Research Of Polymorphic Hash Function Based On Multivariate Polynomials

Cryptography is a key technology of information security, because it can guarantee confidentiality, integrity, and authenticity of data. While the cryptography hash functions can be used for digital signature schemes, verifying the authenticity of information sources and the integrity of information. As an important part of cryptography, hash function has been the research hotspot in the cryptography field. At present, hash functions which have been widely used are MD5 and SHA-1. But MD5 had been broken, SHA-1 algorithm also had been reduced the difficulty of breaking. In 2007, NIST announced a contest to design a hash function which will be given the name SHA-3 and viewed as the FIPS standard. Thus it is very important to design new hash algorithms at the present stage.In the paper, we research the hash function construction and its applications, and analyze strengths and weaknesses of existing hash functions. We mainly research theory and method of constructing hash function based on the difficulty of solving inverse to multivariate polynomials over a finite field. The main works of the paper are as follows:An improved hash function to SHA-1 is proposed, which is based on the idea of polymorphic cipher. In this algorithm, length of the message digest is enhanced to 192 bits, and we use improved Merkle-Damgard iterative structure and movable parts, which increase the difficult of attack analysis. Moreover, our algorithm has been compared with SHA-1 in the security and implementation efficiency. Compared with SHA-1, our algorithm improves a certain security at the expense of a number of the efficiency.A new hash function based on the MQ problem and the polymorphic cipher is proposed, which foundation is the difficulty of solving inverse to multivariate polynomials over a finite field of multivariable public key cryptosystems and the idea of polymorphic cipher. The algorithm can achieve an arbitrary length of input and 256-bit length of output. After analysis and testing, we believe that the hash algorithm has the good security, the avalanche effect and the diffusion effect etc.