Dr. Marzieh Vahid Dastjerdi, Mr. Majid Rahimi,
Volume 14, Issue 1 (9-2025)
Abstract
The objective of this paper is to analyze and evaluate the behaviour of modular addition and subtraction in symmetric cipher attacks. Modular addition is one of the most widely used nonlinear operators in symmetric cryptographic algorithms. In ARX symmetric algorithms, only three operators are utilized: modular addition, rotation, and XOR. In ARX-like algorithms, modular subtraction or a substitution box is employed, in addition to the standard ARX operations. Since modular subtraction exhibits similar behaviour to modular addition, its behaviour against cryptanalytic attacks has not been explicitly studied in the literature. Therefore, this paper aims to provide a comprehensive overview of the behaviour of modular addition and subtraction in differential, linear, integral cryptanalysis based on division property, and rotational attacks, using both manual analysis and automated methods via MILP (Mixed-Integer Linear Programming). We demonstrate that there is no difference between modular addition and subtraction in differential, linear, and rotational cryptanalysis. However, in integral cryptanalysis based on the division property, these two operations behave differently.
