Faster TS field inverse

[mitschabaude]

Closes #1213
bindings: o1-labs/o1js-bindings#235

This adds a faster TS implementation of the field inverse algorithm.

Instead of the classical Extended Euclidian Algorithm, we use the state-of-the-art algorithm from https://eprint.iacr.org/2020/972.pdf. It benefits from doing most of the work in a tight loop which only operates on a few JS numbers with bit shifts and similar small operations, instead of doing lots of costly bigint modulos.

Note: Code changes mostly in the bindings PR

Results

• The new inverse is 3x faster as shown by a new benchmark:

> ./run src/bindings/crypto/benchmarks/inverse.ts

inverse                  50396ns @   20K ops/s
fast inverse             16785ns @   60K ops/s

• Contribution of field inverses to the ECDSA proof goes down from 5% to 1.2% and reduces proving time by about 1.5s

./run-debug src/examples/crypto/ecdsa/run.ts

Further work

The inverse could still be sped up a lot by moving to wasm (1000-5000ns are known to be possible). However, I think it has hit diminishing returns at least until we make the Rust/wasm prover much faster.

[Trivo25]

This could also be a great addition to the changelog 👀