A Novel Construction of AES S-boxes Nasir Siddiqui, Umar Afsar Department of Basic Sciences, University of Engineering and Technology, Taxila, Pakistan nasir.siddiqui@uettaxila.edu.pk, umarsheikh86@gmail.com and Tariq Shah, Ayesha Qureshi Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan stariqshah@gmail.com, ayesha.qureshi6@gmail.com Abstract A construction method of S-boxes is given in []. These S-boxes are generated by the action of symmetric group on AES S-box and these are ͶͲ͵ʹͲ in number. In this paper, we bounce a new method for the construction of ͺ×ͺ S-boxes. Instead of symmetric group , an action of symmetric group ଵ is performed on AES S-box. Accordingly, ͳ! ሺʹͲͻʹʹͺͻͺͺͺͲͲͲሻ new ଵ S-boxes are generated. We analyze the strength of the proposed S-boxes by Balance property, Nonlinearity test (NL), Bit Independence Criterion (BIC), Linear Approximation Probability (LP), Strict Avalanche Criterion (SAC) and Differential Approximation Probability (DP). In addition, by Majority Logic Criterion (MLC) an application of these new S-boxes is observed for image encryption. Furthermore, we evaluate the results of these analyses with AES, APA, Gray, AES, Skipjack, Xyi and Residue prime S-box to know the rank of our proposed S-boxes comparative to other S-boxes. The generated S-boxes are also used to construct ଵ! ሺ ≤ ͳ!ሻsecret keys that are applied to AES in order to make it more secure. Keywords: AES S-box, S-boxes, Symmetric group 1. Introduction On October ʹ, ʹͲͲͲ National Institute of Standards and Technology (NIST) adopted Rijndael block cipher [ͳ] as Advanced Encryption Standard (AES) and published as FIPS ͳͻͻ [ͳͳ] in NovemberʹͲͲͳ.In fact this system was developed by Joan Daemen and Vincent Rijmen the prominent Cryptographers of the time. It is based on 128 bits with flexibility for keys of sizes ͳʹͺ, ͳͻʹ and ʹͷ bits. Whereas the AES encryption consists of ͳͲ rounds of processing for ͳʹͺ bit keys, ͳʹ rounds for ͳͻʹ bit keys and ͳͶ rounds for ʹͷ bit keys. All these are identical except the last one. There are four steps in each round of processing, one single byte based substitution step, a row wise permutation step, a column wise mixing step and the addition of the round key. The transformations in AES including the shift row operation, mixed column operation and add round key are ܨܩሺʹሻ = {Ͳ,ͳ} linear. Substitution of bytes is the only nonlinear component which is able to generate uncertainty for AES. Many cryptanalysts have studied structural properties of AES [5, 10, 12]. While, many researchers tried to enhance the security of the algorithm by constructing new S-boxes for AES. In [], International Journal of Computer Science and Information Security (IJCSIS), Vol. 14, No. 8, August 2016 810 https://sites.google.com/site/ijcsis/ ISSN 1947-5500