Date of Award

4-2016

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Advisor

Dr. Adarna Dieue

Second Advisor

Dr. Kanat Abdukhalikov

Third Advisor

Dr. Moussa Benoumhani

Abstract

We study two families of functions over finite fields; the Multivalued Threshold

Functions and the Multivariate Polynomials. Recent advances made in our Conception and our understanding of Boolean Threshold Functions and Multivariate Threshold Functions have considerably increased the importance of the role that they Play in our days in areas like cryptography, circuit complexity, learning theory, social choice, quantum complexity, and in many other areas. Theoretical aspects of Bovid and Gauche who gave an algebraic first studied threshold functions Approach of Boolean Threshold Functions using group ring theory. We will present some algebraic properties of Boolean threshold functions. For the family of Multivariate Polynomials, it was first used by Matsumoto and Imai to design aCryptosystem. Many others researchers followed their steps with a design of new post Quantum multivariate cryptosystems. Unfortunately, many of them have been proven Insecure. We introduce in this thesis a new multivariate cryptosystem that supposes to resist quantum computers attacks.

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Mathematics Commons

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