Design Of Signature Scheme Based On Multivariate Cryptosystem And The Construction And Application Of Conformal Iterated Function

The emergence of quantum computer, on the one hand, greatly promoted advances incryptography; on the other hand, make it possible to quickly solve the hardness of Big Integerfactoring problem and Discrete Logarithm problem. It brought a serious security threats to theexisting areas of public key cryptography such as RSA, ECC. So, the public key cryptographywhich can resist quantum computer (post quantum cryptography) aroused great concern, and hasbecome a research focus in recent years.Multivariate Cryptography is one of the alternatives to guarantee the security ofcommunication in the post-quantum world. Its security is based on a NP-hard problem of solvinga finite field random multivariate quadratic (MQ), and now there is no efficient quantum attackalgorithm to MQ problem. So the multivariate cryptography has broad prospect for development.Now the main research mostly concentrated on the scheme itself, and the research for theapplication is still little. The special signatures such as proxy signature have a wide range ofapplications, but most of the existing programs cannot resist quantum attack, and multivariatecryptography almost have no applications in these special signature. The first work in thisdissertation is designing proxy signature，re-proxy signature and proxy ring signature based onthe multivariate cryptography, these signatures are not only meet the security requirement of thescheme, but have benefits of fast computing, and high efficiency, last but not least, can resistquantum attack.Public key cryptosystem based on the conformal iteration depth problem is a new publickey cryptosystem with independent intellectual property rights proposed by Chinese scholarGuan Haiming. This public key cryptosystem not only have the advantages of multivariatecryptography, which can resist quantum-computing attacks, but also have similar to the nature ofthe index. Therefore, the second work in this dissertation is that we discuss this public keycryptosystem. We propose two methods of constructing conformal iterative function; construct afeasible conformal iteration function, and further promotion on the nature of its index on theencryption and decryption schemes and signature schemes.