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New Methodology of Block Cipher Analysis Using Chaos Game

Block cipher analysis covers randomness analysis and cryptanalysis. This paper proposes a new method potentially used for randomness analysis and cryptanalysis. The method uses true random sequence concept as a reference for measuring randomness level of a random sequence. By using this concept, this paper defines bias which represents violation of a random sequence from true random sequence. In this paper, block cipher is treated as a mapping function of a discrete time dynamical system. The dynamical system framework is used to make the application of various analysis techniques developed in dynamical system field becomes possible. There are three main parts of the methodology presented in this paper: the dynamical system framework for block cipher analysis, a new chaos game scheme and an extended measure concept related to chaos game and fractal analysis. This paper also presents the general procedures of the proposed method, which includes: symbolic dynamic analysis of discrete dynamical system whose block cipher as its mapping function, random sequence construction, the random sequence usage as input of a chaos game scheme, output measurement of chaos game scheme using extended measure concept, analysis the result of the measurement. The analysis process and of a specific real or sample block cipher and the analysis result are beyond the scope of this paper.