RSA encryption

2026-03-14

Basics of RSA asymmetric encryption.

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

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 $d$ .

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