:INFO
The Transition Happening Right Now
NIST ran the most open cryptographic standardization competition since AES: 69 submissions in 2016, multiple public rounds of cryptanalysis, and final standards published in 2024. The winning algorithms rely on mathematical problems believed to be hard even for quantum computers — primarily the geometry of high-dimensional lattices.


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The Learning With Errors Problem
The Learning With Errors (LWE) problem: given many pairs (a_i, b_i) where b_i = a_i times s + e_i mod q, with s a secret vector and e_i small random noise, recover s. Without the noise this is easy linear algebra. With noise, no efficient classical or qua

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ML-KEM: Key Encapsulation
ML-KEM (formerly Kyber) is the NIST key encapsulation mechanism, based on Module-LWE — LWE structured using module lattices for efficiency. It generates a shared secret that two parties can use for symmetric encryption. Key and ciphertext sizes are around

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ML-DSA: Digital Signatures
ML-DSA (formerly Dilithium) is the primary NIST signature algorithm, based on Module-LWE and Module-SIS (short integer solution over module lattices). Signature size is approximately 2–3 KB. Security is based on the hardness of finding short vectors satis

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SLH-DSA: Hash-Based Signatures
SLH-DSA (formerly SPHINCS+) builds signatures from hash functions using a hypertree of Merkle trees and one-time signature schemes. Its security assumption is minimal: if the underlying hash function is secure, the signature scheme is secure. No new mathe

:CHECKLIST
PQC Migration Checklist
[ ] Inventory all cryptographic primitives in use across services
[ ] Identify which use RSA, ECDH, ECDSA, or DH for key exchange or signatures
[ ] Deploy ML-KEM alongside ECDH as a hybrid for TLS key exchange (X25519+ML-KEM768)
[ ] Update TLS library to a version supporting hybrid post-quantum key exchange
[ ] Plan certificate migration to ML-DSA or use hybrid classical+PQC certificates
[ ] Prioritize systems handling long-lived secrets or data with multi-year confidentiality
[ ] Monitor NIST and library release notes for parameter updates

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Go Deeper: The Geometry of Lattices
Lattice-based cryptography rests on the geometry of high-dimensional lattices — finding the shortest vector in a lattice is a deep mathematical problem connected to number theory, geometry, and the foundations of algorithms. The hardness is preserved under quantum computation because lattice problems lack the periodic structure that Shor exploits.


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:LINK
https://csrc.nist.gov/projects/post-quantum-cryptography
NIST Post-Quantum Cryptography Standardization