Browse Source
git-subtree-dir: ff git-subtree-mainline:hush07955092f3
git-subtree-split:661558e0c8
Jack Grigg
5 years ago
8 changed files with 1782 additions and 0 deletions
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target/ |
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**/*.rs.bk |
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Cargo.lock |
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[package] |
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name = "ff" |
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version = "0.4.0" |
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authors = ["Sean Bowe <ewillbefull@gmail.com>"] |
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description = "Library for building and interfacing with finite fields" |
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documentation = "https://docs.rs/ff/" |
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homepage = "https://github.com/ebfull/ff" |
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license = "MIT/Apache-2.0" |
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repository = "https://github.com/ebfull/ff" |
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|
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[dependencies] |
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byteorder = "1" |
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rand = "0.4" |
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ff_derive = { version = "0.3.0", path = "ff_derive", optional = true } |
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[features] |
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default = [] |
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derive = ["ff_derive"] |
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Apache License |
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@ -0,0 +1,21 @@ |
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The MIT License (MIT) |
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Copyright (c) 2017 Sean Bowe |
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THE SOFTWARE. |
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# ff |
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`ff` is a finite field library written in pure Rust, with no `unsafe{}` code. |
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## Disclaimers |
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* This library does not provide constant-time guarantees. |
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## Usage |
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Add the `ff` crate to your `Cargo.toml`: |
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```toml |
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[dependencies] |
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ff = "0.4" |
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``` |
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The `ff` crate contains `Field`, `PrimeField`, `PrimeFieldRepr` and `SqrtField` traits. See the **[documentation](https://docs.rs/ff/0.4.0/ff/)** for more. |
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### #![derive(PrimeField)] |
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If you need an implementation of a prime field, this library also provides a procedural macro that will expand into an efficient implementation of a prime field when supplied with the modulus. `PrimeFieldGenerator` must be an element of Fp of p-1 order, that is also quadratic nonresidue. |
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First, enable the `derive` crate feature: |
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```toml |
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[dependencies] |
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ff = { version = "0.4", features = ["derive"] } |
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``` |
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And then use the macro like so: |
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```rust |
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extern crate rand; |
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#[macro_use] |
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extern crate ff; |
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#[derive(PrimeField)] |
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#[PrimeFieldModulus = "52435875175126190479447740508185965837690552500527637822603658699938581184513"] |
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#[PrimeFieldGenerator = "7"] |
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struct Fp(FpRepr); |
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``` |
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And that's it! `Fp` now implements `Field` and `PrimeField`. `Fp` will also implement `SqrtField` if supported. The library implements `FpRepr` itself and derives `PrimeFieldRepr` for it. |
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## License |
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Licensed under either of |
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|
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* Apache License, Version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0) |
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* MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT) |
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at your option. |
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|
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### Contribution |
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|
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Unless you explicitly state otherwise, any contribution intentionally |
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submitted for inclusion in the work by you, as defined in the Apache-2.0 |
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license, shall be dual licensed as above, without any additional terms or |
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conditions. |
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[package] |
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name = "ff_derive" |
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version = "0.3.0" |
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authors = ["Sean Bowe <ewillbefull@gmail.com>"] |
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description = "Procedural macro library used to build custom prime field implementations" |
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documentation = "https://docs.rs/ff/" |
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homepage = "https://github.com/ebfull/ff" |
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license = "MIT/Apache-2.0" |
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repository = "https://github.com/ebfull/ff" |
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[lib] |
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proc-macro = true |
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[dependencies] |
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num-bigint = "0.2" |
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num-traits = "0.2" |
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num-integer = "0.1" |
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proc-macro2 = "0.4" |
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quote = "0.6" |
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syn = "0.14" |
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#![allow(unused_imports)] |
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extern crate byteorder; |
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extern crate rand; |
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#[cfg(feature = "derive")] |
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#[macro_use] |
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extern crate ff_derive; |
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#[cfg(feature = "derive")] |
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pub use ff_derive::*; |
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use std::error::Error; |
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use std::fmt; |
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use std::io::{self, Read, Write}; |
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/// This trait represents an element of a field.
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pub trait Field: |
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Sized + Eq + Copy + Clone + Send + Sync + fmt::Debug + fmt::Display + 'static + rand::Rand |
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{ |
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/// Returns the zero element of the field, the additive identity.
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fn zero() -> Self; |
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/// Returns the one element of the field, the multiplicative identity.
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fn one() -> Self; |
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/// Returns true iff this element is zero.
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fn is_zero(&self) -> bool; |
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/// Squares this element.
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fn square(&mut self); |
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/// Doubles this element.
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fn double(&mut self); |
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/// Negates this element.
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fn negate(&mut self); |
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/// Adds another element to this element.
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fn add_assign(&mut self, other: &Self); |
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/// Subtracts another element from this element.
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fn sub_assign(&mut self, other: &Self); |
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/// Multiplies another element by this element.
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fn mul_assign(&mut self, other: &Self); |
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/// Computes the multiplicative inverse of this element, if nonzero.
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fn inverse(&self) -> Option<Self>; |
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/// Exponentiates this element by a power of the base prime modulus via
|
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/// the Frobenius automorphism.
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fn frobenius_map(&mut self, power: usize); |
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/// Exponentiates this element by a number represented with `u64` limbs,
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/// least significant digit first.
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fn pow<S: AsRef<[u64]>>(&self, exp: S) -> Self { |
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let mut res = Self::one(); |
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let mut found_one = false; |
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for i in BitIterator::new(exp) { |
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if found_one { |
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res.square(); |
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} else { |
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found_one = i; |
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} |
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if i { |
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res.mul_assign(self); |
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} |
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} |
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res |
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} |
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} |
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/// This trait represents an element of a field that has a square root operation described for it.
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pub trait SqrtField: Field { |
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/// Returns the Legendre symbol of the field element.
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fn legendre(&self) -> LegendreSymbol; |
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/// Returns the square root of the field element, if it is
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/// quadratic residue.
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fn sqrt(&self) -> Option<Self>; |
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} |
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/// This trait represents a wrapper around a biginteger which can encode any element of a particular
|
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/// prime field. It is a smart wrapper around a sequence of `u64` limbs, least-significant digit
|
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/// first.
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pub trait PrimeFieldRepr: |
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Sized |
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+ Copy |
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+ Clone |
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+ Eq |
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+ Ord |
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+ Send |
||||
|
+ Sync |
||||
|
+ Default |
||||
|
+ fmt::Debug |
||||
|
+ fmt::Display |
||||
|
+ 'static |
||||
|
+ rand::Rand |
||||
|
+ AsRef<[u64]> |
||||
|
+ AsMut<[u64]> |
||||
|
+ From<u64> |
||||
|
{ |
||||
|
/// Subtract another represetation from this one.
|
||||
|
fn sub_noborrow(&mut self, other: &Self); |
||||
|
|
||||
|
/// Add another representation to this one.
|
||||
|
fn add_nocarry(&mut self, other: &Self); |
||||
|
|
||||
|
/// Compute the number of bits needed to encode this number. Always a
|
||||
|
/// multiple of 64.
|
||||
|
fn num_bits(&self) -> u32; |
||||
|
|
||||
|
/// Returns true iff this number is zero.
|
||||
|
fn is_zero(&self) -> bool; |
||||
|
|
||||
|
/// Returns true iff this number is odd.
|
||||
|
fn is_odd(&self) -> bool; |
||||
|
|
||||
|
/// Returns true iff this number is even.
|
||||
|
fn is_even(&self) -> bool; |
||||
|
|
||||
|
/// Performs a rightwise bitshift of this number, effectively dividing
|
||||
|
/// it by 2.
|
||||
|
fn div2(&mut self); |
||||
|
|
||||
|
/// Performs a rightwise bitshift of this number by some amount.
|
||||
|
fn shr(&mut self, amt: u32); |
||||
|
|
||||
|
/// Performs a leftwise bitshift of this number, effectively multiplying
|
||||
|
/// it by 2. Overflow is ignored.
|
||||
|
fn mul2(&mut self); |
||||
|
|
||||
|
/// Performs a leftwise bitshift of this number by some amount.
|
||||
|
fn shl(&mut self, amt: u32); |
||||
|
|
||||
|
/// Writes this `PrimeFieldRepr` as a big endian integer.
|
||||
|
fn write_be<W: Write>(&self, mut writer: W) -> io::Result<()> { |
||||
|
use byteorder::{BigEndian, WriteBytesExt}; |
||||
|
|
||||
|
for digit in self.as_ref().iter().rev() { |
||||
|
writer.write_u64::<BigEndian>(*digit)?; |
||||
|
} |
||||
|
|
||||
|
Ok(()) |
||||
|
} |
||||
|
|
||||
|
/// Reads a big endian integer into this representation.
|
||||
|
fn read_be<R: Read>(&mut self, mut reader: R) -> io::Result<()> { |
||||
|
use byteorder::{BigEndian, ReadBytesExt}; |
||||
|
|
||||
|
for digit in self.as_mut().iter_mut().rev() { |
||||
|
*digit = reader.read_u64::<BigEndian>()?; |
||||
|
} |
||||
|
|
||||
|
Ok(()) |
||||
|
} |
||||
|
|
||||
|
/// Writes this `PrimeFieldRepr` as a little endian integer.
|
||||
|
fn write_le<W: Write>(&self, mut writer: W) -> io::Result<()> { |
||||
|
use byteorder::{LittleEndian, WriteBytesExt}; |
||||
|
|
||||
|
for digit in self.as_ref().iter() { |
||||
|
writer.write_u64::<LittleEndian>(*digit)?; |
||||
|
} |
||||
|
|
||||
|
Ok(()) |
||||
|
} |
||||
|
|
||||
|
/// Reads a little endian integer into this representation.
|
||||
|
fn read_le<R: Read>(&mut self, mut reader: R) -> io::Result<()> { |
||||
|
use byteorder::{LittleEndian, ReadBytesExt}; |
||||
|
|
||||
|
for digit in self.as_mut().iter_mut() { |
||||
|
*digit = reader.read_u64::<LittleEndian>()?; |
||||
|
} |
||||
|
|
||||
|
Ok(()) |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
#[derive(Debug, PartialEq)] |
||||
|
pub enum LegendreSymbol { |
||||
|
Zero = 0, |
||||
|
QuadraticResidue = 1, |
||||
|
QuadraticNonResidue = -1, |
||||
|
} |
||||
|
|
||||
|
/// An error that may occur when trying to interpret a `PrimeFieldRepr` as a
|
||||
|
/// `PrimeField` element.
|
||||
|
#[derive(Debug)] |
||||
|
pub enum PrimeFieldDecodingError { |
||||
|
/// The encoded value is not in the field
|
||||
|
NotInField(String), |
||||
|
} |
||||
|
|
||||
|
impl Error for PrimeFieldDecodingError { |
||||
|
fn description(&self) -> &str { |
||||
|
match *self { |
||||
|
PrimeFieldDecodingError::NotInField(..) => "not an element of the field", |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
impl fmt::Display for PrimeFieldDecodingError { |
||||
|
fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> { |
||||
|
match *self { |
||||
|
PrimeFieldDecodingError::NotInField(ref repr) => { |
||||
|
write!(f, "{} is not an element of the field", repr) |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
/// This represents an element of a prime field.
|
||||
|
pub trait PrimeField: Field { |
||||
|
/// The prime field can be converted back and forth into this biginteger
|
||||
|
/// representation.
|
||||
|
type Repr: PrimeFieldRepr + From<Self>; |
||||
|
|
||||
|
/// Interpret a string of numbers as a (congruent) prime field element.
|
||||
|
/// Does not accept unnecessary leading zeroes or a blank string.
|
||||
|
fn from_str(s: &str) -> Option<Self> { |
||||
|
if s.is_empty() { |
||||
|
return None; |
||||
|
} |
||||
|
|
||||
|
if s == "0" { |
||||
|
return Some(Self::zero()); |
||||
|
} |
||||
|
|
||||
|
let mut res = Self::zero(); |
||||
|
|
||||
|
let ten = Self::from_repr(Self::Repr::from(10)).unwrap(); |
||||
|
|
||||
|
let mut first_digit = true; |
||||
|
|
||||
|
for c in s.chars() { |
||||
|
match c.to_digit(10) { |
||||
|
Some(c) => { |
||||
|
if first_digit { |
||||
|
if c == 0 { |
||||
|
return None; |
||||
|
} |
||||
|
|
||||
|
first_digit = false; |
||||
|
} |
||||
|
|
||||
|
res.mul_assign(&ten); |
||||
|
res.add_assign(&Self::from_repr(Self::Repr::from(u64::from(c))).unwrap()); |
||||
|
} |
||||
|
None => { |
||||
|
return None; |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
Some(res) |
||||
|
} |
||||
|
|
||||
|
/// Convert this prime field element into a biginteger representation.
|
||||
|
fn from_repr(Self::Repr) -> Result<Self, PrimeFieldDecodingError>; |
||||
|
|
||||
|
/// Convert a biginteger representation into a prime field element, if
|
||||
|
/// the number is an element of the field.
|
||||
|
fn into_repr(&self) -> Self::Repr; |
||||
|
|
||||
|
/// Returns the field characteristic; the modulus.
|
||||
|
fn char() -> Self::Repr; |
||||
|
|
||||
|
/// How many bits are needed to represent an element of this field.
|
||||
|
const NUM_BITS: u32; |
||||
|
|
||||
|
/// How many bits of information can be reliably stored in the field element.
|
||||
|
const CAPACITY: u32; |
||||
|
|
||||
|
/// Returns the multiplicative generator of `char()` - 1 order. This element
|
||||
|
/// must also be quadratic nonresidue.
|
||||
|
fn multiplicative_generator() -> Self; |
||||
|
|
||||
|
/// 2^s * t = `char()` - 1 with t odd.
|
||||
|
const S: u32; |
||||
|
|
||||
|
/// Returns the 2^s root of unity computed by exponentiating the `multiplicative_generator()`
|
||||
|
/// by t.
|
||||
|
fn root_of_unity() -> Self; |
||||
|
} |
||||
|
|
||||
|
/// An "engine" is a collection of types (fields, elliptic curve groups, etc.)
|
||||
|
/// with well-defined relationships. Specific relationships (for example, a
|
||||
|
/// pairing-friendly curve) can be defined in a subtrait.
|
||||
|
pub trait ScalarEngine: Sized + 'static + Clone { |
||||
|
/// This is the scalar field of the engine's groups.
|
||||
|
type Fr: PrimeField + SqrtField; |
||||
|
} |
||||
|
|
||||
|
#[derive(Debug)] |
||||
|
pub struct BitIterator<E> { |
||||
|
t: E, |
||||
|
n: usize, |
||||
|
} |
||||
|
|
||||
|
impl<E: AsRef<[u64]>> BitIterator<E> { |
||||
|
pub fn new(t: E) -> Self { |
||||
|
let n = t.as_ref().len() * 64; |
||||
|
|
||||
|
BitIterator { t, n } |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
impl<E: AsRef<[u64]>> Iterator for BitIterator<E> { |
||||
|
type Item = bool; |
||||
|
|
||||
|
fn next(&mut self) -> Option<bool> { |
||||
|
if self.n == 0 { |
||||
|
None |
||||
|
} else { |
||||
|
self.n -= 1; |
||||
|
let part = self.n / 64; |
||||
|
let bit = self.n - (64 * part); |
||||
|
|
||||
|
Some(self.t.as_ref()[part] & (1 << bit) > 0) |
||||
|
} |
||||
|
} |
||||
|
} |
||||
|
|
||||
|
#[test] |
||||
|
fn test_bit_iterator() { |
||||
|
let mut a = BitIterator::new([0xa953d79b83f6ab59, 0x6dea2059e200bd39]); |
||||
|
let expected = "01101101111010100010000001011001111000100000000010111101001110011010100101010011110101111001101110000011111101101010101101011001"; |
||||
|
|
||||
|
for e in expected.chars() { |
||||
|
assert!(a.next().unwrap() == (e == '1')); |
||||
|
} |
||||
|
|
||||
|
assert!(a.next().is_none()); |
||||
|
|
||||
|
let expected = "1010010101111110101010000101101011101000011101110101001000011001100100100011011010001011011011010001011011101100110100111011010010110001000011110100110001100110011101101000101100011100100100100100001010011101010111110011101011000011101000111011011101011001"; |
||||
|
|
||||
|
let mut a = BitIterator::new([ |
||||
|
0x429d5f3ac3a3b759, |
||||
|
0xb10f4c66768b1c92, |
||||
|
0x92368b6d16ecd3b4, |
||||
|
0xa57ea85ae8775219, |
||||
|
]); |
||||
|
|
||||
|
for e in expected.chars() { |
||||
|
assert!(a.next().unwrap() == (e == '1')); |
||||
|
} |
||||
|
|
||||
|
assert!(a.next().is_none()); |
||||
|
} |
||||
|
|
||||
|
pub use self::arith_impl::*; |
||||
|
|
||||
|
mod arith_impl { |
||||
|
/// Calculate a - b - borrow, returning the result and modifying
|
||||
|
/// the borrow value.
|
||||
|
#[inline(always)] |
||||
|
pub fn sbb(a: u64, b: u64, borrow: &mut u64) -> u64 { |
||||
|
let tmp = (1u128 << 64) + u128::from(a) - u128::from(b) - u128::from(*borrow); |
||||
|
|
||||
|
*borrow = if tmp >> 64 == 0 { 1 } else { 0 }; |
||||
|
|
||||
|
tmp as u64 |
||||
|
} |
||||
|
|
||||
|
/// Calculate a + b + carry, returning the sum and modifying the
|
||||
|
/// carry value.
|
||||
|
#[inline(always)] |
||||
|
pub fn adc(a: u64, b: u64, carry: &mut u64) -> u64 { |
||||
|
let tmp = u128::from(a) + u128::from(b) + u128::from(*carry); |
||||
|
|
||||
|
*carry = (tmp >> 64) as u64; |
||||
|
|
||||
|
tmp as u64 |
||||
|
} |
||||
|
|
||||
|
/// Calculate a + (b * c) + carry, returning the least significant digit
|
||||
|
/// and setting carry to the most significant digit.
|
||||
|
#[inline(always)] |
||||
|
pub fn mac_with_carry(a: u64, b: u64, c: u64, carry: &mut u64) -> u64 { |
||||
|
let tmp = (u128::from(a)) + u128::from(b) * u128::from(c) + u128::from(*carry); |
||||
|
|
||||
|
*carry = (tmp >> 64) as u64; |
||||
|
|
||||
|
tmp as u64 |
||||
|
} |
||||
|
} |
Loading…
Reference in new issue