Design And Analysis Of Chaotic Systems Based On Td-ercs Hash Function

Since 2004, two traditional Hash functions, MD5 and SHA-1, which areapplied internationally, have been collided successfully one after anotherby scholars from our country, which has caused wide public concern incryptography, and called for concerted effort to develop new Hashalgorithms. In this dissertation, a new chaotic Hash algorithm, TD-ERCSHash Algorithm, THA for short, is constructed elaborately based on thetheoretic analysis and random tests of Tangent-Delay Ellipse ReflectingCavity map System, TD-ERCS for short. Theoretic analysis andexperiment tests show that THA is an ideal algorithm that can replaceMD5 and SHA-1. The main research results are: 1) Randomness of eachbit in original chaotic sequence of TD-ERCS is completely tested throughNIST random statistic test suite. The result shows that the most bits'randomness is very good, but there are a few bits of worse randomness.The generative method of sequence is improved, so that each bit ofimproved chaotic sequence has good randomness, which provides solidsafely foundation for THA; 2) Detailed and standardized description ofTHA is given, for realization of algorithm in soft or hardware; 3) For theincomplete of two existing collision test methods, two theoretical modelsof collision description are introduced, two collision quantificationtheorems are proved theoretically, two collision quantification standardsare given, and these two test methods are improved by increasing theircomparison; 4) The reasonable position to take as Hash value is analyzedwith the application of the second collision quantification standard. Theresult is in accordance with NIST statistic test result, which proved theaccuracy of the second standard in experiment; 5) The collision of THAwith other traditional Hash algorithms and existing chaotic Hashalgorithms is analyzed relatively with the application of these twocollision quantification standards, so as sensitivity of initial values,diffusion, confusion and calculation speed of THA with other traditionalHash algorithms. The results show that THA has better collision,diffusion and confusion, very good sensitivity of initial values and quickspeed, is a more ideal cryptography Hash function.