Methods of realization of the k-valued functions of the algebra of logic by the modular forms of arithmetic polynomials based on "weighing" by the numbers k i (i = 0, 1, 2, . . .) were considered. The modular polynomial and matrix (number-theoretic) transformations were examined and extended to the case of systems of k-valued functions. A new principle of designing the modular form of one arithmetic polynomial to realize systems of k-valued functions in terms of the Chinese remainder theorem was proposed. The results obtained provide advantages in terms of complexity of the analytical description and realization of the k-valued functions.

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A new method for parallel generation of q-valued pseudorandom sequence based on the presentation of systems generating logical formulae by means of arithmetic polynomials is proposed. Fragment consisting of kelements of q-valued pseudorandom sequence may be obtained by means of single computing of a single recursion numerical formula. It is mentioned that the method of the "arithmetization" of generation may be used and further developed in order to protect the encryption gears from cryptographic onset, resulting in the initiating of mass hardware failures. The achieved results may be widely applied to the realization of perspective high-performance cryptographic facilities for information protection.

We present a new approach to constructing of pseudo-random binary sequences (PRS) generators for the purpose of cryptographic data protection, secured from the perpetrator's attacks, caused by generation of masses of hardware errors and faults. The new method is based on use of linear polynomial arithmetic for the realization of systems of boolean characteristic functions of PRS' generators. "Arithmetizatio" of systems of logic formulas has allowed to apply mathematical apparatus of residue systems for multisequencing of the process of PRS generation and organizing control of computing errors, caused by hardware faults. This has guaranteed high security of PRS generator's functioning and, consequently, security of tools for cryptographic data protection based on those PRSs.

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