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Empirical and statistical comparison of intermediate steps of AES-128 and RSA in terms of time consumption

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Abstract

Cryptographic algorithms are composed of many complex mathematical functions. When analyzing the complexity of these algorithms, one fixes priory the overall complexity of the algorithm as the complexity of the most dominating operations for a group of operations. Generally, it is the count of this operation which determines the complexity of the algorithm in case of compounding operations. We have instead used the weight factor to determine the complexity of an algorithm with many operating functions working simultaneously and have taken time of the operation as a measure of the weight factor. We statistically analyze the two most used operations in RSA, namely “power” and “mod,” through a method of revised difference to compare whether these are statistically similar or dissimilar. We have also calculated the empirical computational complexity of these two operations through the fundamental theorem of finite differences to verify whether these operations are statistically dissimilar and if so then which of the two is dominant. We have also analyzed empirically the complexity of each of the four sub-steps involved in the encryption and decryption of AES-128, to determine which operation dominates the most and consumes most of the time in an overall run time of AES-128.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215, India

    Prashant Pranav & Sandip Dutta

  2. Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi, 835215, India

    Soubhik Chakraborty

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  1. Prashant Pranav
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  2. Sandip Dutta
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  3. Soubhik Chakraborty
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Correspondence to Prashant Pranav.

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Pranav, P., Dutta, S. & Chakraborty, S. Empirical and statistical comparison of intermediate steps of AES-128 and RSA in terms of time consumption. Soft Comput 25, 13127–13145 (2021). https://doi.org/10.1007/s00500-021-06085-6

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