A New Approach for Designing Key-Dependent S-Box Defined over GF (24) in AES

Abstract

Abstract-In this paper a new approach for designing S-box in Advanced Encryption Standard (AES) is proposed. The proposed S-box is constructed from small S-boxes defined over GF (2 4 ) instead of GF (2 8 ) as in traditional AES. Rijndael Algorithm (RA), as one of AES standards, is modified by applying the new approach. The Modified Rijndael Algorithm (MRA) is constructed by replacing the S-box of RA by small S-boxes, and the key expansion procedure of RA is modified consequently. Each one of the small S-boxes has different equation and each equation is extracted using one of the three irreducible polynomials existing in GF (2 4 ). So, detecting different equations by cryptanalysts is very difficult compared to the S-box of RA which uses one equation and one irreducible polynomial. The substitution from small S-boxes is done based on the round key, so this achieves diffusion, confusion and therefore security for MRA. The MRA is tested using avalanche effect and strict avalanche criterion (SAC) to evaluate security. The performance evaluation is calculated and proved that MRA is more suitable for the applications that require security and QoS such as voice over IP (VoIP).Index Terms-AES, key dependent S-box, finite field, cryptographic algorithms, strict avalanche criterion. I. INTRODUCTIONThe Advanced Encryption System (AES) was launched as a symmetrical cryptography standard algorithm by the National Institute of Standard and Technology (NIST) in October 2000, after a four year effort to replace the aging DES, NIST announced the selection of Rijndael, as in [1], [2] as the proposed AES (NIST 2004). Draft of the Federal Information Processing Standard (FIPS), as in [3] for the AES was published in February 2001; Standardization of AES was approved after public review and comments, and published a final standard FIPS as in [3] in December 2001. Standardization was effective in May 2002 (NIST 2004. Rijndael submitted by Joan Daemen and Vincent Rijmen (Daemen 1998), is a symmetric key, iterated block cipher based on the arithmetic in the Galois Field of 2 8 elements -GF (2 8 ). The Rijndael proposal for AES defined a cipher in which the block length and the key length can be independently specified to be 128, 192, or 256 bits. The AES specification uses the same three key size alternatives but limits the block length to 128 bits, as in [4]. The input to the Manuscript received February 17, 2012; revised March 31, 2012. Hanem M. El-Sheikh was with the Faculty of Engineering, Alexandria University, Alexandria, Egypt (e-mail: honymora@yahoo.com).Omayma A. Mohsen is with the Switching Department, and the scientific committee at the National Telecommunication Institute.Abdelhalim Zekry is with the electronics at faculty of Engineering, Ain Shams University, Cairo, Egypt. encryption and decryption algorithms is a single 128-bit block and this block is depicted as a square matrix of bytes. The key that is provided as input is expanded into an array of key schedule words, each word is four bytes and the total key schedule ...

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