Physical Sciences and Mathematics Commons^™

An Adaptive Cryptosystem On A Finite Field, Awnon Bhowmik, Unnikrishnan Menon

Publications and Research

Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information. This paper introduces an adaptive block encryption scheme. This system is based on product, exponent, and modulo operation on a finite field. At the heart of this algorithm lies an innovative and robust trapdoor function that operates in the Galois Field and is responsible for the superior speed and security offered by it. Prime number theorem plays a fundamental role in this system, to keep unwelcome adversaries at bay. This is a …

Cayley Graphs Of Semigroups And Applications To Hashing, Bianca Sosnovski

Dissertations, Theses, and Capstone Projects

In 1994, Tillich and Zemor proposed a scheme for a family of hash functions that uses products of matrices in groups of the form $SL_2(F_{2^n})$. In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over $F_2$.

In this work, we present a new proposal for hash functions based on Cayley graphs of semigroups. In our proposed hash function, the noncommutative semigroup of linear functions under composition is considered as platform for the scheme. We will also …

Exploring Platform (Semi)Groups For Non-Commutative Key-Exchange Protocols, Ha Lam

Dissertations, Theses, and Capstone Projects

In this work, my advisor Delaram Kahrobaei, our collaborator David Garber, and I explore polycyclic groups generated from number fields as platform for the AAG key-exchange protocol. This is done by implementing four different variations of the length-based attack, one of the major attacks for AAG, and submitting polycyclic groups to all four variations with a variety of tests. We note that this is the first time all four variations of the length-based attack are compared side by side. We conclude that high Hirsch length polycyclic groups generated from number fields are suitable for the AAG key-exchange protocol.

Delaram Kahrobaei …