Empirical and Statistical Complexity Analysis of AES-128

Abstract Analysis of algorithms is an interesting topic in the theoretical computer science area of research. An algorithm analyzed with respect to its run time complexity gives an overall idea about the working of the algorithm in the practical scenario. Empirical complexity is a comparatively newer analysis approach which focuses on running the algorithm practically with varying and increasing input and then predicting the complexity of the algorithm. This is then followed by a statistical analysis of the empirical estimate to give a clearer bound on the empirical complexity. Cryptographic algorithms are the sole bearer of providing security for any application and hiding confidential information of national or personal importance. In today’s fast running world, besides security, the run time of the algorithm is also of utmost importance. Cryptographic algorithm constitutes of many complex mathematical functions. In this paper, we have analyzed the most sought after cryptographic algorithm AES-128 in terms of its computational complexity and then practically drawn an asymptotical bound through the empirical complexity approach. Then, a regression analysis on the concluded bound is done to formally settle on the empirical complexity of AES-128.