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Fast Computing Method to XOR Differential Probability of Addition Modulo 2~n

Zhang Qing-gui

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Abstract

This paper analyzes the computational complexity of the algorithm for computing the XOR differential probability of addition modulo 2n. With the idea of time-memory trade-off,by computing and storing the products of matrices algorithm in advance,and replacing the computing of matrices products with looking up tables,it improves the computing algorithm. The computational complexity of new algorithm is less than 7.7% times of that of the existing method.

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What this paper is about

This paper analyzes the computational complexity of the algorithm for computing the XOR differential probability of addition modulo 2n. With the idea of time-memory trade-off,by computing and storing the products of matrices algorithm in advance,and replacing the computing of matrices products with looking up tables,it improves the computing algorithm. The computational complexity of new algorithm is less than 7.7% times of that of the existing method.

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Available abstract

This paper analyzes the computational complexity of the algorithm for computing the XOR differential probability of addition modulo 2n. With the idea of time-memory trade-off,by computing and storing the products of matrices algorithm in advance,and replacing the computing of matrices products with looking up tables,it improves the computing algorithm. The computational complexity of new algorithm is less than 7.7% times of that of the existing method.

Key concepts: Modulo, Computer science, Computational complexity theory, Parallel computing, Differential (mechanical device), Algorithm, Theoretical computer science, Discrete mathematics

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