Present post is an experiment on how to include math formulas in a Jekyll site. It is demonstrated with few steps the working principle of RSA, a widely used public key cryptographic algorithm.
Given a natural positive number , one can define the group . An element is invertible if and only if . The cyclic group is the group of invertible elements belonging to .
The Euler’s Totient Function, or Euler’s function is defined as: .
- if is a prime number, then
- if with and primes, then
The Euler’s Theorem, also known as Fermat-Eluer Theorem, states that
RSA cryptography is based on the above theorem and the listed properties. So the RSA algorithm can be summarized with following steps:
- Choose with and large primes;
- Choose integers ;
- Cipher the message obtaining the ciphertext ;
- Decipher obtaining : .