Computer and Information Security Handbook, 3rd Edition

3. Classical Cryptography

The conceptual foundation of cryptography was laid out around 3000 years ago in India and China. Earlier work in cryptology centered on messages that were expressed using alphanumeric symbols; hence encryption involved simple algorithms such as shifting characters within the string of the message in a defined manner, which is now known as a shift cipher. We will also introduce the necessary mathematics of cryptography: integer and modular arithmetic, linear congruence, Euclidean and Extended Euclidean algorithms, Fermat’s theorem, and ECs. We will specify useful notations in context.

Take the set of integers:

Z={…………,−3,−2,−1,0,1,2,3,……………}

For any integers a and n, we say that n divides a if the remainder is 0 after the ...