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Full-Text Articles in Physical Sciences and Mathematics
Cayley Graphs Of Semigroups And Applications To Hashing, Bianca Sosnovski
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
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 …