Kloosterman Equation based Fast AI Application
Keywords:
AI, Bilinear extension, Cyclic code, Galois fields, Galois Theory, Kloosterman equationAbstract
This paper presents a fast AI algorithm whose mechanism comprises with kloosterman equation defined by . The cyclic code application is developed over the Galois fields whose keys are the solution of this equation. The hardness of this problem comprises the security, thus the proposed cyclic code sets a security protocol defined over the following equation:
Let be a finite field and its elements are . Then the cyclic shift is called the cyclic code over the bilinear extension. This code maps with Galois Theory through algebraic extension for generating the permutation polynomial and its variants over the finite field. The bilinear extension is defined for Galois representations. This discrete structure opens the new dimension in the study of Galois Theory. The fundamental results on Galois Theory through ring theoretic properties are also very interesting results. Hecke algebras and Galois extensions are functioned together by the ring properties.
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