Перегляд за Автор "Kurinnyi, Oleh"

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  • Ескіз
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    Complexity of The Systems of Linear Restrictions over a Finite Field
    (Igor Sikorsky Kyiv Polytechnic Institute, 2023) Kurinnyi, Oleh
    This paper continues the results obtained in [1]. In the previous paper, we formulated the problem of the unknown vector recovering from linear dependencies with this vector, which act as constraints on it. The next step, after finding out some algebraic and combinatorial properties, is to give basic estimates of complexity for the main problem as well as for related problems. Such related problems can be obtained by fixing some parameters of the main problem or applying constraints on the number of restrictions in the system. Such an analysis makes possible to arrange the problem of recovering an unknown vector based on partial information into the general computational complexity framework in order to approach existing theoretical results to its solution. The obtained theoretical results can be used in algebraic cryptanalysis of stream ciphers and cryptosystems based on linear codes.
  • Ескіз
    ДокументВідкритий доступ
    Systems of Linear Restrictions Over a Finite Field
    (Igor Sikorsky Kyiv Polytechnic Institute, 2022) Kurinnyi, Oleh
    This paper considers the problem of recovering an unknown vector based on partial information presented in the form of certain linear dependencies. Such problem is an alternative to the standard one of solving a system of polynomial equations over a finite field, which arises in the context of algebraic cryptanalysis of stream ciphers, and it models a situation when it’s not possible to formulate specific equations with an unknown vector, but certain restrictions on linear dependencies with this vector. To formalize such linear dependencies, the notation of the system of linear restrictions over a finite field is introduced, and the problem of recovering the unknown vector is replaced by the problem of solving the system of linear restrictions over a finite field. In this paper, we researched some properties of this problem using its equivalent forms and important partial cases.