How RSA works?
RSA works through a mathematical process involving key pairs and modular arithmetic. Here's a simplified explanation:
1. **Key Generation:**
- Choose two large prime numbers, p and q.
- Calculate their product, n = p * q.
- Compute φ(n), where φ is Euler's totient function, given by φ(n) = (p-1)(q-1).
- Choose an integer e such that 1 < e < φ(n), and e is coprime to φ(n). This is the public key exponent.
- Calculate the private key exponent d, such that (d * e) ≡ 1 (mod φ(n)).
2. **Public Key (e, n):**
- e is used for encryption.
3. **Private Key (d, n):**
- d is kept secret and used for decryption.
4. **Encryption:**
- Convert the plaintext message into a numerical value M.
- Compute the ciphertext C = M^e mod n.
5. **Decryption:**
- Compute the original message M = C^d mod n.
The security of RSA relies on the difficulty of factoring the product of two large prime numbers (n). While it's computationally easy to calculate n from p and q, factoring n back into p and q is a complex problem, especially when n is large. This makes it challenging for an attacker to derive the private key from the public key.
RSA Architecture.
Designing an RSA-based server and client system involves implementing the key generation, encryption, and decryption processes on both ends. Here's a high-level overview:
**Server Side:**
1. **Key Generation:**
- Generate a pair of large prime numbers, p and q.
- Calculate n = p * q and φ(n) = (p-1)(q-1).
- Choose an encryption key (public key, typically denoted as e) and calculate the corresponding decryption key (private key, denoted as d).
2. **Public Key Distribution:**
- Share the public key (modulus n and public exponent e) openly.
3. **Encryption (Receiving End):**
- Receive the ciphertext from the client.
- Use the private key (d, n) to decrypt the ciphertext and obtain the original message.
**Client Side:**
1. **Key Generation:**
- Similar to the server, generate a pair of large prime numbers (p and q), calculate n and φ(n), and choose encryption (public) and decryption (private) keys.
2. **Public Key Distribution:**
- Share the public key (modulus n and public exponent e) with the server.
3. **Encryption (Sending End):**
- Convert the plaintext message into a numerical value (M).
- Use the server's public key (n, e) to encrypt the message: C = M^e mod n.
- Send the ciphertext to the server.
**Considerations:**
- **Key Management:** Safeguard private keys, as they are critical for decryption.
- **Security:** Use sufficiently large key sizes to ensure security against modern computational threats.
- **Randomness:** Ensure the randomness of prime number generation for key pairs.
- **Communication Security:** Consider using additional protocols (e.g., TLS/SSL) to secure the communication channel between the server and client.
This is a simplified overview, and real-world implementations might involve additional considerations like secure key storage, handling key updates, and protecting against various attacks (e.g., side-channel attacks).