One-way Hash function construction based on tangent-delay ellipse reflecting cavity-map system

Abstract

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.

Hash function based on the generalized Henon map

“…The mean changed bit number and the mean changed bit probability is 80.28 and 50.17%, respectively, which are very close to the ideal values 80 and 50%, which are better than those in Ref. [8] (79.55 and 49.72%). Figures 5(a) and 5(b) show the plot and the histogram of G i when M = 2048.…”

“…[8], this article has adopted text 1 in Ref. [8] as the test text: "Youth means a temperamental predominance of courage over timidity of the appetite, for adventure over the love of ease. This often exists in a man of 60 more than a boy of 20.…”

“…Set the length of the final Hash value to N , then the key's length should be N/8, namely, the secret key is composed of N/8 floats. Let the greatest accuracy be 10 −r , so the key space size is 10 rN 8 . When r = 16 and N = 160, the key space size equals to 10 320 .…”

“…In order to be able to compare with Ref. [8], we adopt the same method and the same test text, then calculate the Hash value of the text. Change 1 bit at one time, and conduct four groups of tests: the first group consists of 256 tests, the second 512, the third 1024, and the fourth 2048.…”

“…[7−12] However, the approach was adopted by Refs. [7,8], that is, using definitive 0-1 sequences to fill the incomplete group, is not secure enough, in light of the conclusions in Ref. [13].…”