МЕТОД ПОБУДОВИ ПРИМІТИВНИХ ПОЛІНОМІВ ДЛЯ КРИПТОГРАФІЧНИХ ПІДСИСТЕМ ГАРАНТОЗДАТНИХ АВТОМАТИЗОВАНИХ СИСТЕМ
The paper proposes a method for constructing primitive polynomials that are used in the design of radio engineering systems, subsystems of cryptographic information protection in reliable automated information processing and control systems at critical infrastructure facilities, as well as in other...
Збережено в:
| Дата: | 2020 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2020
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| Теми: | |
| Онлайн доступ: | https://jais.net.ua/index.php/files/article/view/509 |
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| Назва журналу: | Problems of Control and Informatics |
Репозитарії
Problems of Control and Informatics| Резюме: | The paper proposes a method for constructing primitive polynomials that are used in the design of radio engineering systems, subsystems of cryptographic information protection in reliable automated information processing and control systems at critical infrastructure facilities, as well as in other socially significant information systems. In particular, such polynomials can be used to create elements of cryptographic schemes, including pseudo-random number generators, guaranteed period nodes, substitution nodes (substitution). Using the Rabin criterion for irreducible polynomials and a recursive construction, the paper proposes a method for constructing, based on well-known primitive polynomials over a field of two elements, primitive polynomials over fields of order 2k, where k ³ 2 . The necessary equalities for calculating the coefficients of polynomials are given. This method is relevant in the case of creating subsystems for cryptographic protection of information in modern computer systems that use microcontrollers and microprocessors based on 32 or 64 bit data presentation formats. The indicated method for constructing primitive polynomials over non-simple fields based on the known primitive polynomials over a field of two elements has polynomial complexity. The article provides definitions of the basic concepts, as well as the necessary auxiliary results, which are used to substantiate the algorithm on which the proposed method is based, which can be useful in its implementation, a detailed description of the algorithm is presented and an example of its application is given. |
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