A Unified Approach to Image Recognition and Cryptography via Flexible Weak Inverse Property Quasigroups

Nonassociative algebra presents multiple options for comprehending and dealing with difficulties in graph theory, artificial intelligence, and cryptography. Its distinctive traits introduce genuine concepts and procedures not found in conventional associative algebra, yielding to new results from studies and breakthroughs in multiple disciplines. Vertex algebras are nonassociative binary operations providing a complete breakdown of graph structures. Algebra without associativity can be employed to strengthen the security guaranteed by specific cryptographic algorithms and protocols, as well as to establish new chances for accomplishing cryptographic targets such as encryption, hashing, and digital signatures. Quasigroup ∐, a generalization of both algebraic structures, loop groups, and groups, may possess a crucial role in future applications. This paper investigates the structural properties of the inverse graph when compared to the finite flexible quasigroup ( C 2 θ × K 4 , ⊛ 1 ). It also addresses the implementation of polynomial functions P T ( t ) in image and pattern detection, with emphasis on feature extraction and edge detection. The application of polynomials in imaging systems may improve recognizing object’s accuracy, curve fitting, and machine learning–based grouping, making them essential for computer vision modifications. Along with this, we made use of two classes of finite flexible non‐G‐quasigroups Y 1 and finite weak inverse property G‐quasigroups Y 2 in cryptography.