Post-quantum cryptography

Post-quantum cryptography comprises cryptographic algorithms designed to resist attacks by both classical and quantum computers, including algorithms that could break widely used public-key systems.

Lattice-based cryptography: Cryptography based on computational problems involving high-dimensional lattices. Lattice problems underpin several leading post-quantum encryption and signature schemes.
Shor's algorithm: A quantum algorithm that finds integer factors and discrete logarithms in polynomial time. It would break RSA and elliptic-curve cryptography on a sufficiently capable quantum computer.
ML-KEM: A standardized key-encapsulation mechanism based on module learning with errors. It is the principal standardized post-quantum mechanism for establishing shared secrets.
Elliptic-curve cryptography: Public-key cryptography based on the algebra of elliptic curves over finite fields. Its discrete-logarithm foundation is vulnerable to Shor's algorithm, unlike post-quantum assumptions.
Cryptanalysis: The study of methods for defeating or analyzing cryptographic systems. New classical attacks can invalidate a candidate even when quantum resistance was the original goal.
Code-based cryptography: Cryptography based on the difficulty of decoding general error-correcting codes. Error-correcting-code problems provide a distinct foundation for quantum-resistant public-key encryption.
Grover's algorithm: A quantum search algorithm that can find a target in an unstructured space quadratically faster than classical search. It weakens symmetric-key security less dramatically, motivating larger keys and security margins.
ML-DSA: A standardized digital signature algorithm based on module lattices. It provides a general-purpose post-quantum alternative for signing software and communications.
RSA key exchange: A method for establishing cryptographic keys using RSA encryption. It illustrates a classical public-key technique that a large quantum computer could defeat.
Side-channel attack: An attack that exploits information leaked by a system's physical implementation rather than its mathematical design. Post-quantum algorithms still need implementations resistant to timing, power, and other leakage.

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