A Cryptanalysis Of Basic Components Of ARX

The cryptographic algorithms based on ARX structures use xor,cyclic shift,modular addition and other basic operations.Due to the high efficiency of ARX structure software and hardware implementation,the cryptographic algorithm based on ARX structure has been widely used,such as:Hash function MD4,Skein,block cipher TEA,RC5,sequential cipher Salsa20 and other cryptographic algorithms.And the Salsa20 has been designated to be one of the final algorithm by eSTREAM.Differential cryptanalysis is an important attack method for ARX structural cryptography.The study of the difference properties of ARX basic components is of great significance.This paper uses the addition formula on 2-adic integer ring for the first time to depict bit equations of addition difference equation and its solution set clearly in the residue class ring Z/2~nZ.In this paper,the additive difference spectrum is obtained.The input-output difference with different difference probability is discussed in detail and the formula for calculating the maximum difference probability with arbitrary difference fixed is given.Meanwhile,the author obtains the additive carry expression on the the residue class ring Z/(2~n-1)Z by means of the additive carry analysis on the 2-adic integer ring.Thus,the addition formula on the residue class ring Z/(2~n-1)Z is given.Moreover,the additive difference spectrum over the residue class ring Z/(2~n-1)Z with the same input difference is obtained for the first time.This paper discusses the related cryptographic properties and deepens the understanding of the differential properties of modular cryptography.