Development of McEliece modified asymmetric crypto-code system on elliptic truncated codes

Abstract

Symmetric and asymmetric cryptographic algorithms, providing the required level of cryptographic strength are generally used to ensure security in modern communication systems, and error-correcting coding techniques - to ensure reliability. The use of asymmetric crypto-code systems enables integrated (with one mechanism) provision of the required levels of reliability, security and efficiency in the processing and transmission of confidential information via open channels of telecommunication systems. The research confirms that their usage provides high performance on the level of symmetric encryption algorithms with BSSH, provable cryptographic strength based on theoretical and complexity problems in arbitrary code decoding (1030 – 1035 group operations are provided), and reliability through the use of a shortened algebra-geometric code (Рош10-9 – 10-12 is provided). A major disadvantage of the use of the McEliece cryptographic system are large amounts of critical data (to provide the required cryptographic strength it is necessary to build a system in the GF (210 – 213). In order to reduce the volume of key data (public key), we propose to use shortened codes, that enables to reduce the GF(26 –28), while maintaining a cryptographic strength level, by introducing the character location entropy at initialization vector.

Розглядаються загальна конструкція теоретико-кодових схем (ТКС), несиметрична крипто-кодова система (НККС) на основі ТКС Мак-Еліса на укорочених (модифікованих) еліптичних кодах. Пропонується математична модель НККС Мак-Еліса, алгоритми формування та розшифрування/розкодування криптограми/кодограми, аналізуються витрати на програмну реалізацію крипто-кодових засобів захисту інформації на основі ТКС Мак-Еліса.