An algorithm for one-way Hash function construction based on tangent-delay ellipse reflecting cavity-map system (TD-ERCS) is proposed in this paper. In the algorithm, the plaintext dealt with is first transformed into a systemic parameter sequence linearly, and then TD-ERCS is iterated in order of the parameter sequence directly, the final Hash value of 160 bits is obtained by means of the nonlinear transform on the iteration sequence, and no padding of calculation is added. Users’ keys of the algorithm can be chosen in the region[264, 2160] arbitrarily. Theoretical analysis and basic security tests indicate that our Hash function has good one-way, weak collision property, better security than other chaotic Hash functions, and it can be realized easily with great rapidity. Our algorithm of Hash function is an ideal substitution for conventional Hash function. And also, a natural criterion (theoretical value of 85.33) to evaluate collision property of Hash function is educed in this paper.
We present a universal algorithm for transforming chaotic sequences of either chaotic map systems or chaotic differential dynamic systems into uniform pseudo-random sequences. Theoretically,the algorithm is based on bit-operations represented by floating-point algorithm,not aiming at any definite physical chaotic systems. It has been proved that,any real random variable generally has a type of natural tendency of homogenization which exponentially increases bitwise with random variable. As a result,any real chaotic sequence can be completely transformed into the pseudo-random sequence having uniform identical independent distribution. Adopting logistic map,Hénon map and Lorenz system as examples to test the universal validity of the algorithm,respectively,the experiments demonstrate that the algorithm is correct. We can reasonably expect that the universally valid algorithm should become the technological basis of standardized modular design of chaotic pseudo-random sequence generator in hardware implementation.
To analyze the security of tangent-delay ellipse reflecting cavity-map system (TD-ERCS) from the point view of cryptography, a simple pseudo-random number generator (PRNG) is proposed with parallel TD-ERCS in this paper. Users' keys are n o longer fixed, and can be chosen in the interval [264, 26 72] arbitr arily in the PRNG. By testing the basic statistic characteristics such as equili brium, runs and correlation of the binary pseudo-random sequences (viz. TD-ERCS sequences) being generated from the PRNG, and comparing with m-sequences, the lo gistic sequences, Chebyshev sequences and SCQC sequences, the experimental resul ts show that TD-ERCS sequences have better statistic characteristics.
Based on the physical model of ellipse reflecting cavity, the tangent-delay operation is proposed to change the evolution route of the systems , and a new class of discrete chaotic map systems is deduced based on the tangen t-delay operation. Simulation experiments show that the discrete chaotic systems have many special properties such as the maximum Lyapunov exponent is over zero , unchangeable equiprobability distribution and zero correlation in total field, there exists a square chaotic attractor when tangent delays one unit, and becom e ergodic state when tangent delays more units than one. The discrete chaotic sy stems can generate 2 independent pseudo-random sequences together. All of the pr operties suggest that the class of chaos systems possesses the potential applica tion in encryption.
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