kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2025-22-4-131-142kaz29-2289Research ArticleКОМПЬЮТЕРНЫЕ НАУКИCOMPUTER SCIENCEО МЕТОДЕ ГЕНЕРАЦИИ ЛИНЕЙНОГО СЛОЯON THE DIFFUSION LAYER GENERATION METHODhttps://orcid.org/0000-0002-8208-4716ГорловЛ. В.GorlovL. V.

докторант

г. Алматы

PhD student

Almaty

lev.gorlov@gmail.comhttps://orcid.org/0000-0003-3827-179XСейловаН. А.SeilovaN. A.

к.т.н., доцент

г. Алматы

Cand. Tech. Sc., Associate Professor

Almaty

nseilova@iitu.edu.kzhttps://orcid.org/0000-0001-9036-6556ОхрименкоТ. А.OkhrimenkoT. A.

к.т. н., доцент

г. Киев

Cand. Tech. Sc., Associate Professor

Kiev

t.okhrimenko@nau.edu.uaКазахский национальный университет им. аль-ФарабиКазахстанAl-Farabi Kazakh National UniversityKazakhstanМеждународный университет информационных технологийКазахстанInternational University of Information TechnologiesKazakhstanНациональный авиационный университетУкраинаNational Aviation UniversityUkraine202523122025224131142Copyright © Горлов Л.В., Сейлова Н.А., Охрименко Т.А., 20252025Горлов Л.В., Сейлова Н.А., Охрименко Т.А.Gorlov L.V., Seilova N.A., Okhrimenko T.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/2289

В данной статье представлен автоматизированный метод генерации параметров линейных функций, используемых в диффузионном слое блочных симметричных алгоритмов шифрования. Основное внимание уделяется проектированию линейных слоев, построенных исключительно на операциях циклического сдвига и побитовых операциях «исключающее ИЛИ», которые являются эффективными и аппаратно-ориентированными. Такие слои играют решающую роль в достижении сильной диффузии, фундаментального криптографического требования. Предлагаемый метод оценивает конфигурации-кандидаты путем исчерпывающего перечисления значений сдвига, вычисления количества ветвей и оценки их лавинных характеристик. Вводится набор количественных метрик диффузии для управления процессом выбора, включая одно- и многораундовые лавинные эффекты и показатели активации на уровне байтов. Сформулирована агрегированная функция качества для сравнительной оценки. Разработанный программный инструмент определил оптимальные параметры сдвига для 128-битных блоков, обрабатываемых как четыре 32-битных слова, что позволило достичь количества ветвлений 5 всего за 12 операций XOR. Предложенный подход способствует практическому синтезу легковесных и безопасных криптографических примитивов, подходящих как для классических, так и для ограниченных платформ.

This paper presents an automated method for generating the parameters of linear functions used in the diffusion layer of block symmetric encryption algorithms. The focus is on designing linear layers constructed solely from cyclic shift operations and bitwise XORs, which are both efficient and hardware-friendly. Such layers play a critical role in achieving strong diffusion, a fundamental cryptographic requirement. The proposed method evaluates candidate configurations by exhaustively enumerating shift values, calculating their branch number, and assessing their avalanche characteristics. A set of quantitative diffusion metrics is introduced to guide the selection process, including single- and multi-round avalanche effects and activation rates at the byte level. An aggregated quality function is formulated to allow comparative assessment. The developed software tool identified optimal shift parameters for 128-bit blocks processed as four 32-bit words, achieving a branch number of 5 with only 12 XOR operations. The proposed approach contributes to the practical synthesis of lightweight and secure cryptographic primitives suitable for both classical and constrained platforms.

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The authors declare that there are no conflicts of interest present.