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// SPDX-License-Identifier: CC0-1.0
//! Provides [`Scalar`] and related types.
//!
//! In elliptic curve cryptography scalars are non-point values that can be used to multiply
//! points. The most common type of scalars are private keys. However not all scalars are private
//! keys. They can even be public *values*. To make handling them safer and easier this module
//! provides the `Scalar` type and related.
//!
use core::{fmt, ops};
use crate::constants;
/// Positive 256-bit integer guaranteed to be less than the secp256k1 curve order.
///
/// The difference between `PrivateKey` and `Scalar` is that `Scalar` doesn't guarantee being
/// securely usable as a private key.
///
/// **Warning: the operations on this type are NOT constant time!**
/// Using this with secret values is not advised.
// Internal represenation is big endian to match what `libsecp256k1` uses.
// Also easier to implement comparison.
// Debug impl omitted for now, the bytes may be secret
#[derive(Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct Scalar([u8; 32]);
impl_pretty_debug!(Scalar);
impl_non_secure_erase!(Scalar, 0, [0u8; 32]);
const MAX_RAW: [u8; 32] = [
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE,
0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x40,
];
impl Scalar {
/// Scalar representing `0`
pub const ZERO: Scalar = Scalar(constants::ZERO);
/// Scalar representing `1`
pub const ONE: Scalar = Scalar(constants::ONE);
/// Maximum valid value: `curve_order - 1`
pub const MAX: Scalar = Scalar(MAX_RAW);
/// Generates a random scalar
#[cfg(feature = "rand-std")]
pub fn random() -> Self { Self::random_custom(rand::thread_rng()) }
/// Generates a random scalar using supplied RNG
#[cfg(feature = "rand")]
pub fn random_custom<R: rand::Rng>(mut rng: R) -> Self {
let mut bytes = [0u8; 32];
loop {
rng.fill_bytes(&mut bytes);
// unlikely to go past MAX
if let Ok(scalar) = Scalar::from_be_bytes(bytes) {
break scalar;
}
}
}
/// Tries to deserialize from big endian bytes
///
/// **Security warning:** this function is not constant time!
/// Passing secret data is not recommended.
///
/// # Errors
///
/// Returns error when the value is above the curve order.
pub fn from_be_bytes(value: [u8; 32]) -> Result<Self, OutOfRangeError> {
// Lexicographic ordering of arrays of the same length is same as ordering of BE numbers
if value <= MAX_RAW {
Ok(Scalar(value))
} else {
Err(OutOfRangeError {})
}
}
/// Tries to deserialize from little endian bytes
///
/// **Security warning:** this function is not constant time!
/// Passing secret data is not recommended.
///
/// # Errors
///
/// Returns error when the value is above the curve order.
pub fn from_le_bytes(mut value: [u8; 32]) -> Result<Self, OutOfRangeError> {
value.reverse();
Self::from_be_bytes(value)
}
/// Serializes to big endian bytes
pub fn to_be_bytes(self) -> [u8; 32] { self.0 }
/// Serializes to little endian bytes
pub fn to_le_bytes(self) -> [u8; 32] {
let mut res = self.0;
res.reverse();
res
}
// returns a reference to internal bytes
// non-public to not leak the internal representation
pub(crate) fn as_be_bytes(&self) -> &[u8; 32] { &self.0 }
pub(crate) fn as_c_ptr(&self) -> *const u8 {
use secp256k1_sys::CPtr;
self.as_be_bytes().as_c_ptr()
}
}
impl<I> ops::Index<I> for Scalar
where
[u8]: ops::Index<I>,
{
type Output = <[u8] as ops::Index<I>>::Output;
#[inline]
fn index(&self, index: I) -> &Self::Output { &self.0[index] }
}
impl From<crate::SecretKey> for Scalar {
fn from(value: crate::SecretKey) -> Self { Scalar(value.secret_bytes()) }
}
/// Error returned when the value of scalar is invalid - larger than the curve order.
// Intentionally doesn't implement `Copy` to improve forward compatibility.
// Same reason for `non_exhaustive`.
#[allow(missing_copy_implementations)]
#[derive(Debug, Clone, Eq, PartialEq, Hash)]
#[non_exhaustive]
pub struct OutOfRangeError {}
impl fmt::Display for OutOfRangeError {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
fmt::Display::fmt("the value is not a member of secp256k1 field", f)
}
}
#[cfg(feature = "std")]
impl std::error::Error for OutOfRangeError {}