Computational Complexity Analysis for a Class of Symmetric Cryptosystems Using Simple Arithmetic Operations and Memory Access Time

Abstract

A secure cryptosystem could be very complicated, time consuming and hard to implement. Therefore, the complexity of the cryptosystem should be taken into account during design and implementation. In this work, the authors introduce a comprehensive and platform independent complexity analysis for a class of symmetric block cryptosystems, by which it will be easier to evaluate the performance of some used cryptosystems. Previous works lacked the comprehensiveness in their analysis, due to the fact that the memory access time was completely ignored, which greatly degrades the accuracy of the analysis and limits it to one data block only. In this paper the authors analytically compute the complexity for a class of symmetric cryptosystems in terms of the number of the clock cycles required and in terms of the required time for encryption/decryption, independently of the hardware or software used in the encryption/decryption process. Moreover, this is the first complexity analysis that considers the required time to access and retrieve information from memory, which makes the analysis more comprehensive and accurate than previous work as well as being general for any number of encryption data blocks. In addition, computer simulations are used to truly evaluate the accuracy of the analysis and to show how the analytical results match the simulation results.