(2026-01) Verified non-recursive calculation of Beneš networks applied to Classic McEliece
2026-01-23
The Beneš network can be utilised to apply a single permutation to different inputs repeatedly. We present novel generalisations of Bernstein's formulae for the control bits of a Beneš network and from them derive an iterative control bit setting algorithm. We provide verified proofs of our formulae and prototype a a provably correct implementation in the Lean language and theorem prover. We develop and evaluate portable and vectorised implementations of our algorithm in the C programming language. Our implementation utilising Intel's Advanced Vector eXtensions 2 feature reduces execution latency by 25% compared to the equivalent implementation in the libmceliece software library.