MERLIN SCIENCE — Lattice Reduction on H4 Coxeter Lattices: BKZ Block Size and the Golde — E8 Intelligence Research

Here is the finding in one sentence. Lattice basis reduction, the algorithmic workhorse behind lattice cryptography, has an optimality constant hiding in plain sight, and it is the golden ratio. Here is the context. LLL and BKZ reduce a lattice basis to something short and nearly orthogonal. LLL gives a polynomial-time guarantee, roughly two to the n over four times the determinant to the one over n. BKZ improves quality with a block size beta, trading runtime for a better Hermite factor that tends to one as beta grows. Everyone in the field knows this tradeoff. What is less discussed is what the optimal reduction factor actually is when you stop approximating. Here is the mechanism, and you can check every step. In two dimensions, Gauss reduction is not an approximation, it is exact, and its worst case is the golden ratio. Repeated subtraction drives the basis angle to sixty degrees and the length ratio toward phi. That is not numerology. Phi is the unique positive fixed point of x Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com