1use core::borrow::Borrow;
  2use core::fmt::Debug;
  3use core::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};
  4use merlin::Transcript;
  5use rand::{CryptoRng, RngCore};
  6
  7/// Represents an element of a prime field
  8pub trait PrimeField:
  9  Sized
 10  + Eq
 11  + Copy
 12  + Clone
 13  + Default
 14  + Send
 15  + Sync
 16  + Debug
 17  + Add<Output = Self>
 18  + Sub<Output = Self>
 19  + Mul<Output = Self>
 20  + Neg<Output = Self>
 21  + for<'a> Add<&'a Self, Output = Self>
 22  + for<'a> Mul<&'a Self, Output = Self>
 23  + for<'a> Sub<&'a Self, Output = Self>
 24  + AddAssign
 25  + MulAssign
 26  + SubAssign
 27  + for<'a> AddAssign<&'a Self>
 28  + for<'a> MulAssign<&'a Self>
 29  + for<'a> SubAssign<&'a Self>
 30{
 31  /// returns the additive identity of the field
 32  fn zero() -> Self;
 33
 34  /// returns the multiplicative identity of the field
 35  fn one() -> Self;
 36
 37  /// converts the supplied bytes into an element of the field
 38  fn from_bytes_mod_order_wide(bytes: &[u8]) -> Option<Self>;
 39
 40  /// returns an uniformly random element from the finite field
 41  fn random(rng: &mut (impl RngCore + CryptoRng)) -> Self;
 42}
 43
 44/// Represents an element of a group
 45pub trait Group:
 46  Clone
 47  + Copy
 48  + Debug
 49  + Eq
 50  + Sized
 51  + GroupOps
 52  + GroupOpsOwned
 53  + ScalarMul<<Self as Group>::Scalar>
 54  + ScalarMulOwned<<Self as Group>::Scalar>
 55{
 56  type Scalar: PrimeField + ChallengeTrait;
 57  type CompressedGroupElement: CompressedGroup<GroupElement = Self>;
 58
 59  fn vartime_multiscalar_mul<I, J>(scalars: I, points: J) -> Self
 60  where
 61    I: IntoIterator,
 62    I::Item: Borrow<Self::Scalar>,
 63    J: IntoIterator,
 64    J::Item: Borrow<Self>,
 65    Self: Clone;
 66
 67  fn compress(&self) -> Self::CompressedGroupElement;
 68
 69  fn from_uniform_bytes(bytes: &[u8]) -> Option<Self>;
 70}
 71
 72/// Represents a compressed version of a group element
 73pub trait CompressedGroup: Clone + Copy + Debug + Eq + Sized + Send + Sync + 'static {
 74  type GroupElement: Group;
 75
 76  fn decompress(&self) -> Option<Self::GroupElement>;
 77
 78  fn as_bytes(&self) -> &[u8];
 79}
 80
 81/// A helper trait to generate challenges using a transcript object
 82pub trait ChallengeTrait {
 83  fn challenge(label: &'static [u8], transcript: &mut Transcript) -> Self;
 84}
 85
 86/// A helper trait for types with a group operation.
 87pub trait GroupOps<Rhs = Self, Output = Self>:
 88  Add<Rhs, Output = Output> + Sub<Rhs, Output = Output> + AddAssign<Rhs> + SubAssign<Rhs>
 89{
 90}
 91
 92impl<T, Rhs, Output> GroupOps<Rhs, Output> for T where
 93  T: Add<Rhs, Output = Output> + Sub<Rhs, Output = Output> + AddAssign<Rhs> + SubAssign<Rhs>
 94{
 95}
 96
 97/// A helper trait for references with a group operation.
 98pub trait GroupOpsOwned<Rhs = Self, Output = Self>: for<'r> GroupOps<&'r Rhs, Output> {}
 99impl<T, Rhs, Output> GroupOpsOwned<Rhs, Output> for T where T: for<'r> GroupOps<&'r Rhs, Output> {}
100
101/// A helper trait for types implementing group scalar multiplication.
102pub trait ScalarMul<Rhs, Output = Self>: Mul<Rhs, Output = Output> + MulAssign<Rhs> {}
103
104impl<T, Rhs, Output> ScalarMul<Rhs, Output> for T where T: Mul<Rhs, Output = Output> + MulAssign<Rhs>
105{}
106
107/// A helper trait for references implementing group scalar multiplication.
108pub trait ScalarMulOwned<Rhs, Output = Self>: for<'r> ScalarMul<&'r Rhs, Output> {}
109impl<T, Rhs, Output> ScalarMulOwned<Rhs, Output> for T where T: for<'r> ScalarMul<&'r Rhs, Output> {}