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Information × Registration Number 0219U101669, 0114U001789 , R & D reports Title Applications of exponential sums in cryptographi popup.stage_title Head Varbanets Pavlo D., Доктор фізико-математичних наук Registration Date 11-10-2019 Organization Odessa I.I.Mechnikov National University popup.description2 The arithmetic functions and trigonometric sums are investigated with this research work. There are constructed the sequences of PRN’s and there are studied its cryp-tographic applications. Some applications of modular functions also considered there. The main point of the work is to construct the inversive congruential se-quences of PRN’s of the 1st and 2nd order, as well as construct a new type of such sequences and establish the new estimates of the function of expansions for them. A new type of pseudorandom number sequences was constructed. In this work we also estimates the Fourier coefficients of special modular functions; we prove a new theorem for the density of the Heck Z-function of the Gaussian number field; an analog of Ramachandra's theorem for arithmetic functions over an imaginary quadratic field is constructed; two-dimensional sums of the exponential divisor function are introduced and estimated. The main scientific results are developed and expanded the new methods of studying the arithmetic functions over rings of integer rational and integer Gaussian numbers, in particular, on arithmetic progres-sion (with increasing progression difference), obtained the non-trivial estimates of residual terms in the problem of divisors and divisors of elliptic-type congruence bonds; the new estimates of special trigonometric sums of the Klosterman type are constructed, in particular, the hybrid trigonometric sums, the asymmetric Kloster-man sums and twisted Klosterman sums on the norm subgroups; is has been gener-alized the function of divisors; the Klosterman codes were developed over the fi-nite fields. Based on the obtained results, the new inversive and linear-inversive pseudorandom number generators were constructed and the distribution of these sequences were proved. Among the none-less important results it can be pointed out the constructed asymptotic formula for the half-line Laplace transformation for sums of pairwise product of Hecke Z-values with the   Product Description popup.authors popup.nrat_date 2020-04-02 Close