#01 1. Shor's Algorithm and the Harvest Now, Decrypt Later Threat Model
The cryptography that today's internet finance, confidential communication and cloud-native microservices rest on, namely RSA (hardness of integer factorization) and ECDSA / ECDH (hardness of the elliptic-curve discrete logarithm), can all be broken outright, and quickly, by Shor's algorithm on a sufficiently large quantum computer.
The harsher reality is this: criminal groups and nation-state actors are already executing a "Harvest Now, Decrypt Later" strategy, intercepting and warehousing enormous volumes of encrypted traffic in data centers, waiting for practical quantum computing to unlock all of it at once.
#02 2. Lattice Cryptography and the Mathematics of Module-LWE
Unlike classical number-theoretic problems, a lattice is a discrete grid of points in n-dimensional Euclidean space generated by a set of basis vectors. Finding the lattice point closest to an arbitrary random point (CVP), or the shortest non-zero vector (SVP), remains exponentially hard even for quantum algorithms.
ML-KEM (Kyber) is built on learning with errors over module lattices: small Gaussian error is injected into polynomial multiplication, making it impossible to recover the original key material without the secret key.