Est. MMXXV

AfterRSA

Post-Quantum Cryptography — theory, code, news & deep dives

Vol. I  ·  No. 1 MMXXV afterrsa.com
On the Horizon

The Mathematics That Survives Quantum Computers

RSA has secured the internet since 1977. Its security rests upon a single assumption — that factoring the product of two large primes is computationally infeasible. For nearly five decades, that assumption has held.

A sufficiently powerful quantum computer running Shor's algorithm dissolves it entirely. The question is no longer whether such a machine will exist, but when.

AfterRSA documents the cryptography being built in its place — the lattice problems, the hardness assumptions, the algorithms and the institutions working to secure what comes next.

origin v* b₁ b₂

Fig. I — Integer lattice Λ(B) with basis vectors b₁, b₂ and shortest vector v*

The Shortest Vector Problem: given a lattice basis, find the shortest non-zero vector. No known algorithm — classical or quantum — solves this efficiently in high dimensions.

Contents of This Publication
I. Theory

Lattice mathematics, reduction proofs, hardness assumptions & paper breakdowns

II. Code

Python & Rust implementations, liboqs, benchmarks & side-channel analysis

III. News

NIST PQC standards, CVEs, industry migration & Q-Day developments

IV. Deep Dives

Long-form walkthroughs of Kyber, Dilithium, FALCON & FHE schemes

Topics Under Study
Learning With Errors Ring-LWE Module-LWE CRYSTALS-Kyber ML-KEM (FIPS 203) CRYSTALS-Dilithium ML-DSA (FIPS 204) FALCON / NTRU SLH-DSA (FIPS 205) Fully Homomorphic Encryption BGV / BFV Schemes CKKS Approximation Bootstrapping Shortest Vector Problem Basis Reduction Shor's Algorithm Hybrid Schemes liboqs / OpenSSL PQC NIST Standardisation Harvest Now Decrypt Later
Correspondence