Cryptography

RSA

Background:

RSA(Rivest–Shamir–Adleman) is a asymmetric cryptosystem that uses prime numbers to ensure data communication. RSA hinges on the unique property of factoring such that it is very difficult to factor a large number when you don’t know it’s prime composition. In fact, it is proven that there does not exist an efficient non-quantum integer factorization algorithm.

Operation:

RSA algorithm hinges around the following equation:

\[(m^{e})^{d} \equiv m \mod n\]

Where:

• $(n,e)$ is the public key pair
• $d$ is the private key. $d$ is a composite product of two prime numbers $p$ and $q$.
• $m$ is the plaintext message

Using this equations, we have the following operations: