RSA encryption

I learned a lot about assymetric key cryptography today! It was kind of neat. I'll write down about RSA here.

RSA encryption

• Example of public-private key pair algorithm.
• Text encrypted in blocks of 2048 or 4096 bits.
• Based on exponentiation and modulus arithmetic.
• Select two large primes $p, q$.
• Calculate $n = pq$.
• Calculate $\phi(n) = (p-1)(q-1)$.
• Select integer $e < \phi(n), \gcd(e, \phi(n)) = 1$
• Calculate $d \equiv e^{-1} \mod \phi(n), 1 < d < \phi(n)$
• Public key is $(e, n)$, private is $(d, n)$
• Encryption happens as follows: let plaintext be $P$. Ciphertext is computed as $C = P^e \mod n$
• For decryption raise ciphertext to the power of $d$.