Abstract
This paper investigates a method to increase cryptographic strength of the classical ElGamal digital signature scheme by applying operations in a finite field of square matrices, thus increasing the order of the cyclic multiplicative group and complicating the discrete logarithm computing procedure. The study presents an implementation example of the scheme, describes the procedures for signature generation and verification, and compares the statistical properties of computational processes in the matrix field and the classical prime residue field. The testing results (the NIST Statistical Test Suite) have confirmed that exponentiation in the matrix field demonstrates performance metrics not inferior to conventional exponentiation in the field of integers. The proposed approach appears to be promising for cryptographic applications with increased security requirements.