliability of the sources of information. A valid signature message can make receiver verify the identity of the signer,signature date and the truth of signed message.Signcryption is a cryptographic primitive that fulfills both the functions of digital signature and public key encryption simultaneously, at a cost significantly lower than that required by the traditional signature-then-encryption approach. If combining the digital signature with special properties and signcryption, it can produce some signcryption with special properties. Thus the development of signcryption technology has aroused great interest to many scholars in recent years.The conic curve over ring Zn is a new type algebraic curve. As the plaintext can be embedded easily onto the conic curve, and the inverse, the element order and points operation on conic curve can be calculated more simply and easily, the cryptography on conic curve has been gradually developed and perfected in recent years. Various properties of digital signatures and digital signcryption on conic curve has been achieved and digital simulated. The main purpose of this paper is further to study the properties of cryptographic on conic curve, and some special digital signatures and digital signcryption were obtained by using the cryptology based on conic curve. The main results include the following:The first part, a new concurrent signature protocol was proposed in this paper by using the public key cryptosystem on conic curve. Compared with the exist one, it not only has higher efficiency, but also was proved to be unforgeable, fair, ambiguous under the random oracle model.Second, a new perfect concurrent signature scheme was put forward by use the public key cryptosystem on conic curve. As the keystone fix of ambiguity signatures is generated by both sides together, it achieves the true fairness to both sides. On the other hand, to avoid the traceability attack, each fix-keystone is bound with signed plaintext respectively. At the same time, the scheme is unforgeable also based on the difficult problem of discrete logarithm in conic curves, thus the scheme has the properties of more strong fairness and more security.Third, a certificateless strong designated verifier signature scheme was presented by using the public key cryptosystem and signature scheme on conic curve, which solves the key management problem and the key escrow problems and privacy protection in tradition public key cryptography. It was proved that there are properties of unforgeable and strong designated under the discrete logarithm problem on conic curve and large number factorization problem under the random oracle model. Compared it with the exist scheme, it reduces two times pair operation and one time hash operation. Thus it has higher efficiency in sign and verify algorithms.Fourth, in view of the shortcoming of computation in e-probabilistic non-repudiation protocol without trusted third party(TTP), a new fair non-repudiation protocol without TTP on conic curve was obtained. In this protocol, it not only solves the unsafe and unfair problems for the strong computing power of opposite part, but also reduces the information exchange agreements from n+1 times to 3 times. In addition, it is completely free from dependence on the TTP, and the priority of any party not exists, which achieve truly fairness and abuse-free and more security.Fifth, a high efficient certificateless broadcast signcryption scheme and a multiple signcryption schemes were given by using the public key cryptosystem on conic curve.Compared with the exist scheme in present, they all achieve a great progress in information computation. Furthermore, they were both proved as secure schemes under the random oracle model.