Calculation of the differential probabilities for the sum of k numbers modulo 2n. | Applied Discrete Mathematics. Supplement. 2022. № 15. DOI: 10.17223/2226308X/15/14

Calculation of the differential probabilities for the sum of k numbers modulo 2n.

We study the di erential probabilities xdp+ k ( 1; : : : ; k ! 0) of the function f(x1; : : : ; xk) = x1 + + xk mod 2n, 0; 1; : : : ; k 2 Zn2 , where di erences are expressed using bitwise \\exclusive or". These values are used in di erential cryptanalysis of cryptographic primitives which contain bitwise \\exclusive or" and addition modulo 2n, such as ARX-constructions. We propose analytic expressions of matrices that are used for calculating xdp+ k . We also study the di erential probability adp ( ; ! ) of the function x y, ; ; 2 Zn2 , where di erences are expressed using addition modulo 2n, and describe all triples of di erences whose probabilities are greater than 1=4.

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Keywords

ARX, exclusive or, modular addition, differential cryptanalysis, differential probabilities

Authors

Name	Organization	E-mail
Mokrousov Anton S.	Novosibirsk State University	settingx@mail.ru

Всего: 1

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