Research On Digital Signature And Identity Authentication Based On Chebyshev Polynomials

The information technology is developing fastly. Many advantages are given to ourlife by the development of the information technology. But at the same time, more andmore problems are exposed in the information security. We are aware of the importanceof the Information security. As we all know, the cryptography is the core of theInformation security. The cryptosystem based on the traditional problem is used widely,such as, RSA. But the technology of the quantum makes the traditional cryptosystemless security. At the moment, the Chaotic Cryptography is appearing as a new directionof the cryptography.At first, a new Hash function is represented based on Chebyshev polynomials andcellular neural network, after analyzing many traditional Hash function. The new Hashfunction is diffusion, confusion, weak collision and sensitivity to initial conditions byusing the parameters generated by the Chebyshev polynomials. What’s more, a newone-group-signature is raised based on our Hash function. It can not only satisfytraceability, and also a signature signed by one member doesn’t leak out other members’information. This scheme has a high efficiency and a property of quantum-resistant.Secondly, this paper presents a digital signature scheme based on the periodicityand semi-group property of Chebyshev polynomials, and we also give a group signaturescheme. The security of the schemes depends upon the intractability of the integerfactorization problem and discrete logarithms of Chebyshev polynomials. And the groupsignature satisfies the correctness, anonymity, irrelevance and resistance to jointcollaboration.In the end, a new scheme based on the identity authentication and key agreementscheme in the past is proposed. The scheme makes better use of the property of theChebyshev polynomial based on the finite fields. The scheme presented can not onlymake the identity authentication and get the security key between two users, but alsohave good security. It is proved that the scheme can resist the attack from the passwordguessing, the ciphertext, the middleman and the replay. And also we give a simulationof this scheme and the simulation shows that it has high efficiency.