Foundational mathematics
As the subject of cryptography is based on mathematics, this section will introduce some basic concepts that will help you understand the concepts presented later. An explanation with proofs and relevant background for all of these terms would require somewhat complex mathematics, which is beyond the scope of this book. More details on these topics can be found in any standard number theory, algebra, or cryptography book:
- Modular arithmetic: Also known as clock arithmetic, numbers in modular arithmetic wrap around when they reach a certain fixed number. This fixed number is a positive number called modulus (sometimes abbreviated to mod), and all operations are performed concerning this fixed number. In other words, this type of arithmetic deals with the remainders after the division operation. For example, 50 mod 11 is 6 because 50/11 leaves a remainder of 6.
- Sets: These are collections of distinct objects, for example, X = {1, 2, 3, 4, 5...
