diff --git a/src/field/extension_field/quadratic.rs b/src/field/extension_field/quadratic.rs index dfb861c2..16743f12 100644 --- a/src/field/extension_field/quadratic.rs +++ b/src/field/extension_field/quadratic.rs @@ -55,13 +55,12 @@ impl> Field for QuadraticExtension { const TWO: Self = Self([F::TWO, F::ZERO]); const NEG_ONE: Self = Self([F::NEG_ONE, F::ZERO]); - const CHARACTERISTIC: u64 = F::CHARACTERISTIC; - // `p^2 - 1 = (p - 1)(p + 1)`. The `p - 1` term has a two-adicity of `F::TWO_ADICITY`. As // long as `F::TWO_ADICITY >= 2`, `p` can be written as `4n + 1`, so `p + 1` can be written as // `2(2n + 1)`, which has a 2-adicity of 1. const TWO_ADICITY: usize = F::TWO_ADICITY + 1; - const CHARACTERISTIC_TWO_ADICITY: usize = F::CHARACTERISTIC_TWO_ADICITY; + const CHARACTERISTIC_WITH_TWO_ADICITY: Option<(u64, usize)> = + F::CHARACTERISTIC_WITH_TWO_ADICITY; const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self(F::EXT_MULTIPLICATIVE_GROUP_GENERATOR); const POWER_OF_TWO_GENERATOR: Self = Self(F::EXT_POWER_OF_TWO_GENERATOR); diff --git a/src/field/extension_field/quartic.rs b/src/field/extension_field/quartic.rs index 1a34d40a..77329c94 100644 --- a/src/field/extension_field/quartic.rs +++ b/src/field/extension_field/quartic.rs @@ -56,14 +56,13 @@ impl> Field for QuarticExtension { const TWO: Self = Self([F::TWO, F::ZERO, F::ZERO, F::ZERO]); const NEG_ONE: Self = Self([F::NEG_ONE, F::ZERO, F::ZERO, F::ZERO]); - const CHARACTERISTIC: u64 = F::ORDER; - // `p^4 - 1 = (p - 1)(p + 1)(p^2 + 1)`. The `p - 1` term has a two-adicity of `F::TWO_ADICITY`. // As long as `F::TWO_ADICITY >= 2`, `p` can be written as `4n + 1`, so `p + 1` can be written as // `2(2n + 1)`, which has a 2-adicity of 1. A similar argument can show that `p^2 + 1` also has // a 2-adicity of 1. const TWO_ADICITY: usize = F::TWO_ADICITY + 2; - const CHARACTERISTIC_TWO_ADICITY: usize = F::CHARACTERISTIC_TWO_ADICITY; + const CHARACTERISTIC_WITH_TWO_ADICITY: Option<(u64, usize)> = + F::CHARACTERISTIC_WITH_TWO_ADICITY; const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self(F::EXT_MULTIPLICATIVE_GROUP_GENERATOR); const POWER_OF_TWO_GENERATOR: Self = Self(F::EXT_POWER_OF_TWO_GENERATOR); diff --git a/src/field/field_types.rs b/src/field/field_types.rs index dec22c9d..14426212 100644 --- a/src/field/field_types.rs +++ b/src/field/field_types.rs @@ -47,13 +47,12 @@ pub trait Field: const TWO: Self; const NEG_ONE: Self; - const CHARACTERISTIC: u64; - /// The 2-adicity of this field's multiplicative group. const TWO_ADICITY: usize; - /// The 2-adicity of this field's multiplicative group. - const CHARACTERISTIC_TWO_ADICITY: usize; + /// The field's characteristic and it's 2-adicity. + /// Set to `None` when the characteristic doesn't fit in a u64. + const CHARACTERISTIC_WITH_TWO_ADICITY: Option<(u64, usize)>; /// Generator of the entire multiplicative group, i.e. all non-zero elements. const MULTIPLICATIVE_GROUP_GENERATOR: Self; @@ -205,29 +204,32 @@ pub trait Field: // exp exceeds t, we repeatedly multiply by 2^-t and reduce // exp until it's in the right range. - let p = Self::CHARACTERISTIC; + if let Some((p, two_adicity)) = Self::CHARACTERISTIC_WITH_TWO_ADICITY { + // NB: The only reason this is split into two cases is to save + // the multiplication (and possible calculation of + // inverse_2_pow_adicity) in the usual case that exp <= + // TWO_ADICITY. Can remove the branch and simplify if that + // saving isn't worth it. - // NB: The only reason this is split into two cases is to save - // the multiplication (and possible calculation of - // inverse_2_pow_adicity) in the usual case that exp <= - // TWO_ADICITY. Can remove the branch and simplify if that - // saving isn't worth it. + if exp > two_adicity { + // NB: This should be a compile-time constant + let inverse_2_pow_adicity: Self = + Self::from_canonical_u64(p - ((p - 1) >> two_adicity)); - if exp > Self::CHARACTERISTIC_TWO_ADICITY { - // NB: This should be a compile-time constant - let inverse_2_pow_adicity: Self = - Self::from_canonical_u64(p - ((p - 1) >> Self::CHARACTERISTIC_TWO_ADICITY)); + let mut res = inverse_2_pow_adicity; + let mut e = exp - two_adicity; - let mut res = inverse_2_pow_adicity; - let mut e = exp - Self::CHARACTERISTIC_TWO_ADICITY; - - while e > Self::CHARACTERISTIC_TWO_ADICITY { - res *= inverse_2_pow_adicity; - e -= Self::CHARACTERISTIC_TWO_ADICITY; + while e > two_adicity { + res *= inverse_2_pow_adicity; + e -= two_adicity; + } + res * Self::from_canonical_u64(p - ((p - 1) >> e)) + } else { + Self::from_canonical_u64(p - ((p - 1) >> exp)) } - res * Self::from_canonical_u64(p - ((p - 1) >> e)) } else { - Self::from_canonical_u64(p - ((p - 1) >> exp)) + dbg!("yo"); + Self::TWO.inverse().exp_u64(exp as u64) } } @@ -450,15 +452,6 @@ pub trait PrimeField: Field { } } -pub trait SmallCharacteristicField: Field { - const SMALLCHAR: u64; - - #[inline] - fn inverse_2exp(exp: usize) -> Self { - todo!() - } -} - /// An iterator over the powers of a certain base element `b`: `b^0, b^1, b^2, ...`. #[derive(Clone)] pub struct Powers { diff --git a/src/field/goldilocks_field.rs b/src/field/goldilocks_field.rs index 7bdd3c77..14c0a281 100644 --- a/src/field/goldilocks_field.rs +++ b/src/field/goldilocks_field.rs @@ -66,10 +66,10 @@ impl Field for GoldilocksField { const ONE: Self = Self(1); const TWO: Self = Self(2); const NEG_ONE: Self = Self(Self::ORDER - 1); - const CHARACTERISTIC: u64 = Self::ORDER; const TWO_ADICITY: usize = 32; - const CHARACTERISTIC_TWO_ADICITY: usize = Self::TWO_ADICITY; + const CHARACTERISTIC_WITH_TWO_ADICITY: Option<(u64, usize)> = + Some((Self::ORDER, Self::TWO_ADICITY)); // Sage: `g = GF(p).multiplicative_generator()` const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self(7); diff --git a/src/field/prime_field_testing.rs b/src/field/prime_field_testing.rs index 9dae4896..1b7b97eb 100644 --- a/src/field/prime_field_testing.rs +++ b/src/field/prime_field_testing.rs @@ -144,7 +144,7 @@ macro_rules! test_prime_field_arithmetic { fn inverse_2exp() { type F = $field; - let v = ::PrimeField::TWO_ADICITY; + let v = ::TWO_ADICITY; for e in [0, 1, 2, 3, 4, v - 2, v - 1, v, v + 1, v + 2, 123 * v] { let x = F::TWO.exp_u64(e as u64); diff --git a/src/field/secp256k1_base.rs b/src/field/secp256k1_base.rs index 32615187..3e0d0ef0 100644 --- a/src/field/secp256k1_base.rs +++ b/src/field/secp256k1_base.rs @@ -11,7 +11,6 @@ use rand::Rng; use serde::{Deserialize, Serialize}; use crate::field::field_types::Field; -use crate::field::goldilocks_field::GoldilocksField; /// The base field of the secp256k1 elliptic curve. /// @@ -78,10 +77,8 @@ impl Field for Secp256K1Base { 0xFFFFFFFFFFFFFFFF, ]); - // TODO: fix - const CHARACTERISTIC: u64 = 0; const TWO_ADICITY: usize = 1; - const CHARACTERISTIC_TWO_ADICITY: usize = Self::TWO_ADICITY; + const CHARACTERISTIC_WITH_TWO_ADICITY: Option<(u64, usize)> = None; // Sage: `g = GF(p).multiplicative_generator()` const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self([5, 0, 0, 0]); diff --git a/src/field/secp256k1_scalar.rs b/src/field/secp256k1_scalar.rs index 44907b7a..595a27a3 100644 --- a/src/field/secp256k1_scalar.rs +++ b/src/field/secp256k1_scalar.rs @@ -12,7 +12,6 @@ use rand::Rng; use serde::{Deserialize, Serialize}; use crate::field::field_types::Field; -use crate::field::goldilocks_field::GoldilocksField; /// The base field of the secp256k1 elliptic curve. /// @@ -81,11 +80,8 @@ impl Field for Secp256K1Scalar { 0xFFFFFFFFFFFFFFFF, ]); - // TODO: fix - const CHARACTERISTIC: u64 = 0; - const TWO_ADICITY: usize = 6; - const CHARACTERISTIC_TWO_ADICITY: usize = 6; + const CHARACTERISTIC_WITH_TWO_ADICITY: Option<(u64, usize)> = None; // Sage: `g = GF(p).multiplicative_generator()` const MULTIPLICATIVE_GROUP_GENERATOR: Self = Self([7, 0, 0, 0]);