2009One-way Hash Function Construction Based on Conservative Chaotic Systems

One-way Hash Function Construction Based on Conservative Chaotic Systems ZHANG Qing-huaˈ ZHANG Hanˈ LI Zhao-hui College of Information Technical Science Nankai University Tianjin 300071, China qhzhang@mail.nankai.edu.cn

Abstract—An algorithm for one-way hash function construction based on conservative chaotic system is proposed. The plaintext is divided into a group of message blocks by a fixed length and each message block is iterated some times through standard map. Both the iterations results of every round and the plaintext block determine the two initial values and the steps of iterations in next round. Some items of the result in the final round are chosen to be transformed into Hash value of 128 bits. Theoretical analysis and computer simulation show that this algorithm has good effect in irreversibility, weak collision and sensitivity to initial values. The method is safer in security than the Hash function based on low- dimensional dissipative chaotic maps and it is easy to realize.

Keywords:conservative chaotic systems;standard map;Hash function

I. INTRODUCTION After the conventional Hash function such as MD5, SHA was successfully attacked, research on the design of safe and efficient Hash function remains a hotspot. Chaos system is ergodic, mixed and sensitive; these characteristics make chaos theory have an important application value in modern cryptography [1]. At present,

some algorithms for one-way Hash function based on chaotic map have already been brought forward [2 - 4]. Most Hash algorithms using chaos in existing literatures are based on dissipative chaotic systems. But in some conditions if the attacker gets a continuous of plaintext-ciphertext pairs and the length of ciphertext meets certain conditions, phase space of the chaotic system can be reconstructed through a set of chaotic sequence’s consecutive points. Thus, chaos equation form may be constructed to get information of plaintext, which will result in the failure of encryption [5-7]. While, The Standard map as

a kind of conservative system in the emergence of chaotic behavior, has the good characteristics of the chaotic systems, and doesn’t have the so-called chaotic attractor. For the conservative chaotic systems, the attacker can not predict by reconstructing through ciphertext without attractor structure. So, the conservative chaotic systems with high security are ideal model in cryptography application . Some parallel algorithms for chaos-based Hash function construction are proposed in [2][3], which means each group of the plaintext operates independently. The parallel

algorithms are characterized by quick speed, but they have their fatal defects due to lack of enough diffusion and confusion of the plaintext. In [8], the collision problem of one kind of methods for constructing chaos-based hash function is described. Some key problems are pointed out which should be taken care of, and a number of good principles of algorithm for constructing one-way hash function based on chaotic map was proposed. In this paper, an algorithm for one-way Hash function construction based on Merkle-Damgard framework [9][10] is

introduced. In this algorithm, the entire message blocks perform some rounds of iteration through Standard map. One output of the iterations of each round determines one of the initial values of the next round, and the other output determines the steps of the next round. And the other initial value of the next round was given by the corresponding message block. The method of this design enhances the diffusion of Hash function, and overcomes the inherent defects of dissipative chaotic systems. So, the Hash algorithm has a higher security. Theoretical analysis and computer simulation show that this algorithm has good effect in anti-conflict and avalanche effect. The algorithm is easy to express and satisfies all the performance requirement of Hash function in an efficient and flexible manner. 󰀃

II. THE GENERALIZED STANDARD MAP

Standard map is one kind of typical conservative chaotic system defined as follows.

1112(sin)mod2()modiiiiii

xkH

yyH

H

xxyH

SS󰀎

󰀎󰀎

­ 󰀎°

®

° 󰀎

¯

(1)

Where [0,1),[0,1),0xyk󰂏󰂏!.

Hereinto, k is the controlled variable. When H=1, the certain critical value of k called kcrit is 0.971635406Ă [11].

When k is larger than the certain critical value, chaos motion in system is expanded from the part to the whole space and system demonstrates whole chaos. In order to make standard map in the whole chaos, H value is the maximum value of the ASCII, H=255, and 2kS in this algorithm.