papers/lux-lattice-cryptography-primer/sections/99-conclusion.tex

\section{Conclusion}


Lattice cryptography is not magic---it is linear algebra with noise. LWE says: linear
equations are easy; noisy linear equations are hard. Ring-LWE says: we can exploit
polynomial ring structure for efficiency without losing hardness. Module-LWE says: we
can parameterize security by matrix dimension for flexibility.

The NIST standards (ML-KEM, ML-DSA) are specific instantiations with concrete parameters
chosen for practical security. Pulsar extends them to threshold operations for
decentralized signing. The NTT makes all of it fast.

This paper covered the theory. Our companion papers cover the practice: NTT with SIMD
acceleration, EVM precompiles for on-chain verification, and the formal proofs that
tie it all together.

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