Modular Forms of Systems of k-valued Functions of the Algebra of Logic

Abstract

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.

Parallel generator of q-valued pseudorandom sequences based on arithmetic polynomials

“…2 Figure 2. Structural diagram of the operation of the parallel q-LFSR in accordance with the formula (4) We know that the arbitrary MVFLA may be represented as arithmetical polynomial defines as [7][8][9]:…”

“…Let computing the values of the required MVFLA. To do that, we should represent the result of calculation of MVFLA in q-valued notation system and apply the masking operator Ξ t {M (S)} [9]:…”

Secure Generators of q-Valued Pseudo-random Sequences on Arithmetic Polynomials

“…It is known that random MFAL can be represented in the form of an arithmetic polynomial in simple way [16,17]:…”

“…Similar to [16,17] let us implement the MFAL system (6) by computing some arithmetic polynomial. In order to do this, we associate the MFAL system (6) with a system of arithmetic polynomials of the form (7), we obtain: L m (a p , a p+1 , .…”