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On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation. / Kolomeec, Nikolay; Sutormin, Ivan; Bykov, Denis et al.

In: Cryptography and Communications, 15.01.2025.

Research output: Contribution to journal › Article › peer-review

Harvard

Kolomeec, N, Sutormin, I, Bykov, D, Panferov, M & Bonich, T 2025, 'On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation', Cryptography and Communications. https://doi.org/10.1007/s12095-025-00773-y

APA

Kolomeec, N., Sutormin, I., Bykov, D., Panferov, M., & Bonich, T. (2025). On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation. Cryptography and Communications. https://doi.org/10.1007/s12095-025-00773-y

Vancouver

Kolomeec N, Sutormin I, Bykov D, Panferov M, Bonich T. On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation. Cryptography and Communications. 2025 Jan 15. doi: 10.1007/s12095-025-00773-y

Author

Kolomeec, Nikolay ; Sutormin, Ivan ; Bykov, Denis et al. / On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation. In: Cryptography and Communications. 2025.

BibTeX

@article{01416e33cc4340bfae75c4acfbb0dcb3,
title = "On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation",
abstract = "Properties of the additive differential probability of the composition of bitwise XOR and a bit rotation are investigated, where the differences are expressed using addition modulo . This composition is widely used in ARX constructions consisting of additions modulo , bit rotations and bitwise XORs. Differential cryptanalysis of such primitives may involve maximums of , where some of its input or output differences are fixed. Although there is an efficient way to calculate this probability (Velichkov et al, 2011), many of its properties are still unknown. In this work, we find maximums of , where the rotation is one bit left/right and one of its input differences is fixed. Some symmetries of are obtained as well. We provide all its impossible differentials in terms of regular expression patterns and estimate the number of them. This number turns out to be maximal for the one bit left rotation and noticeably less than the number of impossible differentials of bitwise XOR.",
author = "Nikolay Kolomeec and Ivan Sutormin and Denis Bykov and Matvey Panferov and Tatyana Bonich",
note = "The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075–15–2022–282 with the Ministry of Science and Higher Education of the Russian Federation. ",
year = "2025",
month = jan,
day = "15",
doi = "10.1007/s12095-025-00773-y",
language = "English",
journal = "Cryptography and Communications",
issn = "1936-2447",
publisher = "Springer Publishing Company",

}

RIS

TY - JOUR

T1 - On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation

AU - Kolomeec, Nikolay

AU - Sutormin, Ivan

AU - Bykov, Denis

AU - Panferov, Matvey

AU - Bonich, Tatyana

N1 - The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075–15–2022–282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2025/1/15

Y1 - 2025/1/15

N2 - Properties of the additive differential probability of the composition of bitwise XOR and a bit rotation are investigated, where the differences are expressed using addition modulo . This composition is widely used in ARX constructions consisting of additions modulo , bit rotations and bitwise XORs. Differential cryptanalysis of such primitives may involve maximums of , where some of its input or output differences are fixed. Although there is an efficient way to calculate this probability (Velichkov et al, 2011), many of its properties are still unknown. In this work, we find maximums of , where the rotation is one bit left/right and one of its input differences is fixed. Some symmetries of are obtained as well. We provide all its impossible differentials in terms of regular expression patterns and estimate the number of them. This number turns out to be maximal for the one bit left rotation and noticeably less than the number of impossible differentials of bitwise XOR.

AB - Properties of the additive differential probability of the composition of bitwise XOR and a bit rotation are investigated, where the differences are expressed using addition modulo . This composition is widely used in ARX constructions consisting of additions modulo , bit rotations and bitwise XORs. Differential cryptanalysis of such primitives may involve maximums of , where some of its input or output differences are fixed. Although there is an efficient way to calculate this probability (Velichkov et al, 2011), many of its properties are still unknown. In this work, we find maximums of , where the rotation is one bit left/right and one of its input differences is fixed. Some symmetries of are obtained as well. We provide all its impossible differentials in terms of regular expression patterns and estimate the number of them. This number turns out to be maximal for the one bit left rotation and noticeably less than the number of impossible differentials of bitwise XOR.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85217239704&origin=inward&txGid=d6ce18c8b1c8da41a881c2dde2a2479b

U2 - 10.1007/s12095-025-00773-y

DO - 10.1007/s12095-025-00773-y

M3 - Article

JO - Cryptography and Communications

JF - Cryptography and Communications

SN - 1936-2447

ER -

ID: 64713795