RSA Encryption Lab

RSA is an asymmetric encryption algorithm using two related keys:

1. Choose two distinct prime numbers p and q
2. Calculate n = p × q (the modulus)
3. Calculate φ(n) = (p-1)(q-1) (Euler's totient)
4. Choose e coprime to φ(n) (public exponent)
5. Calculate d such that e × d ≡ 1 (mod φ(n))

To encrypt a message m, compute: c = me mod n

Anyone with the public key (e, n) can encrypt messages, but only the private key holder can decrypt them.

To decrypt ciphertext c, compute: m = cd mod n

The private key (d, n) reverses the encryption, recovering the original message. This works due to Euler's theorem.

RSA security relies on the difficulty of factoring large numbers:

• • Given n, finding p and q is computationally hard
• • Real RSA uses 2048+ bit primes (not small ones like this demo)
• • Breaking RSA would require factoring enormous numbers
• • Quantum computers could threaten RSA (Shor's algorithm)