RSA Calculator
Explore how RSA encryption works using small prime numbers. This educational calculator generates public and private keys, encrypts a message, and decrypts it back to demonstrate the complete RSA process.
RSA (Rivest-Shamir-Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission. This calculator demonstrates the algorithm with small numbers so you can see every step.
How RSA Works
- Choose two primes p and q. Compute n = p x q.
- Compute Euler's totient: phi(n) = (p-1)(q-1).
- Choose public exponent e such that 1 < e < phi(n) and gcd(e, phi(n)) = 1. The value 65537 is a common choice.
- Compute private exponent d such that e x d = 1 (mod phi(n)).
- Encrypt: ciphertext c = m^e mod n.
- Decrypt: plaintext m = c^d mod n.
Why It Works
The security relies on the difficulty of factoring n back into p and q. Multiplying two primes is fast, but reversing that multiplication (factoring) is computationally hard for very large numbers. Real RSA uses primes with hundreds of digits.
Important Note
This calculator uses small numbers for educational purposes. Real RSA implementations use 2048-bit or larger keys, which involve primes with over 300 digits each.