Comparison of Methods for Solving the Mathematical Safe Problem on Matrices by the Arithmetic Complexity of Algorithms for Locks Over the Field of Redundancies Modulo a Prime Number

Consider in general the mathematical safe defined in 1, where all locks are arranged in a rectangular table size where , (i = 1, 2, . . ., m; j = 1, 2,.., n). The locks of i-row and j-column pluralize as . Let's consider a problem where the locks belong to the same type and have an arbitrary number of states over the redundancy field Fk , where , where К is the modulo of a prime number.