Physical Sciences and Mathematics Commons^™

Latin Squares And Their Applications To Cryptography, Nathan O. Schmidt

Boise State University Theses and Dissertations

A latin square of order-n is an n x n array over a set of n symbols such that every symbol appears exactly once in each row and exactly once in each column. Latin squares encode features of algebraic structures. When an algebraic structure passes certain "latin square tests", it is a candidate for use in the construction of cryptographic systems. A transversal of a latin square is a list of n distinct symbols, one from each row and each column. The question regarding the existence of transversals in latin squares that encode the Cayley tables of finite groups …

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 …

Finding Prime Numbers: Miller Rabin And Beyond, Christina Mcintosh

Furman University Electronic Journal of Undergraduate Mathematics

This expository paper motivates and explains the Miller Rabin test and gives some generalizations of it. The Miller Rabin test is a standard probabilistic test used to find large prime numbers quickly.

The Evolution Of Cryptology, Gwendolyn Rae Souza

Electronic Theses, Projects, and Dissertations

We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of …

Efficient And Adaptively Secure Constructions Of Identity-Based Cyrptographic Primitives., Somindu Chaya Ramanna Dr.

Doctoral Theses

Public-key encryption (PKE) is an elegant solution to the fundamental problem of cryptography – secure communication between two parties over a public (insecure) channel. The basic idea is that every user A holds two keys – a public key (PKA) and a secret key (SKA). A user who wants to send a message to A encrypts it with PKA and sends the resulting ciphertext along the public channel. A, at the other end of the channel, decrypts the ciphertext using SKA and obtains the message. SKA is known to user A alone. Any third party intercepting data on the public …

Some Results On Analysis And Implementation Of Hc-128 Stream Cipher., Shashwat Raizada Dr.

Doctoral Theses

The HC-128 stream cipher is a successful entrant in the eStream candidate list (software profile) and is the lighter variant of HC-256 stream cipher. Apart from the analysis by the designer of the cipher (Hongjun Wu) to conjecture the security of this cipher, there are only a few other observations on this cipher despite being the focus of researchers during the three phases of eStream evaluation and later efforts in the community. Till date none of the security claims in favor of HC-128 by the designer could be broken. One may expect HC-128 stream cipher to be popular in commercial …