RSA Encryption Algorithm
Learn the RSA public-key cryptosystem with step-by-step key generation, encryption, and decryption. Understand the mathematical foundations of modern cryptography.
RSA Parameters
Quick Examples:
Results
Original Message
HELLO
Step-by-Step Process
No steps to show yet. Start by generating RSA keys.
RSA Algorithm Explanation
Key Generation Process:
- 1. Choose Primes: Select two large prime numbers p and q
- 2. Calculate n: Compute n = p × q (public modulus)
- 3. Calculate φ(n): Compute φ(n) = (p-1)(q-1) (Euler's totient)
- 4. Choose e: Select e such that gcd(e, φ(n)) = 1
- 5. Calculate d: Find d such that (d × e) ≡ 1 (mod φ(n))
- 6. Keys: Public (n,e), Private (n,d)
Encryption/Decryption:
- Encryption: C = M^e mod n
- Decryption: M = C^d mod n
- Security: Based on difficulty of factoring large numbers
- Key Size: Typically 1024, 2048, or 4096 bits
- Applications: Digital signatures, secure communication
- Asymmetric: Different keys for encryption/decryption
Important Notes for Exams:
- • RSA security depends on the difficulty of factoring n = p × q
- • The private key d is kept secret, while public key (n,e) can be shared
- • For large messages, RSA is often used to encrypt symmetric keys (hybrid cryptography)
- • Padding schemes like OAEP are used in practice to prevent attacks
- • RSA can also be used for digital signatures by reversing the key usage