Summary: An Introduction to Cryptography
There are many mathematical issues that arise in analyzing even these basic cryptographic systems – especially ones dealing with primes and composites.
- Two impractical, but historically important, sources of new prime numbers are Fermat primes and Mersenne primes.
- The road to modern primality testing starts with the notion of Pseudoprimes. It isn’t the end of the road, because we still have prime impostors in Subsection 12.2.2.
- Hence we dig further into Miller’s test for base \(a\), which comes from our observations of how powers work in modular arithmetic.
- Finally, in Section 12.4 we see a modern, probabilistic primality test .
- Factoring is very important in testing the security of cryptography. We examine some very basic techniques, including The Fermat factorization algorithm.
- We see just a bit of more modern methods in Section 12.6, which should prepare you for more advanced ideas.
As always, there are Exercises to practice, but also to understand the theory better.
