Analysis of ARX encryption schemes resistance to the integral attack and impracticable differentials attack

Abstract

Common ARX (Addition-Rotation-XOR) encryption algorithms are analyzed. These algorithms are Chacha, Speckey, Simon, Chaskey, Sparkle. These algorithms use three basic operations: modular addition, XOR addition, and rotation. 16-bit reduced models of these algorithms are developed, methods of analysis are selected and developed, and the analysis of the resistance of these algorithms to the most effective attacks (integral attack and attack of impossible differentials) for this class of algorithms is performed. According to the selected indicator – the number of elementary operations that is necessary to obtain parameters of random substitution and the absence of impossible differentials and integrals – the most effective ARX algorithms are determined. These are Speckey, which operates on two 8-bit subblocks and requires 36 elementary operations, and Chaskey, which operates on four 4-bit subblocks and requires 72 elementary operations. If we assume that one 8-bit operation is equivalent to two 4-bit operations, then these schemes are equal in terms of the chosen indicator. The worst performers were the 8-bit Simon scheme and the 4-bit ChaCha scheme, which require almost twice as many operations as the best schemes. A conclusion was also made about the importance of using not one, but several XOR operations of key addition for the overall cryptographic strength of ARX algorithms.