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Information × Registration Number 0224U002335, 0123U104713 , R & D reports Title Cryptoanalysis-resistant methods and means of encryption in polynomial systems of residual classes popup.stage_title Head Iakymenko Ihor Z., Кандидат технічних наук Registration Date 12-02-2024 Organization Western Ukrainian National University popup.description2 The theoretical foundations of symmetric cryptographic algorithms based on the polynomial residue number system have been developed. The main feature of this approach is that when reconstructing a polynomial using the method of undetermined coefficients, multiplication is performed on arbitrarily chosen polynomials (keys). The keys also consist of mutually prime modules of the residue number system. Schemes and examples of implementing the developed polynomial symmetric encryption algorithm are provided. Mathematical support for the proposed polynomial symmetric encryption in the residue number system has been developed. In order to assess its security, research has been conducted and analytical expressions have been derived indicating that cryptanalysis of the proposed algorithm requires combinatorial complexity, leading to an NP-complete problem. It has been established that the security significantly increases with an increase in the degree and dimension of the Galois field � p, reaching its maximum when the number of modules equals half of the possible number of irreducible polynomials with specified degrees of polynomials and orders of Galois fields. This means that finding an efficient algorithm to solve this problem requires significant computational resources and time. The proposed cryptographic algorithm based on the polynomial residue number system can be used to provide reliable protection of confidential information in systems with limited computational resources. Product Description popup.authors Ihnatev Ihor V. Davletova Alina Ya. Yatskiv Vasyl V. popup.nrat_date 2024-02-12 Close