1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332
//! Low-level ECDSA primitives.
//!
//! # ⚠️ Warning: Hazmat!
//!
//! YOU PROBABLY DON'T WANT TO USE THESE!
//!
//! These primitives are easy-to-misuse low-level interfaces.
//!
//! If you are an end user / non-expert in cryptography, do not use these!
//! Failure to use them correctly can lead to catastrophic failures including
//! FULL PRIVATE KEY RECOVERY!
use crate::{Error, Result};
use core::cmp;
use elliptic_curve::{generic_array::typenum::Unsigned, FieldBytes, PrimeCurve};
#[cfg(feature = "arithmetic")]
use {
crate::{RecoveryId, SignatureSize},
elliptic_curve::{
ff::{Field, PrimeField},
group::{Curve as _, Group},
ops::{Invert, LinearCombination, MulByGenerator, Reduce},
point::AffineCoordinates,
scalar::IsHigh,
subtle::CtOption,
CurveArithmetic, ProjectivePoint, Scalar,
},
};
#[cfg(feature = "digest")]
use {
elliptic_curve::FieldBytesSize,
signature::{
digest::{core_api::BlockSizeUser, Digest, FixedOutput, FixedOutputReset},
PrehashSignature,
},
};
#[cfg(feature = "rfc6979")]
use elliptic_curve::{FieldBytesEncoding, ScalarPrimitive};
#[cfg(any(feature = "arithmetic", feature = "digest"))]
use crate::{elliptic_curve::generic_array::ArrayLength, Signature};
/// Try to sign the given prehashed message using ECDSA.
///
/// This trait is intended to be implemented on a type with access to the
/// secret scalar via `&self`, such as particular curve's `Scalar` type.
#[cfg(feature = "arithmetic")]
pub trait SignPrimitive<C>:
AsRef<Self>
+ Into<FieldBytes<C>>
+ IsHigh
+ PrimeField<Repr = FieldBytes<C>>
+ Reduce<C::Uint, Bytes = FieldBytes<C>>
+ Sized
where
C: PrimeCurve + CurveArithmetic<Scalar = Self>,
SignatureSize<C>: ArrayLength<u8>,
{
/// Try to sign the prehashed message.
///
/// Accepts the following arguments:
///
/// - `k`: ephemeral scalar value. MUST BE UNIFORMLY RANDOM!!!
/// - `z`: message digest to be signed. MUST BE OUTPUT OF A CRYPTOGRAPHICALLY
/// SECURE DIGEST ALGORITHM!!!
///
/// # Returns
///
/// ECDSA [`Signature`] and, when possible/desired, a [`RecoveryId`]
/// which can be used to recover the verifying key for a given signature.
fn try_sign_prehashed<K>(
&self,
k: K,
z: &FieldBytes<C>,
) -> Result<(Signature<C>, Option<RecoveryId>)>
where
K: AsRef<Self> + Invert<Output = CtOption<Self>>,
{
sign_prehashed(self, k, z).map(|(sig, recid)| (sig, (Some(recid))))
}
/// Try to sign the given message digest deterministically using the method
/// described in [RFC6979] for computing ECDSA ephemeral scalar `k`.
///
/// Accepts the following parameters:
/// - `z`: message digest to be signed.
/// - `ad`: optional additional data, e.g. added entropy from an RNG
///
/// [RFC6979]: https://datatracker.ietf.org/doc/html/rfc6979
#[cfg(feature = "rfc6979")]
fn try_sign_prehashed_rfc6979<D>(
&self,
z: &FieldBytes<C>,
ad: &[u8],
) -> Result<(Signature<C>, Option<RecoveryId>)>
where
Self: From<ScalarPrimitive<C>> + Invert<Output = CtOption<Self>>,
D: Digest + BlockSizeUser + FixedOutput<OutputSize = FieldBytesSize<C>> + FixedOutputReset,
{
let k = Scalar::<C>::from_repr(rfc6979::generate_k::<D, _>(
&self.to_repr(),
&C::ORDER.encode_field_bytes(),
z,
ad,
))
.unwrap();
self.try_sign_prehashed::<Self>(k, z)
}
}
/// Verify the given prehashed message using ECDSA.
///
/// This trait is intended to be implemented on type which can access
/// the affine point represeting the public key via `&self`, such as a
/// particular curve's `AffinePoint` type.
#[cfg(feature = "arithmetic")]
pub trait VerifyPrimitive<C>: AffineCoordinates<FieldRepr = FieldBytes<C>> + Copy + Sized
where
C: PrimeCurve + CurveArithmetic<AffinePoint = Self>,
SignatureSize<C>: ArrayLength<u8>,
{
/// Verify the prehashed message against the provided ECDSA signature.
///
/// Accepts the following arguments:
///
/// - `z`: message digest to be verified. MUST BE OUTPUT OF A
/// CRYPTOGRAPHICALLY SECURE DIGEST ALGORITHM!!!
/// - `sig`: signature to be verified against the key and message
fn verify_prehashed(&self, z: &FieldBytes<C>, sig: &Signature<C>) -> Result<()> {
verify_prehashed(&ProjectivePoint::<C>::from(*self), z, sig)
}
/// Verify message digest against the provided signature.
#[cfg(feature = "digest")]
fn verify_digest<D>(&self, msg_digest: D, sig: &Signature<C>) -> Result<()>
where
D: FixedOutput<OutputSize = FieldBytesSize<C>>,
{
self.verify_prehashed(&msg_digest.finalize_fixed(), sig)
}
}
/// Bind a preferred [`Digest`] algorithm to an elliptic curve type.
///
/// Generally there is a preferred variety of the SHA-2 family used with ECDSA
/// for a particular elliptic curve.
///
/// This trait can be used to specify it, and with it receive a blanket impl of
/// [`PrehashSignature`], used by [`signature_derive`][1]) for the [`Signature`]
/// type for a particular elliptic curve.
///
/// [1]: https://github.com/RustCrypto/traits/tree/master/signature/derive
#[cfg(feature = "digest")]
pub trait DigestPrimitive: PrimeCurve {
/// Preferred digest to use when computing ECDSA signatures for this
/// elliptic curve. This is typically a member of the SHA-2 family.
type Digest: BlockSizeUser
+ Digest
+ FixedOutput<OutputSize = FieldBytesSize<Self>>
+ FixedOutputReset;
}
#[cfg(feature = "digest")]
impl<C> PrehashSignature for Signature<C>
where
C: DigestPrimitive,
<FieldBytesSize<C> as core::ops::Add>::Output: ArrayLength<u8>,
{
type Digest = C::Digest;
}
/// Partial implementation of the `bits2int` function as defined in
/// [RFC6979 § 2.3.2] as well as [SEC1] § 2.3.8.
///
/// This is used to convert a message digest whose size may be smaller or
/// larger than the size of the curve's scalar field into a serialized
/// (unreduced) field element.
///
/// [RFC6979 § 2.3.2]: https://datatracker.ietf.org/doc/html/rfc6979#section-2.3.2
/// [SEC1]: https://www.secg.org/sec1-v2.pdf
pub fn bits2field<C: PrimeCurve>(bits: &[u8]) -> Result<FieldBytes<C>> {
// Minimum allowed bits size is half the field size
if bits.len() < C::FieldBytesSize::USIZE / 2 {
return Err(Error::new());
}
let mut field_bytes = FieldBytes::<C>::default();
match bits.len().cmp(&C::FieldBytesSize::USIZE) {
cmp::Ordering::Equal => field_bytes.copy_from_slice(bits),
cmp::Ordering::Less => {
// If bits is smaller than the field size, pad with zeroes on the left
field_bytes[(C::FieldBytesSize::USIZE - bits.len())..].copy_from_slice(bits);
}
cmp::Ordering::Greater => {
// If bits is larger than the field size, truncate
field_bytes.copy_from_slice(&bits[..C::FieldBytesSize::USIZE]);
}
}
Ok(field_bytes)
}
/// Sign a prehashed message digest using the provided secret scalar and
/// ephemeral scalar, returning an ECDSA signature.
///
/// Accepts the following arguments:
///
/// - `d`: signing key. MUST BE UNIFORMLY RANDOM!!!
/// - `k`: ephemeral scalar value. MUST BE UNIFORMLY RANDOM!!!
/// - `z`: message digest to be signed. MUST BE OUTPUT OF A CRYPTOGRAPHICALLY
/// SECURE DIGEST ALGORITHM!!!
///
/// # Returns
///
/// ECDSA [`Signature`] and, when possible/desired, a [`RecoveryId`]
/// which can be used to recover the verifying key for a given signature.
#[cfg(feature = "arithmetic")]
#[allow(non_snake_case)]
pub fn sign_prehashed<C, K>(
d: &Scalar<C>,
k: K,
z: &FieldBytes<C>,
) -> Result<(Signature<C>, RecoveryId)>
where
C: PrimeCurve + CurveArithmetic,
K: AsRef<Scalar<C>> + Invert<Output = CtOption<Scalar<C>>>,
SignatureSize<C>: ArrayLength<u8>,
{
// TODO(tarcieri): use `NonZeroScalar<C>` for `k`.
if k.as_ref().is_zero().into() {
return Err(Error::new());
}
let z = <Scalar<C> as Reduce<C::Uint>>::reduce_bytes(z);
// Compute scalar inversion of 𝑘
let k_inv = Option::<Scalar<C>>::from(k.invert()).ok_or_else(Error::new)?;
// Compute 𝑹 = 𝑘×𝑮
let R = ProjectivePoint::<C>::mul_by_generator(k.as_ref()).to_affine();
// Lift x-coordinate of 𝑹 (element of base field) into a serialized big
// integer, then reduce it into an element of the scalar field
let r = Scalar::<C>::reduce_bytes(&R.x());
let x_is_reduced = r.to_repr() != R.x();
// Compute 𝒔 as a signature over 𝒓 and 𝒛.
let s = k_inv * (z + (r * d));
// NOTE: `Signature::from_scalars` checks that both `r` and `s` are non-zero.
let signature = Signature::from_scalars(r, s)?;
let recovery_id = RecoveryId::new(R.y_is_odd().into(), x_is_reduced);
Ok((signature, recovery_id))
}
/// Verify the prehashed message against the provided ECDSA signature.
///
/// Accepts the following arguments:
///
/// - `q`: public key with which to verify the signature.
/// - `z`: message digest to be verified. MUST BE OUTPUT OF A
/// CRYPTOGRAPHICALLY SECURE DIGEST ALGORITHM!!!
/// - `sig`: signature to be verified against the key and message.
#[cfg(feature = "arithmetic")]
pub fn verify_prehashed<C>(
q: &ProjectivePoint<C>,
z: &FieldBytes<C>,
sig: &Signature<C>,
) -> Result<()>
where
C: PrimeCurve + CurveArithmetic,
SignatureSize<C>: ArrayLength<u8>,
{
let z = Scalar::<C>::reduce_bytes(z);
let (r, s) = sig.split_scalars();
let s_inv = *s.invert_vartime();
let u1 = z * s_inv;
let u2 = *r * s_inv;
let x = ProjectivePoint::<C>::lincomb(&ProjectivePoint::<C>::generator(), &u1, q, &u2)
.to_affine()
.x();
if *r == Scalar::<C>::reduce_bytes(&x) {
Ok(())
} else {
Err(Error::new())
}
}
#[cfg(test)]
mod tests {
use super::bits2field;
use elliptic_curve::dev::MockCurve;
use hex_literal::hex;
#[test]
fn bits2field_too_small() {
assert!(bits2field::<MockCurve>(b"").is_err());
}
#[test]
fn bits2field_size_less() {
let prehash = hex!("AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA");
let field_bytes = bits2field::<MockCurve>(&prehash).unwrap();
assert_eq!(
field_bytes.as_slice(),
&hex!("00000000000000000000000000000000AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA")
);
}
#[test]
fn bits2field_size_eq() {
let prehash = hex!("AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA");
let field_bytes = bits2field::<MockCurve>(&prehash).unwrap();
assert_eq!(field_bytes.as_slice(), &prehash);
}
#[test]
fn bits2field_size_greater() {
let prehash = hex!("AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB");
let field_bytes = bits2field::<MockCurve>(&prehash).unwrap();
assert_eq!(
field_bytes.as_slice(),
&hex!("AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA")
);
}
}