On Dynamic chaotic S-BOX Ghada Zaibi, Abdennaceur Kachouri
Fabrice Peyrard, Daniele Foumier-Prunaret
GE dept. National school of engineering of Sfax ENIS Sfax, Tunisia
[email protected] [email protected]
LATTIS INSA Toulouse Toulouse, France
[email protected] [email protected]
Abstract- The substitution table or S-Box is considered as the core of the block ciphers. The good design of the S-Box can increase the cipher security and simplicity. The aim of this paper is to demonstrate the efficiency of the dynamic S-Boxes based on one-dimensional chaotic maps compared to classic S-Box and to evaluate the more suitable one dimensional map to construct a dynamic S-Box used in the AES algorithm. The security analysis shows that the dynamic S-Boxes based on one-dimensional chaotic map (logistic and PWLCM) have very low linear and differential probabilities. In fact, they have better immunity against linear attacks than Static S-Box and comparable differential probability value. The new investigated criterion is the strict avalanche criterion (SAC). The results show that the piecewise linear chaotic map (PWLCM) has the closest value to 0.5. In order to validate the efficiency of the S-Boxes and their Inverse S-Boxes images were encrypted using the modified AES algorithm and their histograms were compared. We find that dynamic chaotic S-Boxes have slightly more uniform histograms than static S-Box, so the AES using dynamic chaotic S-Box is secure and as efficient as the classic algorithm.
Keywords-component; S-Box; chaos;AES; security analysis
I.
INTRODUCTION
The S-Box is a substitution box and the only nonlinear component assuring the confusion property of the conventional block ciphers such as DES (Data Encryption Standard), International Data Encryption Algorithm (IDEA) and the Advanced Encryption Standard (AES). The strength of these algorithms depends on the design of cryptographically strong S-Box. The study of the S-Boxes design accelerates the development of cryptography. In recent years, chaos has attracted a great deal of attention in many fields especially in cryptography. Using chaos may have potential benefits such as added security and low complexity due its random-like behavior that exhibits sensitive dependence on initial conditions [1]. According to the chaotic systems properties it seems to be convenient and simple to obtain "good" S-Boxes by modifying slightly the initial conditions or system parameters. Many approaches for obtaining S-Boxes based on chaos have been presented, and they severely rely on iterating and discretizing chaotic maps [2], [3], [4].
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In this paper, these different methods are presented. The cryptographic properties of the constructed S-Boxes such as the nonlinearity, strict avalanche criterion, the equiprobable input/output XOR distribution are analyzed in detail. A comparison with the cryptographic properties of the classic AES S-Box is made and some mistake that occurs in some reference is corrected. The dynamic chaotic S-Boxes were used instead of classic one in the AES algorithm to encrypt images and compare histograms of encrypted images, in order to extract the efficiency of the modified AES algorithm. The remainder of this paper is divided into four sections. Section II illustrates different design methodology of dynamic S-Box based on chaos and inverse S-Box. In section III a detailed analysis of the resulting S-Box is given and a comparison of all criteria with Static S-Box is made. Histograms of encrypted images are compared in section IV of experiments. Finally a conclusion is drawn. II.
DESIGN OF S-BOXES BASED ON CHAOTIC MAPS
The S-Box is the only nonlinear element in the AES algorithm. Mixing AES with Chaos is used to more immunize this algorithm against linear, differential, or even algebraic attacks. The two chaotic maps used in this paper are defined as: •
PWLCM (PieceWise Linear Chaotic Maps): X(t)/p
X(t+l)=F (X(t))= p
0 s X(t) < P
(X(t)-p)/(O.5-p) p~X(t)
