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The article presents hardware modified additive Fibonacci generators, which use modular addition, with the base of the prime number. Generators differ from the classical presence in their composition of the logic circuit, which is the base of arithmetic addition of an additional component, thus enhancing the chaotic nature of the formation of random numbers. The analysis of statistical characteristics of these generators for large values of arguments is carried out. The implementation of the proposed generator structures allows, in comparison with known devices significant increasing the repetition period of the generated pseudo-random sequence for the vast majority of initial settings of structural elements of the circuit while providing satisfactory statistical characteristics of the output sequence. This will contribute to the improvement of the characteristics of existing systems that include generators of pseudorandom sequences and to the expansion of their scope of use.
