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Information × Registration Number 0221U102217, 0114U002784 , R & D reports Title Computer logic and its application popup.stage_title Head Symonova Iryna H, Кандидат фізико-математичних наук Registration Date 29-01-2021 Organization Odessa I. I. Mechnikov National University popup.description2 New Tilich-Zemor hash functions based on the sequences of products of special matrices over a ring of residuals modulo the degree of a prime number from an imaginary field of Gaussian numbers are investigated. An algorithm is constructed that is easily implemented by software, using algebraic operations on the ring of surpluses modulo the degree of a simple rational number, which is indecomposable in the ring of Gaussian integers. It is proved that the secrecy of this scheme is equivalent in the calculated complexity to the known complexities of the problems of modern mathematics. The calculated impossibility of obtaining collisions is proved Studies of cryptographic properties of hash functions, which are generated by theoretical-group properties of normal subgroups of a group of ring residuals of integers of a field of Gaussian numbers (as well as arbitrary imaginary quadratic expansion of a field of rational numbers) modulo the degree of a prime number from a field of Gaussian numbers. The calculated impossibility of obtaining collisions is proved. The calculated impossibility of obtaining collisions is proved. Studies of cryptographic properties of hash functions, which are generated by theoretical-group properties of normal subgroups of a group of ring residuals of integers of a field of Gaussian numbers (as well as arbitrary imaginary quadratic expansion of a field of rational numbers) modulo the degree of a prime number from a field of Gaussian numbers.   Product Description popup.authors Balandina Nataliya M Fedorovskiy Serhiy V Yakimova Nataliya A popup.nrat_date 2021-01-29 Close