Question about field size

[pememoni]

Hey hey, I recently found this Valida and really excited about all of the smart choices and innovations that you are doing! I was curious about the 32-bit field size, as far as I know, most of the other similar projects e.g. Boojum , Polygon are using Goldilocks. Is there an interesting theoretical or engineering reason behind this decision?

[dlubarov]

Hey! We think 32-bit fields are a good long-term direction since they let us get much better throughput (like field operations per unit time) on CPUs and GPUs. (Even though modern CPUs support 64-bit integer arithmetic, it's scalar-only, whereas most CPUs have vectorized 32-bit multiplication.)

I think the optimal field choice is somewhat application-specific, but for applications that generally use less than 32 bits of space in each witness element anyway (e.g. lookup heavy applications), 32-bit seems like a good fit.