Cryptography by means of linear algebra and number theory

ABSTRACT: This thesis focuses on the techniques of cryptography in linear algebra and number theory. We first give the necessary review on modular arithmetic. Under Linear Algebra, Hill cipher cryptographic technique and its variations are studied. Under number theory, on the other hand, the definition of Euler function, and some important theorems in this regard are given. The cryptographic techniques such as the Caesar cipher, Exponential transformations and the Public key cryptographic techniques are explained. Finally, some more advanced cryptographic techniques such as the Digraph trans-formations are given. Keywords: Hill cipher, Euler theorem, Caesar cipher, Exponential method, Public Key method, Monoalphabetic cipher, Digraph transformations. …………………………………………………………………………………………………………………………