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Information × Registration Number 0225U005204, (0123U102968) , R & D reports Title Exponential sums in Number Theory and Cryptography popup.stage_title Тригонометричні суми в теорії чисел і криптографії Head Sergey (Serhii) P. Varbanets, Доктор фізико-математичних наук Registration Date 27-12-2025 Organization Odesa I.I. Mechnikov National University popup.description1 Obtaining the new estimates of exponential sums of Kloosterman and Gauss type and applying in cryptography- popup.description2 The properties of Kloosterman sums over the ring of integers of the imaginary quadratic field Q(−d1/2)\mathbb{Q}(\sqrt{-d_1/2})Q(−d1/2) have been investigated. Sharp bounds for Kloosterman sums, as well as their generalizations, have been obtained in connection with problems concerning the distribution of solutions to certain congruences. Special congruences relevant to the construction of pseudorandom number sequences have been studied, together with nonlinear congruential pseudorandom number generators. Furthermore, the behavior of Kloosterman sums on an elliptic curve defined over a finite extension of the imaginary quadratic extension of the rational field, arranged in an arithmetic progression, has been examined. Methods have been developed for constructing pseudorandom number generators derived from analogues of elliptic curves over algebraic extensions of the rational field. Special congruences on elliptic curves used for generating pseudorandom sequences have been analyzed. An elliptic-curve-based hash function has been constructed, and its cryptographic applications have been discussed. Additional special congruences relevant to pseudorandom sequence generation have been investigated. Moreover, methods have been designed for constructing pseudorandom number generators based on elliptic-curve analogues defined over a finite ring. Product Description popup.authors Sergii (Serhii, Sergey) P. Varbanets popup.nrat_date 2025-12-27 Close