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Development of Methods for Constructing MDS Matrices of a Special Type Over a Field GF (256)

ФИО студента: Ivan Duvanov

Руководитель: Mikhail Rozhkov

Кампус/факультет: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Программа: Cyber Security (Specialist)

Оценка: 7

Год защиты: 2020

In this work, studies are conducted to develop and evaluate the effectiveness of methods for constructing MDS matrices of a special kind over the GF field (256). We study cyclic matrices of size n × n, 12≤n≤16, in each row of which there are 4 units and a given number of different elements (from 7 to 12). To reduce the complexity of checking MDS properties, an important characteristic is the number of different minors of a given size. In this work, we obtained exact values for the number of minors without duplicates in the case of a 12 × 12 matrix in each row of which there are 3 units and 7 different elements above the final field GF (256). Experimental studies were conducted to estimate the frequency of occurrence of duplicates of a randomly selected minor of a given dimension k × k, 5≤k≤11 for matrices of size n × n, 13≤n≤16. The results obtained in the work indicate the possibility of reducing the complexity of checking the MDS properties of matrices of the considered type (the expected decrease is 20-30 times).

Full text (added January 14, 2020)

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