feat: binary field #90
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src/field/binary/extension.rs
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| #[derive(Debug, Clone, Copy, Hash, PartialEq, Eq, PartialOrd, Ord)] | ||
| pub struct BinaryFieldExtension<const K: usize> | ||
| where [(); 1 << K]: { | ||
| /// coefficients of field element | ||
| pub coefficients: [BinaryField; 1 << K], | ||
| } |
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This guy is a const expr fiend now!!
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everywhere I go, I see compile time constants now :)
src/field/binary/mod.rs
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| /// binary field containing element `{0,1}` | ||
| #[derive(Debug, Default, Hash, Clone, Copy, PartialEq, Eq, PartialOrd, Ord)] | ||
| pub struct BinaryField(u8); |
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Perhaps a type alias instead with:
| pub struct BinaryField(u8); | |
| pub type BinaryField = PrimeField<2>; |
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I believe that would collapse a lot of this module here.
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that'll work flawlessly, but i believe it wouldn't allow us to showcase the main properties of binary field, i.e. addition being bitwise XOR and multiplication bitwise AND.
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What if you use a trait impl override/default/specialization? There are some Rust unstable feats that may help here to let us specialize to the binary case.
I thought we had it in the project, but don't seem to anymore. Anyway, here is an RFC for it:
https://rust-lang.github.io/rfcs/1210-impl-specialization.html
There could be others.
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@Autoparallel i need some more time to check and iterate on this. so, i'll open a new PR for this. don't want to block AES implementations due to this change, so merging it.
lonerapier
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@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. |
src/field/binary_towers/extension.rs
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| pub coefficients: [BinaryField; 1 << K], | ||
| } | ||
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| impl<const K: usize> BinaryFieldExtension<K> |
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Should I be thinking of BinaryFieldExtension<K> as the binary tower with height K?
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Yup correct, BinarFieldExtension<K> is isomorphic to
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Ah nice. Probably a nit, but what do you think of naming this BinaryTower so we can think of GaloisField<K, 2> as degree K extensions over PrimeField<2>?
Let it be known that it doesn't bother me either way, you should choose what you think is proper :)
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It changes the following:
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:
primitive_element_generatorin extension fields