Comparative analysis of ARX encryption schemes
Keywords:cryptanalysis, strength, ARX algorithm, modular addition, cyclic shift, differential cryptanalysis, difference, linear cryptanalysis, algebraic cryptanalysis, random substitution.
AbstractARX encryption algorithms are analyzed, that is, those that use only three operations: modular addition, XOR addition and cyclic shift. 16-bit reduced models of the most famous algorithms of this class are being developed. Among these algorithms are Salsa, Chacha, Cypress, Speckey, Simon, Chaskey. Some of them operate with 4-bit words, others with 8-bit words. By an exhaustive search for models of these algorithms some cryptographic parameters are determined. These parameters are the maximum probability of passing the difference (determines the resistance of the cipher to attacks of differential cryptanalysis); maximum probability of linear approximation (determines the resistance of the cipher to attacks of linear cryptanalysis); non-linear order (determines the resistance of the cipher to interpolation attacks, algebraic cryptanalysis). It is demonstrated that most models with an increase in the number of rounds come to the parameters of random permutations. It is determined that the Simon algorithm model does not possess this property. Several modifications of this algorithm are proposed. Comparing the number of necessary operations to achieve random substitution performance, the most successful ARX schemes were determined. The most efficient 4-bit scheme is the reduced Chaskey model, and the most effective 8-bit one is the modification of the Simon scheme which was proposed in this work. It is shown that, potentially, ARX schemes with a large format of operations are more flexible and efficient, since they require approximately half the number of operations to provide cryptographic parameters of random substitution.
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