Lattice-based cryptography

<p>Lattice-based cryptography is the generic term for constructions of <a href="/facts/Cryptographic_primitive/fy6vq5YM">cryptographic primitives</a> that involve <a href="/facts/Lattice_(group)/2ls9Iv9N">lattices</a>, either in the construction itself or in the security proof. Lattice-based constructions support important standards of <a href="/facts/Post-quantum_cryptography/1qeqUQve">post-quantum cryptography</a>.  Unlike more widely used and known public-key schemes such as the <a href="/facts/RSA_(cryptosystem)/XTzyfHuq">RSA</a>, <a href="/facts/Diffie-Hellman/xR4YQcaD">Diffie-Hellman</a> or <a href="/facts/Elliptic-curve_cryptography/YbjcXIWk">elliptic-curve</a> cryptosystems — which could, theoretically, be defeated using <a href="/facts/Shor%2527s_algorithm/9JwEtznC">Shor's algorithm</a> on a <a href="/facts/Quantum_computing/nbbcgmvq">quantum computer</a> — some lattice-based constructions appear to be resistant to attack by both classical and quantum computers. Furthermore, many lattice-based constructions are considered to be secure under the <a href="/facts/Computational_hardness_assumption/ewjpb1I7">assumption</a> that certain well-studied computational <a href="/facts/Lattice_problem/YHXNNrrG">lattice problems</a> cannot be solved efficiently.
</p><p>In 2024 <a href="/facts/NIST/gr9Fnh85">NIST</a> announced the Module-Lattice-Based Digital Signature Standard for post-quantum cryptography.
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Lattice-based cryptography open-in-new

Lattice-based cryptography