Asymmetric Encryption: RSA and Elliptic Curves

Asymmetric encryption uses a mathematically linked key pair: a public key (shared freely) and a private key (kept secret). Data encrypted with the public key can only be decrypted with the private key, and vice versa.

RSA (Rivest–Shamir–Adleman, 1977) is based on the difficulty of factoring large prime numbers. Security depends on key size: RSA-2048 is current minimum; RSA-4096 for high-security use. RSA is slower than symmetric encryption — used for key exchange, not bulk data.

RSA key generation:

ECC provides equivalent security to RSA with much smaller key sizes. A 256-bit ECC key is comparable to a 3072-bit RSA key. Smaller keys mean faster operations and less bandwidth — critical for TLS handshakes and mobile devices.

Widely used curves:

• P-256 (secp256r1) — NIST standard, used in TLS
• X25519 — designed by Bernstein, efficient key exchange, no patent concerns
• Ed25519 — EdDSA signature scheme, used in SSH keys

In practice, asymmetric and symmetric encryption are combined:

1. Asymmetric: encrypt a random symmetric key with recipient's public key
2. Symmetric: encrypt the actual data with that key

This is how TLS works: RSA/ECDH negotiates session keys; AES encrypts the session data.

Diffie-Hellman (DH) allows two parties to establish a shared secret over an insecure channel without exchanging a key. The shared secret is used to derive a symmetric session key. ECDH (Elliptic Curve DH) is the modern variant used in TLS 1.3.

Perfect Forward Secrecy (PFS): each session uses ephemeral DH keys that are discarded after use. Even if the server's private key is later compromised, past recorded sessions cannot be decrypted. TLS 1.3 mandates PFS; look for ECDHE cipher suites in TLS 1.2.

RSA serves two purposes:

• Encryption: encrypt with public key → only private key holder can decrypt
• Signing: sign with private key → anyone with public key can verify authenticity

Use OAEP padding for encryption; PSS padding for signatures. Never use PKCS#1 v1.5 for encryption.

Quantum computers running Shor's algorithm could break RSA and ECC. NIST is standardizing post-quantum cryptography algorithms (CRYSTALS-Kyber for key exchange, CRYSTALS-Dilithium for signatures). Migration will take years — start inventorying crypto-dependent systems now.

Asymmetric keys require secure management: generate on trusted hardware, protect private keys with passphrase or HSM, rotate keys periodically, revoke compromised keys via CRL/OCSP. Lost private keys mean losing access to all encrypted data.

Which approach combines asymmetric and symmetric encryption, using asymmetric to exchange a key and symmetric to encrypt data?

Asymmetric encryption uses public/private key pairs. RSA is proven but slow; ECC provides equivalent security with smaller keys. Hybrid encryption combines both for practical use. Diffie-Hellman enables secure key exchange; ECDHE provides forward secrecy. Quantum threats loom — watch NIST PQC standardization.