diff --git a/src/fr.rs b/src/fr.rs index 3986200..4e5aa51 100644 --- a/src/fr.rs +++ b/src/fr.rs @@ -1,3 +1,6 @@ +//! This module provides an implementation of the Jubjub scalar field $\mathbb{F}_r$ +//! where `r = 0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7` + use core::convert::TryInto; use core::fmt; use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign}; @@ -6,7 +9,8 @@ use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption}; use crate::util::{adc, mac, sbb}; -/// Represents an element of `GF(r)`. +/// Represents an element of the scalar field $\mathbb{F}_r$ of the Jubjub elliptic +/// curve construction. // The internal representation of this type is four 64-bit unsigned // integers in little-endian order. Elements of Fr are always in // Montgomery form; i.e., Fr(a) = aR mod r, with R = 2^256. @@ -40,6 +44,7 @@ impl ConstantTimeEq for Fr { } impl PartialEq for Fr { + #[inline] fn eq(&self, other: &Self) -> bool { self.ct_eq(other).unwrap_u8() == 1 } @@ -70,19 +75,7 @@ impl<'a> Neg for &'a Fr { #[inline] fn neg(self) -> Fr { - // Subtract `self` from `MODULUS` to negate. Ignore the final - // borrow because it cannot underflow; self is guaranteed to - // be in the field. - let (d0, borrow) = sbb(MODULUS.0[0], self.0[0], 0); - let (d1, borrow) = sbb(MODULUS.0[1], self.0[1], borrow); - let (d2, borrow) = sbb(MODULUS.0[2], self.0[2], borrow); - let (d3, _) = sbb(MODULUS.0[3], self.0[3], borrow); - - // `tmp` could be `MODULUS` if `self` was zero. Create a mask that is - // zero if `self` was zero, and `u64::max_value()` if self was nonzero. - let mask = u64::from((self.0[0] | self.0[1] | self.0[2] | self.0[3]) == 0).wrapping_sub(1); - - Fr([d0 & mask, d1 & mask, d2 & mask, d3 & mask]) + self.neg() } } @@ -100,24 +93,16 @@ impl<'a, 'b> Sub<&'b Fr> for &'a Fr { #[inline] fn sub(self, rhs: &'b Fr) -> Fr { - self.subtract(rhs) + self.sub(rhs) } } impl<'a, 'b> Add<&'b Fr> for &'a Fr { type Output = Fr; - #[allow(clippy::suspicious_arithmetic_impl)] #[inline] fn add(self, rhs: &'b Fr) -> Fr { - let (d0, carry) = adc(self.0[0], rhs.0[0], 0); - let (d1, carry) = adc(self.0[1], rhs.0[1], carry); - let (d2, carry) = adc(self.0[2], rhs.0[2], carry); - let (d3, _) = adc(self.0[3], rhs.0[3], carry); - - // Attempt to subtract the modulus, to ensure the value - // is smaller than the modulus. - Fr([d0, d1, d2, d3]) - &MODULUS + self.add(rhs) } } @@ -128,7 +113,7 @@ impl<'a, 'b> Mul<&'b Fr> for &'a Fr { fn mul(self, rhs: &'b Fr) -> Fr { // Schoolbook multiplication - self.multiply(rhs) + self.mul(rhs) } } @@ -171,20 +156,20 @@ impl Default for Fr { impl Fr { /// Returns zero, the additive identity. #[inline] - pub fn zero() -> Fr { + pub const fn zero() -> Fr { Fr([0, 0, 0, 0]) } /// Returns one, the multiplicative identity. #[inline] - pub fn one() -> Fr { + pub const fn one() -> Fr { R } /// Doubles this field element. #[inline] - pub fn double(&self) -> Fr { - self + self + pub const fn double(&self) -> Fr { + self.add(self) } /// Attempts to convert a little-endian byte representation of @@ -268,9 +253,9 @@ impl Fr { } /// Converts from an integer represented in little endian - /// into its (congruent) representation in Fr. + /// into its (congruent) `Fr` representation. pub const fn from_raw(val: [u64; 4]) -> Self { - Fr(val).multiply(&R2) + (&Fr(val)).mul(&R2) } /// Squares this element. @@ -508,11 +493,12 @@ impl Fr { let (r7, _) = adc(r7, carry2, carry); // Result may be within MODULUS of the correct value - Fr([r4, r5, r6, r7]).subtract(&MODULUS) + (&Fr([r4, r5, r6, r7])).sub(&MODULUS) } + /// Multiplies this element by another element #[inline] - const fn multiply(&self, rhs: &Self) -> Self { + pub const fn mul(&self, rhs: &Self) -> Self { // Schoolbook multiplication let (r0, carry) = mac(0, self.0[0], rhs.0[0], 0); @@ -538,8 +524,9 @@ impl Fr { Fr::montgomery_reduce(r0, r1, r2, r3, r4, r5, r6, r7) } + /// Subtracts another element from this element. #[inline] - const fn subtract(&self, rhs: &Self) -> Self { + pub const fn sub(&self, rhs: &Self) -> Self { let (d0, borrow) = sbb(self.0[0], rhs.0[0], 0); let (d1, borrow) = sbb(self.0[1], rhs.0[1], borrow); let (d2, borrow) = sbb(self.0[2], rhs.0[2], borrow); @@ -554,6 +541,37 @@ impl Fr { Fr([d0, d1, d2, d3]) } + + /// Adds this element to another element. + #[inline] + pub const fn add(&self, rhs: &Self) -> Self { + let (d0, carry) = adc(self.0[0], rhs.0[0], 0); + let (d1, carry) = adc(self.0[1], rhs.0[1], carry); + let (d2, carry) = adc(self.0[2], rhs.0[2], carry); + let (d3, _) = adc(self.0[3], rhs.0[3], carry); + + // Attempt to subtract the modulus, to ensure the value + // is smaller than the modulus. + (&Fr([d0, d1, d2, d3])).sub(&MODULUS) + } + + /// Negates this element. + #[inline] + pub const fn neg(&self) -> Self { + // Subtract `self` from `MODULUS` to negate. Ignore the final + // borrow because it cannot underflow; self is guaranteed to + // be in the field. + let (d0, borrow) = sbb(MODULUS.0[0], self.0[0], 0); + let (d1, borrow) = sbb(MODULUS.0[1], self.0[1], borrow); + let (d2, borrow) = sbb(MODULUS.0[2], self.0[2], borrow); + let (d3, _) = sbb(MODULUS.0[3], self.0[3], borrow); + + // `tmp` could be `MODULUS` if `self` was zero. Create a mask that is + // zero if `self` was zero, and `u64::max_value()` if self was nonzero. + let mask = (((self.0[0] | self.0[1] | self.0[2] | self.0[3]) == 0) as u64).wrapping_sub(1); + + Fr([d0 & mask, d1 & mask, d2 & mask, d3 & mask]) + } } impl<'a> From<&'a Fr> for [u8; 32] { diff --git a/src/lib.rs b/src/lib.rs index d8cf0bc..e226b12 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -23,6 +23,12 @@ #![deny(missing_docs)] #![deny(unsafe_code)] +// This lint is described at +// https://rust-lang.github.io/rust-clippy/master/index.html#suspicious_arithmetic_impl +// In our library, some of the arithmetic will necessarily involve various binary +// operators, and so this lint is triggered unnecessarily. +#![allow(clippy::suspicious_arithmetic_impl)] + #[cfg(feature = "std")] #[macro_use] extern crate std;