Digital Near-Rings over the Galois Field GF(2) and Their Applications to Logic Circuits, Finite Automata, and Cryptography

Author(s)	Dr. Venkata Rama rao Kunapuli, Ms. Anuradha Kunapuli
Country	India
Abstract	This paper introduces the concept of digital near-rings defined over the Galois field GF(2) = {0, 1}, the algebraic foundation of digital electronics. We investigate the algebraic properties of finite digital near-rings, construct several examples, derive their Cayley tables, and study their ideals and homomorphisms. Applications to logic circuits, finite automata, cryptography, and coding theory are presented. The work demonstrates that digital near-rings provide a unified mathematical framework for binary computation and secure information processing.
Keywords	Digital Near-Ring, Galois Field, GF(2), Binary Algebra, Logic Gates, Finite Automata, Cryptography, Digital Electronics.
Field	Mathematics > Maths + Physics
Published In	Volume 7, Issue 4, July-August 2026
Published On	2026-08-14

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