Asymmetric Key Encryption
Asymmetric Key Encryption
This domain tests public-key mechanics: which hard problem backs each algorithm, what each one can and cannot do, and how hybrid encryption makes asymmetric cryptography practical.
Core rules
- Two keys, two directions. Encrypt with the public key → only the private key decrypts (confidentiality). Sign with the private key → anyone holding the public key verifies (authenticity, non-repudiation). Neither key substitutes for the other's role.
- RSA - security rests on integer factorization of n = p·q. The public exponent e and private exponent d satisfy e·d ≡ 1 mod φ(n). Use OAEP padding; textbook RSA is deterministic and malleable.
- Diffie-Hellman - key agreement, not encryption. Security rests on the discrete logarithm problem. Unauthenticated DH is open to man-in-the-middle substitution; ephemeral DHE/ECDHE give forward secrecy.
- ECC - elliptic-curve discrete logarithms; 256-bit ECC ≈ 3072-bit RSA in strength, with far smaller keys and faster operations.
- ElGamal - randomized encryption from the DH problem, doubling ciphertext size.
- Hybrid model - asymmetric cryptography wraps or agrees a symmetric session key; the symmetric cipher moves the data. TLS, S/MIME and PGP all work this way.
Worked example
RSA with p = 61, q = 53: n = 3233, φ(n) = 3120. Choose e = 17, coprime to 3120. Then d = 2753 because 17 × 2753 mod 3120 = 1. Encrypt m = 65: c = 65^17 mod 3233 = 2790. Decrypt: 2790^2753 mod 3233 = 65. The arithmetic works, but n = 3233 factors instantly - this is a teaching example, not a key.
Traps
- Claiming Diffie-Hellman encrypts data.
- Choosing static RSA key transport when forward secrecy is required.
- Comparing key sizes across algorithm families (2048-bit RSA is not "eight times stronger" than 256-bit ECC).
- Omitting padding on RSA and assuming the raw operation is safe.