The solution of some classes of matrix games | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2016. № 4(34). DOI: 10.17223/20710410/34/2

He approach of G. Simmons to estimating an authentication code (A-code) security is used for solving matrix games. The approach simulates the behavior of the information sender and receiver and an attacker (opponent) as players in matrix games. The imitation attack is represented by a game, the matrix of which coincides with the incidence matrix of A-code. The step of player 1 is the choice of a matrix line (an encoding rule), the step of player 2 is the choice of a matrix column (the simulated message). The substitution attack is represented by a game in which the step of player 1 is the choice of encoding rule (e), the step of player 2 is the choice of a mapping (^>) without immovable points which maps the set of A-code messages to itself. The element a(e, 2, the solutions are obtained with the help of these theorems. In theorems 3 and 5, the values v₁ and v₂ of games with the matrices in sizes N х N and N х (N - 1) respectively, representing the imitation and substitution attacks, as well as the optimum mixed strategies of players, are obtained. The value v₂ is expressed through the probability of choosing one of two source states and v₁ = 2/N. Theorem 4 generalizes the result of theorem 3 for A-code with k states of source, 2 ^ k ^ N.