gen-state-the-rsa-algorithm-precisely-and-explain-why-it-matters-0469

State the RSA algorithm precisely and explain why it matters in 2-3 sentences.

# RSA Algorithm **Key Generation:** 1. Choose two large prime numbers p and q 2. Compute n = pq and φ(n) = (p-1)(q-1) 3. Choose public exponent e where 1 < e < φ(n) and gcd(e, φ(n)) = 1 4. Compute private exponent d where d ≡ e⁻¹ (mod φ(n)) 5. Public key: (n, e); Private key: (n, d) **Encryption:** C ≡ M^e (mod n) **Decryption:** M ≡ C^d (mod n) ## Why It Matters RSA enabled practical public-key cryptography, allowing two parties to communicate securely without pre-sharing secret keys—this revolutionized internet security for applications like HTTPS, email encryption, and digital signatures. Its security relies on the computational difficulty of factoring large numbers, making it infeasible for attackers to derive the private key from the public key. RSA became a cornerstone of modern cryptographic infrastructure, enabling secure e-commerce, banking, and digital communications at global scale.