Extension field #44

lonerapier · 2024-05-07T00:19:30Z

This PR closes issue #40

It changes the following:

adds 2 degree extension field for PlutoField. I've not made field extension generic over degree. let me know if that is required.

0xJepsen · 2024-05-07T14:06:49Z

src/field/gf_101_2.rs

+use crate::field::FiniteField;
+
+/// Pluto curve with modulus 101 supports two degree extension field. This can be verified
+/// by finding out embedding degree of the curve, i.e. smallest k: r|q^k-1


When reading about the embedding degree I was trying to see this by hand but came across some questions. In our case r is our curve order which is 17 and p is field order which is 101. How does 17 | 101 ^2 - 1 which is 17 | 10200. 17 doesn't divide 10200. Also 10200 mod 101 is just 17 | 100. Do I have an error in my arithmetic? Are we working in a field here?

17 doesn't divide 10200.

Umm, Waylon 17 does divide 10200.

In our case r is our curve order which is 17

Also, our curve order is 102 (101 points + 1 point at infinity). 17 is the largest prime factor of $r$, thus, 17 is the order of the largest subgroup generated by the curve. Verified using this sage script.

E1 = EllipticCurve(F, [0, 3]) print(E1.order()) P1 = E1(1, 2) print(P1.order()) k = 17 cofactor = 6 # use cofactor clearing to find generator of prime order subgroup # take a random point, and multiply by cofactor until it's INF point G = E1.random_point() INF = E1(0) print(G, cofactor * G) while cofactor * G == INF: print("as") G = E1.random_point() Ps = cofactor * G print(cofactor * G, Ps.order())

that's a classic 😅

0xJepsen · 2024-05-07T14:08:06Z

src/field/gf_101_2.rs

+#[derive(Clone, Default, Copy, Eq, PartialEq, Hash, Debug, Serialize, Deserialize)]
+
+/// Quadratic Extension field element represented as polynomial of degree 1 in form:
+/// a_0 + a_1*t where {a_0, a_1} \in \mathhbb{F}. Uses irreducible poly of the form:


I think this is the right approach but curious how or if we should use this in our polynomial module. I know @Autoparallel you have been working on the FFTs and polynomial interface. Maybe you have some insight here?

Let me get the polynomial PR up.

0xJepsen · 2024-05-07T14:10:58Z

src/field/gf_101_2.rs

+
+/// Quadratic Extension field element represented as polynomial of degree 1 in form:
+/// a_0 + a_1*t where {a_0, a_1} \in \mathhbb{F}. Uses irreducible poly of the form:
+/// (X^2-K).


should this be X^2 -K or X^2 + K? X^2 + 2 is irreducible in F_{101} and should be used to generate our extension field.

I think both work as (correct me if I'm wrong) 2 is not a square in GF_{101}.

yeah, both of them are irreducible, added it in the field sage script as well

ronkathon/math/field.sage

Lines 47 to 51 in 9c0ba70

Ft.<t> = F[]

# irreducible element: t^2-2

P = Ft(t ^ 2 - 2)

assert P.is_irreducible()

src/field/gf_101_2.rs

Autoparallel

I'm good with this to go in as is :)

Autoparallel · 2024-05-07T15:02:03Z

src/field/gf_101.rs

@@ -83,6 +83,8 @@ impl FiniteField for GF101 {
  fn neg_one() -> Self { Self::new(Self::ORDER - 1) }

  fn generator() -> Self { Self::new(2) }
+
+  fn from_canonical_u32(n: u32) -> Self { Self::new(n) } // TODO: recheck


This is a nit, but we don't really need this if we just use GF101::new() right?

but then that's struct specific function right? We need a trait specific function to create new values, for example: in extension fields, each subvalue in extension field element is base field element.

ronkathon/src/field/gf_101_2.rs

Line 69 in 9c0ba70

Self { value: [F::from_canonical_u32(15), F::from_canonical_u32(20)] }

Is there a better way in Rust to do this? Sorry, still in my learning path for Rust.

Autoparallel · 2024-05-07T15:03:01Z

src/field/gf_101_2.rs

+#[derive(Clone, Default, Copy, Eq, PartialEq, Hash, Debug, Serialize, Deserialize)]
+
+/// Quadratic Extension field element represented as polynomial of degree 1 in form:
+/// a_0 + a_1*t where {a_0, a_1} \in \mathhbb{F}. Uses irreducible poly of the form:


Let me get the polynomial PR up.

Autoparallel · 2024-05-07T15:03:36Z

src/field/gf_101_2.rs

+
+/// Quadratic Extension field element represented as polynomial of degree 1 in form:
+/// a_0 + a_1*t where {a_0, a_1} \in \mathhbb{F}. Uses irreducible poly of the form:
+/// (X^2-K).


I think both work as (correct me if I'm wrong) 2 is not a square in GF_{101}.

src/field/gf_101_2.rs

lonerapier · 2024-05-07T18:28:59Z

@0xJepsen @Autoparallel changes done. let me know if any others are needed

commit 2637594 Author: Waylon Jepsen <[email protected]> Date: Thu May 9 10:38:12 2024 -0600 curves: Second curve group and some test (#49) * chore: tests + scalar multiplication * fmt * wip: compiles, but generator point is broken * wip * fix mul, generator and add hardcoded tests (#51) * fix mul, generator and add hardcoded tests * fix generator test * wip * fix: test fails when rng has no inverse --------- Co-authored-by: Sambhav <[email protected]> commit def9371 Author: Waylon Jepsen <[email protected]> Date: Thu May 9 09:36:25 2024 -0600 docs: readme (#46) * docs: readme * wip: pairing check * docs * Update README.md Co-authored-by: Colin Roberts <[email protected]> * Update README.md Co-authored-by: Colin Roberts <[email protected]> --------- Co-authored-by: Colin Roberts <[email protected]> commit ab0d374 Author: Sambhav <[email protected]> Date: Wed May 8 03:00:15 2024 +0530 Extension field (#44) * feat: extension field init * add test * add more tests and comments * move pow impl default to trait commit f9aa66e Author: Waylon Jepsen <[email protected]> Date: Tue May 7 09:00:35 2024 -0600 curves in sage (#39) commit 63ce62f Author: Waylon Jepsen <[email protected]> Date: Mon May 6 17:46:22 2024 -0600 fix: lock commit d1c84eb Author: Colin Roberts <[email protected]> Date: Mon May 6 16:39:25 2024 -0700 feat: home-baked `FiniteField` trait (#38) * feat: new `FiniteField` trait Now everything compiles again. Will work to clean this all up and get all the tests to pass. * fix: `GF101` tests pass * fix: reimplement monty optimizations * clean: udeps --------- Co-authored-by: Waylon Jepsen <[email protected]> commit 96c8b66 Merge: fb27e5f 62a9a57 Author: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> Date: Mon May 6 23:26:56 2024 +0000 Merge pull request #42 from pluto/dependabot/cargo/anyhow-1.0.83 Bump anyhow from 1.0.82 to 1.0.83 commit 62a9a57 Author: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com> Date: Mon May 6 23:26:43 2024 +0000 Bump anyhow from 1.0.82 to 1.0.83 Bumps [anyhow](https://github.com/dtolnay/anyhow) from 1.0.82 to 1.0.83. - [Release notes](https://github.com/dtolnay/anyhow/releases) - [Commits](dtolnay/anyhow@1.0.82...1.0.83) --- updated-dependencies: - dependency-name: anyhow dependency-type: direct:production update-type: version-update:semver-patch ... Signed-off-by: dependabot[bot] <[email protected]>

lonerapier added 2 commits May 7, 2024 05:48

feat: extension field init

37b8f66

add test

50651e1

0xJepsen requested a review from Autoparallel May 7, 2024 01:16

add more tests and comments

9c0ba70

lonerapier force-pushed the extension_field branch from 0524294 to 9c0ba70 Compare May 7, 2024 06:30

0xJepsen reviewed May 7, 2024

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Autoparallel approved these changes May 7, 2024

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0xJepsen linked an issue May 7, 2024 that may be closed by this pull request

Extension fields #40

Closed

move pow impl default to trait

8f93f8b

0xJepsen merged commit ab0d374 into pluto:main May 7, 2024
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lonerapier deleted the extension_field branch May 8, 2024 05:16

github-actions bot mentioned this pull request Jul 1, 2024

chore: release v0.1.0 #111

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Extension field #44

Extension field #44

lonerapier commented May 7, 2024 •

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lonerapier commented May 7, 2024

	Ft.<t> = F[]

	# irreducible element: t^2-2
	P = Ft(t ^ 2 - 2)
	assert P.is_irreducible()

Extension field #44

Extension field #44

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lonerapier commented May 7, 2024

lonerapier commented May 7, 2024 •

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0xJepsen May 7, 2024 •

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