ABSTRACT
In the study of contemporary cryptography, it is virtually always necessary to recognize that the way of representing information is no longer in human language alphabet, but rather in the “alphabet” consisting of the two binary symbols, 0 and 1. We will see in this chapter that in order to do the necessary calculations for encryption and decryption in this binary environment, we need to use certain models of computation that cannot rely on integers, rational numbers, or real numbers.
Hence this chapter will develop the underlying approaches to computation in what is known as “modular arithmetic” and beyond modular arithmetic to a very related computational model called Galois fields.
The second part of this chapter will introduce necessary matrix algebra or linear algebra computations.
