Public-key cryptography

Public-key cryptography (asymmetric cryptography) uses mathematically linked key pairs: a public key that can be shared openly and a private key that stays secret. Anyone can encrypt to a public key or verify a signature with it, while only the private key can decrypt or sign. This removes the need to distribute secret keys in advance, the problem that limited cryptography before New Directions in Cryptography introduced the idea in 1976.

#What quantum computers break, and what they do not

All widely deployed public-key schemes, including RSA, Diffie-Hellman, and elliptic-curve cryptography, rest on integer factoring or discrete logarithms. Shor's algorithm (Shor's algorithm) solves both in polynomial time, so a large quantum computer breaks classical key exchange and digital signature scheme schemes outright. Symmetric cryptography and hash functions are only quadratically affected and survive with larger parameters. Replacing the public-key layer with quantum-resistant constructions is the goal of post-quantum cryptography and the NIST standardization project.