Mathematical Methods of Cryptography

Asymptotic properties of the set of solutions for the distorted systems of equations

A. V. Volgin

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Moscow

Abstract: Two homogeneous systems of equations with functions of $k$-valued logic are considered. The functions in the second system are obtained by independent random distortions of the functions in the first one. It is proposed that the number of equations and variables in these systems increase. For the sets of their solutions, some conditions on probabilistic properties of distortions are formulated. Among them are the conditions under which (1) the probability of equality of these sets aspires to 1; (2) the probability of their intersection aspires to 1; and (3) the number of common solutions in them has a binomial limit distribution.

Keywords: system of equations, functions of $k$-valued logic, distorted functions.

UDC: 519.24