Asymmetric Encryption (Public-Key Cryptography)

Definition

Asymmetric encryption uses key pairs—a public key for encryption and a private key for decryption. This enables secure communication without prior shared secrets. Traditional schemes (RSA, ECC) are vulnerable to quantum attacks; post-quantum alternatives like Kyber provide asymmetric encryption resistant to both classical and quantum computers.

Technical Explanation

Asymmetric schemes rely on mathematical trapdoor functions—easy to compute forward (public key → ciphertext) but infeasible to reverse without the private key. Classical schemes use factoring (RSA) or discrete logarithms (ECC); Shor's algorithm breaks both.

Post-quantum asymmetric cryptography uses different trapdoors: lattice problems (Kyber, Dilithium), hash constructions (SPHINCS+), or code problems (McEliece). These resist known quantum algorithms while maintaining the public/private key paradigm essential for modern communications.

SynX Relevance

SynX replaces quantum-vulnerable asymmetric cryptography (ECDSA, ECDH) with quantum-resistant alternatives. Kyber-768 provides asymmetric key encapsulation; SPHINCS+ provides asymmetric signatures. The public/private key model remains—only the underlying mathematics changed for quantum resistance.

Frequently Asked Questions

Why is asymmetric crypto more vulnerable than symmetric?: Shor's algorithm provides exponential speedup against factoring/discrete-log; Grover's gives only quadratic speedup against symmetric.
Are Kyber keys bigger than ECDSA keys?: Yes—Kyber-768 public keys are ~1,184 bytes vs ~33 bytes for ECDSA. Security requires size trade-offs.
Can asymmetric encryption be eliminated?: Not practically—key distribution and digital signatures require asymmetric paradigms.

Quantum-safe public-key cryptography. Modern asymmetric security with SynX