Parallel linear generator of multivalued pseudorandom sequences with operation errors control

A parallel linear generator of multi-valued pseudorandom sequences, which operates under conditions of generating hardware errors caused by destructive adversary actions is proposed. The main types of modification of the pseudorandom sequence in case of adversary attack are considered. A distinctive feature of the iterative process of ensuring the reliability of computational operations is the "arithmetic" of computational operations by representing a system of generating recurring logical formulas as a system of many-valued logic algebra functions. The subsequent realization of multivalued logic algebra functions by means of arithmetic polynomials allowed us to parallelize the process of generating multivalued pseudorandom sequences and level out the existing complexity (specificity) of cryptographic transformations of logical data types which limit the use of redundant coding methods. As a result, a solution that allows to apply redundant modular codes to control the accuracy of the computational operations performed by the nodes of pseudorandom sequence generation is proposed. Moreover, unlike the known solutions, the proposed method provides obtaining fragments of a pseudorandom sequence on the basis of one recursive arithmetic formula with parallel calculation errors control. The use of modular forms made it possible to transfer computations from the rational numbers field arithmetic to integer arithmetic of a simple field.
Among the existing variety of codes correcting errors (maximally spaced codes), a special place is occupied by multivalued Reed–Solomon codes. Reed–Solomon codes usage in the formation of pseudorandom sequences allows the formation of code-like structures that monitor and ensure the reliability of computational operations. The calculated probability of failure-free operation of the parallel linear generator of multivalued pseudorandom sequences with an error control function based on the principle of functioning — sliding redundancy is obtained. The achieved results can find wide application at realization of perspective high-efficiency cryptographic information protection facility.