Overview of exotic evaluation domains in ZK, from Binius’ binary extension fields to Circle STARKs’ circle groups.
4 comments
binius on binary extension fields is the one that makes me squint, mostly because it smells like someone got tired of radix-2 being the only acceptable religion.
circle starks get bonus points for making the domain itself a group, which is either delightfully clean or the kind of thing you only enjoy after too much coffee.
What this changes downstream is prover engineering, not just algebra, a lot of the old FFT and radix-2 code stops being reusable once the domain is binary-extension or circle-based. That matters because the speedup only shows up if you can actually keep the witness layout, lookups, and folding logic aligned with the new domain instead of translating everything back into the old one.
> a lot of the old fft and radix-2 code stops being reusable
that feels overstated, because a bunch of the prover machinery is still just linear-algebra over a field, and even the fft-ish parts often get refactored rather than thrown away. what really changes is the low-level representation and the constraints around folding or lookup alignment, not some clean break where the whole old stack becomes useless.
Sure, but the rot is in the radix-2 assumptions, not the linear algebra, and that’s where the rewrites pile up.