feat: binary field - Githubissues

pluto / ronkathon

Cryptography Educational Foundations

https://pluto.xyz/blog/ronkathon-learn-cryptography-from-first-principles

Apache License 2.0

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feat: binary field #90

Closed lonerapier closed 3 months ago

lonerapier commented 3 months ago

It changes the following:

binary field
binary field extensions using tower field arithmetic

I've kept the implementation closer to theory as described in Section 2.3 of Binius. let me know if anything needs more work.

TODO:

[ ] figure out primitive_element_generator in extension fields
[x] docs and tests
[x] demonstrate power of binary fields by showing examples of embedding and small-by-large multiplication as described in the paper

lonerapier commented 3 months ago

@0xJepsen @Autoparallel this is ready for review now, I have added binary fields using our ronk traits in tests.

my reasoning being, I want to showcase the ease of arithmetic in binary fields and their efficient embedding and small by large multiplication properties. this obviously bloats the code a bit

can remove this entirely, and directly use our traits, if we feel that's the better approach.