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Pseudorandom sequence generation is used in many industries, including cryptographic information security devices, measurement technology, and communication systems. The purpose of the present work is to research additive Fibonacci generators (AFG) and modified AFG (MAFG) with modules p prime numbers, designed primarily for their hardware implementation. The known AFG and MAFG, as with any cryptographic generators of pseudorandom sequences, are used in arguments with tremendous values. At the same time, there are specific difficulties in defining of their statistical characteristics. In this regard, the following research methodologies were used in work: for each variant of AFG and MAFG, two models were created—abstract, which is not directly related to the circuit solution, and hardware, which corresponds to the proposed structure; for relatively small values of arguments, the identity of models was proved; the research of statistical characteristics, with large values of arguments, was carried out using an abstract model and static tests NIST. Proven identity of hardware and abstract models suggest that the principles laid down in the organization of AFG and MAFG structures with modules of prime numbers ensure their effective hardware implementation in compliance with all requirements for their statistical characteristics and the possibility of application in cryptographic information security devices.