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// -*- mode: rust; -*-
//
// This file is part of ed25519-dalek.
// Copyright (c) 2017-2019 isis lovecruft
// See LICENSE for licensing information.
//
// Authors:
// - isis agora lovecruft <isis@patternsinthevoid.net>
//! ed25519 public keys.
use core::convert::TryFrom;
use core::fmt::Debug;
use core::hash::{Hash, Hasher};
use curve25519_dalek::{
digest::{generic_array::typenum::U64, Digest},
edwards::{CompressedEdwardsY, EdwardsPoint},
montgomery::MontgomeryPoint,
scalar::Scalar,
};
use ed25519::signature::Verifier;
use sha2::Sha512;
#[cfg(feature = "pkcs8")]
use ed25519::pkcs8;
#[cfg(feature = "serde")]
use serde::{Deserialize, Deserializer, Serialize, Serializer};
#[cfg(feature = "digest")]
use crate::context::Context;
#[cfg(feature = "digest")]
use signature::DigestVerifier;
use crate::{
constants::PUBLIC_KEY_LENGTH,
errors::{InternalError, SignatureError},
hazmat::ExpandedSecretKey,
signature::InternalSignature,
signing::SigningKey,
};
/// An ed25519 public key.
///
/// # Note
///
/// The `Eq` and `Hash` impls here use the compressed Edwards y encoding, _not_ the algebraic
/// representation. This means if this `VerifyingKey` is non-canonically encoded, it will be
/// considered unequal to the other equivalent encoding, despite the two representing the same
/// point. More encoding details can be found
/// [here](https://hdevalence.ca/blog/2020-10-04-its-25519am).
/// If you want to make sure that signatures produced with respect to those sorts of public keys
/// are rejected, use [`VerifyingKey::verify_strict`].
// Invariant: VerifyingKey.1 is always the decompression of VerifyingKey.0
#[derive(Copy, Clone, Default, Eq)]
pub struct VerifyingKey {
/// Serialized compressed Edwards-y point.
pub(crate) compressed: CompressedEdwardsY,
/// Decompressed Edwards point used for curve arithmetic operations.
pub(crate) point: EdwardsPoint,
}
impl Debug for VerifyingKey {
fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
write!(f, "VerifyingKey({:?}), {:?})", self.compressed, self.point)
}
}
impl AsRef<[u8]> for VerifyingKey {
fn as_ref(&self) -> &[u8] {
self.as_bytes()
}
}
impl Hash for VerifyingKey {
fn hash<H: Hasher>(&self, state: &mut H) {
self.as_bytes().hash(state);
}
}
impl PartialEq<VerifyingKey> for VerifyingKey {
fn eq(&self, other: &VerifyingKey) -> bool {
self.as_bytes() == other.as_bytes()
}
}
impl From<&ExpandedSecretKey> for VerifyingKey {
/// Derive this public key from its corresponding `ExpandedSecretKey`.
fn from(expanded_secret_key: &ExpandedSecretKey) -> VerifyingKey {
VerifyingKey::from(EdwardsPoint::mul_base(&expanded_secret_key.scalar))
}
}
impl From<&SigningKey> for VerifyingKey {
fn from(signing_key: &SigningKey) -> VerifyingKey {
signing_key.verifying_key()
}
}
impl From<EdwardsPoint> for VerifyingKey {
fn from(point: EdwardsPoint) -> VerifyingKey {
VerifyingKey {
point,
compressed: point.compress(),
}
}
}
impl VerifyingKey {
/// Convert this public key to a byte array.
#[inline]
pub fn to_bytes(&self) -> [u8; PUBLIC_KEY_LENGTH] {
self.compressed.to_bytes()
}
/// View this public key as a byte array.
#[inline]
pub fn as_bytes(&self) -> &[u8; PUBLIC_KEY_LENGTH] {
&(self.compressed).0
}
/// Construct a `VerifyingKey` from a slice of bytes.
///
/// # Warning
///
/// The caller is responsible for ensuring that the bytes passed into this
/// method actually represent a `curve25519_dalek::curve::CompressedEdwardsY`
/// and that said compressed point is actually a point on the curve.
///
/// # Example
///
/// ```
/// use ed25519_dalek::VerifyingKey;
/// use ed25519_dalek::PUBLIC_KEY_LENGTH;
/// use ed25519_dalek::SignatureError;
///
/// # fn doctest() -> Result<VerifyingKey, SignatureError> {
/// let public_key_bytes: [u8; PUBLIC_KEY_LENGTH] = [
/// 215, 90, 152, 1, 130, 177, 10, 183, 213, 75, 254, 211, 201, 100, 7, 58,
/// 14, 225, 114, 243, 218, 166, 35, 37, 175, 2, 26, 104, 247, 7, 81, 26];
///
/// let public_key = VerifyingKey::from_bytes(&public_key_bytes)?;
/// #
/// # Ok(public_key)
/// # }
/// #
/// # fn main() {
/// # doctest();
/// # }
/// ```
///
/// # Returns
///
/// A `Result` whose okay value is an EdDSA `VerifyingKey` or whose error value
/// is a `SignatureError` describing the error that occurred.
#[inline]
pub fn from_bytes(bytes: &[u8; PUBLIC_KEY_LENGTH]) -> Result<VerifyingKey, SignatureError> {
let compressed = CompressedEdwardsY(*bytes);
let point = compressed
.decompress()
.ok_or(InternalError::PointDecompression)?;
// Invariant: VerifyingKey.1 is always the decompression of VerifyingKey.0
Ok(VerifyingKey { compressed, point })
}
/// Create a verifying context that can be used for Ed25519ph with
/// [`DigestVerifier`].
#[cfg(feature = "digest")]
pub fn with_context<'k, 'v>(
&'k self,
context_value: &'v [u8],
) -> Result<Context<'k, 'v, Self>, SignatureError> {
Context::new(self, context_value)
}
/// Returns whether this is a _weak_ public key, i.e., if this public key has low order.
///
/// A weak public key can be used to generate a signature that's valid for almost every
/// message. [`Self::verify_strict`] denies weak keys, but if you want to check for this
/// property before verification, then use this method.
pub fn is_weak(&self) -> bool {
self.point.is_small_order()
}
// A helper function that computes `H(R || A || M)` where `H` is the 512-bit hash function
// given by `CtxDigest` (this is SHA-512 in spec-compliant Ed25519). If `context.is_some()`,
// this does the prehashed variant of the computation using its contents.
#[allow(non_snake_case)]
fn compute_challenge<CtxDigest>(
context: Option<&[u8]>,
R: &CompressedEdwardsY,
A: &CompressedEdwardsY,
M: &[u8],
) -> Scalar
where
CtxDigest: Digest<OutputSize = U64>,
{
let mut h = CtxDigest::new();
if let Some(c) = context {
h.update(b"SigEd25519 no Ed25519 collisions");
h.update([1]); // Ed25519ph
h.update([c.len() as u8]);
h.update(c);
}
h.update(R.as_bytes());
h.update(A.as_bytes());
h.update(M);
Scalar::from_hash(h)
}
// Helper function for verification. Computes the _expected_ R component of the signature. The
// caller compares this to the real R component. If `context.is_some()`, this does the
// prehashed variant of the computation using its contents.
// Note that this returns the compressed form of R and the caller does a byte comparison. This
// means that all our verification functions do not accept non-canonically encoded R values.
// See the validation criteria blog post for more details:
// https://hdevalence.ca/blog/2020-10-04-its-25519am
#[allow(non_snake_case)]
fn recompute_R<CtxDigest>(
&self,
context: Option<&[u8]>,
signature: &InternalSignature,
M: &[u8],
) -> CompressedEdwardsY
where
CtxDigest: Digest<OutputSize = U64>,
{
let k = Self::compute_challenge::<CtxDigest>(context, &signature.R, &self.compressed, M);
let minus_A: EdwardsPoint = -self.point;
// Recall the (non-batched) verification equation: -[k]A + [s]B = R
EdwardsPoint::vartime_double_scalar_mul_basepoint(&k, &(minus_A), &signature.s).compress()
}
/// The ordinary non-batched Ed25519 verification check, rejecting non-canonical R values. (see
/// [`Self::recompute_R`]). `CtxDigest` is the digest used to calculate the pseudorandomness
/// needed for signing. According to the spec, `CtxDigest = Sha512`.
///
/// This definition is loose in its parameters so that end-users of the `hazmat` module can
/// change how the `ExpandedSecretKey` is calculated and which hash function to use.
#[allow(non_snake_case)]
pub(crate) fn raw_verify<CtxDigest>(
&self,
message: &[u8],
signature: &ed25519::Signature,
) -> Result<(), SignatureError>
where
CtxDigest: Digest<OutputSize = U64>,
{
let signature = InternalSignature::try_from(signature)?;
let expected_R = self.recompute_R::<CtxDigest>(None, &signature, message);
if expected_R == signature.R {
Ok(())
} else {
Err(InternalError::Verify.into())
}
}
/// The prehashed non-batched Ed25519 verification check, rejecting non-canonical R values.
/// (see [`Self::recompute_R`]). `CtxDigest` is the digest used to calculate the
/// pseudorandomness needed for signing. `MsgDigest` is the digest used to hash the signed
/// message. According to the spec, `MsgDigest = CtxDigest = Sha512`.
///
/// This definition is loose in its parameters so that end-users of the `hazmat` module can
/// change how the `ExpandedSecretKey` is calculated and which hash function to use.
#[cfg(feature = "digest")]
#[allow(non_snake_case)]
pub(crate) fn raw_verify_prehashed<CtxDigest, MsgDigest>(
&self,
prehashed_message: MsgDigest,
context: Option<&[u8]>,
signature: &ed25519::Signature,
) -> Result<(), SignatureError>
where
CtxDigest: Digest<OutputSize = U64>,
MsgDigest: Digest<OutputSize = U64>,
{
let signature = InternalSignature::try_from(signature)?;
let ctx: &[u8] = context.unwrap_or(b"");
debug_assert!(
ctx.len() <= 255,
"The context must not be longer than 255 octets."
);
let message = prehashed_message.finalize();
let expected_R = self.recompute_R::<CtxDigest>(Some(ctx), &signature, &message);
if expected_R == signature.R {
Ok(())
} else {
Err(InternalError::Verify.into())
}
}
/// Verify a `signature` on a `prehashed_message` using the Ed25519ph algorithm.
///
/// # Inputs
///
/// * `prehashed_message` is an instantiated hash digest with 512-bits of
/// output which has had the message to be signed previously fed into its
/// state.
/// * `context` is an optional context string, up to 255 bytes inclusive,
/// which may be used to provide additional domain separation. If not
/// set, this will default to an empty string.
/// * `signature` is a purported Ed25519ph signature on the `prehashed_message`.
///
/// # Returns
///
/// Returns `true` if the `signature` was a valid signature created by this
/// [`SigningKey`] on the `prehashed_message`.
///
/// # Note
///
/// The RFC only permits SHA-512 to be used for prehashing, i.e., `MsgDigest = Sha512`. This
/// function technically works, and is probably safe to use, with any secure hash function with
/// 512-bit digests, but anything outside of SHA-512 is NOT specification-compliant. We expose
/// [`crate::Sha512`] for user convenience.
#[cfg(feature = "digest")]
#[allow(non_snake_case)]
pub fn verify_prehashed<MsgDigest>(
&self,
prehashed_message: MsgDigest,
context: Option<&[u8]>,
signature: &ed25519::Signature,
) -> Result<(), SignatureError>
where
MsgDigest: Digest<OutputSize = U64>,
{
self.raw_verify_prehashed::<Sha512, MsgDigest>(prehashed_message, context, signature)
}
/// Strictly verify a signature on a message with this keypair's public key.
///
/// # On The (Multiple) Sources of Malleability in Ed25519 Signatures
///
/// This version of verification is technically non-RFC8032 compliant. The
/// following explains why.
///
/// 1. Scalar Malleability
///
/// The authors of the RFC explicitly stated that verification of an ed25519
/// signature must fail if the scalar `s` is not properly reduced mod $\ell$:
///
/// > To verify a signature on a message M using public key A, with F
/// > being 0 for Ed25519ctx, 1 for Ed25519ph, and if Ed25519ctx or
/// > Ed25519ph is being used, C being the context, first split the
/// > signature into two 32-octet halves. Decode the first half as a
/// > point R, and the second half as an integer S, in the range
/// > 0 <= s < L. Decode the public key A as point A'. If any of the
/// > decodings fail (including S being out of range), the signature is
/// > invalid.)
///
/// All `verify_*()` functions within ed25519-dalek perform this check.
///
/// 2. Point malleability
///
/// The authors of the RFC added in a malleability check to step #3 in
/// §5.1.7, for small torsion components in the `R` value of the signature,
/// *which is not strictly required*, as they state:
///
/// > Check the group equation \[8\]\[S\]B = \[8\]R + \[8\]\[k\]A'. It's
/// > sufficient, but not required, to instead check \[S\]B = R + \[k\]A'.
///
/// # History of Malleability Checks
///
/// As originally defined (cf. the "Malleability" section in the README of
/// this repo), ed25519 signatures didn't consider *any* form of
/// malleability to be an issue. Later the scalar malleability was
/// considered important. Still later, particularly with interests in
/// cryptocurrency design and in unique identities (e.g. for Signal users,
/// Tor onion services, etc.), the group element malleability became a
/// concern.
///
/// However, libraries had already been created to conform to the original
/// definition. One well-used library in particular even implemented the
/// group element malleability check, *but only for batch verification*!
/// Which meant that even using the same library, a single signature could
/// verify fine individually, but suddenly, when verifying it with a bunch
/// of other signatures, the whole batch would fail!
///
/// # "Strict" Verification
///
/// This method performs *both* of the above signature malleability checks.
///
/// It must be done as a separate method because one doesn't simply get to
/// change the definition of a cryptographic primitive ten years
/// after-the-fact with zero consideration for backwards compatibility in
/// hardware and protocols which have it already have the older definition
/// baked in.
///
/// # Return
///
/// Returns `Ok(())` if the signature is valid, and `Err` otherwise.
#[allow(non_snake_case)]
pub fn verify_strict(
&self,
message: &[u8],
signature: &ed25519::Signature,
) -> Result<(), SignatureError> {
let signature = InternalSignature::try_from(signature)?;
let signature_R = signature
.R
.decompress()
.ok_or_else(|| SignatureError::from(InternalError::Verify))?;
// Logical OR is fine here as we're not trying to be constant time.
if signature_R.is_small_order() || self.point.is_small_order() {
return Err(InternalError::Verify.into());
}
let expected_R = self.recompute_R::<Sha512>(None, &signature, message);
if expected_R == signature.R {
Ok(())
} else {
Err(InternalError::Verify.into())
}
}
/// Verify a `signature` on a `prehashed_message` using the Ed25519ph algorithm,
/// using strict signture checking as defined by [`Self::verify_strict`].
///
/// # Inputs
///
/// * `prehashed_message` is an instantiated hash digest with 512-bits of
/// output which has had the message to be signed previously fed into its
/// state.
/// * `context` is an optional context string, up to 255 bytes inclusive,
/// which may be used to provide additional domain separation. If not
/// set, this will default to an empty string.
/// * `signature` is a purported Ed25519ph signature on the `prehashed_message`.
///
/// # Returns
///
/// Returns `true` if the `signature` was a valid signature created by this
/// [`SigningKey`] on the `prehashed_message`.
///
/// # Note
///
/// The RFC only permits SHA-512 to be used for prehashing, i.e., `MsgDigest = Sha512`. This
/// function technically works, and is probably safe to use, with any secure hash function with
/// 512-bit digests, but anything outside of SHA-512 is NOT specification-compliant. We expose
/// [`crate::Sha512`] for user convenience.
#[cfg(feature = "digest")]
#[allow(non_snake_case)]
pub fn verify_prehashed_strict<MsgDigest>(
&self,
prehashed_message: MsgDigest,
context: Option<&[u8]>,
signature: &ed25519::Signature,
) -> Result<(), SignatureError>
where
MsgDigest: Digest<OutputSize = U64>,
{
let signature = InternalSignature::try_from(signature)?;
let ctx: &[u8] = context.unwrap_or(b"");
debug_assert!(
ctx.len() <= 255,
"The context must not be longer than 255 octets."
);
let signature_R = signature
.R
.decompress()
.ok_or_else(|| SignatureError::from(InternalError::Verify))?;
// Logical OR is fine here as we're not trying to be constant time.
if signature_R.is_small_order() || self.point.is_small_order() {
return Err(InternalError::Verify.into());
}
let message = prehashed_message.finalize();
let expected_R = self.recompute_R::<Sha512>(Some(ctx), &signature, &message);
if expected_R == signature.R {
Ok(())
} else {
Err(InternalError::Verify.into())
}
}
/// Convert this verifying key into Montgomery form.
///
/// This can be used for performing X25519 Diffie-Hellman using Ed25519 keys. The output of
/// this function is a valid X25519 public key whose secret key is `sk.to_scalar_bytes()`,
/// where `sk` is a valid signing key for this `VerifyingKey`.
///
/// # Note
///
/// We do NOT recommend this usage of a signing/verifying key. Signing keys are usually
/// long-term keys, while keys used for key exchange should rather be ephemeral. If you can
/// help it, use a separate key for encryption.
///
/// For more information on the security of systems which use the same keys for both signing
/// and Diffie-Hellman, see the paper
/// [On using the same key pair for Ed25519 and an X25519 based KEM](https://eprint.iacr.org/2021/509).
pub fn to_montgomery(&self) -> MontgomeryPoint {
self.point.to_montgomery()
}
}
impl Verifier<ed25519::Signature> for VerifyingKey {
/// Verify a signature on a message with this keypair's public key.
///
/// # Return
///
/// Returns `Ok(())` if the signature is valid, and `Err` otherwise.
fn verify(&self, message: &[u8], signature: &ed25519::Signature) -> Result<(), SignatureError> {
self.raw_verify::<Sha512>(message, signature)
}
}
/// Equivalent to [`VerifyingKey::verify_prehashed`] with `context` set to [`None`].
#[cfg(feature = "digest")]
impl<MsgDigest> DigestVerifier<MsgDigest, ed25519::Signature> for VerifyingKey
where
MsgDigest: Digest<OutputSize = U64>,
{
fn verify_digest(
&self,
msg_digest: MsgDigest,
signature: &ed25519::Signature,
) -> Result<(), SignatureError> {
self.verify_prehashed(msg_digest, None, signature)
}
}
/// Equivalent to [`VerifyingKey::verify_prehashed`] with `context` set to [`Some`]
/// containing `self.value()`.
#[cfg(feature = "digest")]
impl<MsgDigest> DigestVerifier<MsgDigest, ed25519::Signature> for Context<'_, '_, VerifyingKey>
where
MsgDigest: Digest<OutputSize = U64>,
{
fn verify_digest(
&self,
msg_digest: MsgDigest,
signature: &ed25519::Signature,
) -> Result<(), SignatureError> {
self.key()
.verify_prehashed(msg_digest, Some(self.value()), signature)
}
}
impl TryFrom<&[u8]> for VerifyingKey {
type Error = SignatureError;
#[inline]
fn try_from(bytes: &[u8]) -> Result<Self, Self::Error> {
let bytes = bytes.try_into().map_err(|_| InternalError::BytesLength {
name: "VerifyingKey",
length: PUBLIC_KEY_LENGTH,
})?;
Self::from_bytes(bytes)
}
}
#[cfg(all(feature = "alloc", feature = "pkcs8"))]
impl pkcs8::EncodePublicKey for VerifyingKey {
fn to_public_key_der(&self) -> pkcs8::spki::Result<pkcs8::Document> {
pkcs8::PublicKeyBytes::from(self).to_public_key_der()
}
}
#[cfg(feature = "pkcs8")]
impl TryFrom<pkcs8::PublicKeyBytes> for VerifyingKey {
type Error = pkcs8::spki::Error;
fn try_from(pkcs8_key: pkcs8::PublicKeyBytes) -> pkcs8::spki::Result<Self> {
VerifyingKey::try_from(&pkcs8_key)
}
}
#[cfg(feature = "pkcs8")]
impl TryFrom<&pkcs8::PublicKeyBytes> for VerifyingKey {
type Error = pkcs8::spki::Error;
fn try_from(pkcs8_key: &pkcs8::PublicKeyBytes) -> pkcs8::spki::Result<Self> {
VerifyingKey::from_bytes(pkcs8_key.as_ref()).map_err(|_| pkcs8::spki::Error::KeyMalformed)
}
}
#[cfg(feature = "pkcs8")]
impl From<VerifyingKey> for pkcs8::PublicKeyBytes {
fn from(verifying_key: VerifyingKey) -> pkcs8::PublicKeyBytes {
pkcs8::PublicKeyBytes::from(&verifying_key)
}
}
#[cfg(feature = "pkcs8")]
impl From<&VerifyingKey> for pkcs8::PublicKeyBytes {
fn from(verifying_key: &VerifyingKey) -> pkcs8::PublicKeyBytes {
pkcs8::PublicKeyBytes(verifying_key.to_bytes())
}
}
#[cfg(feature = "pkcs8")]
impl TryFrom<pkcs8::spki::SubjectPublicKeyInfoRef<'_>> for VerifyingKey {
type Error = pkcs8::spki::Error;
fn try_from(public_key: pkcs8::spki::SubjectPublicKeyInfoRef<'_>) -> pkcs8::spki::Result<Self> {
pkcs8::PublicKeyBytes::try_from(public_key)?.try_into()
}
}
#[cfg(feature = "serde")]
impl Serialize for VerifyingKey {
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
{
serializer.serialize_bytes(&self.as_bytes()[..])
}
}
#[cfg(feature = "serde")]
impl<'d> Deserialize<'d> for VerifyingKey {
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
where
D: Deserializer<'d>,
{
struct VerifyingKeyVisitor;
impl<'de> serde::de::Visitor<'de> for VerifyingKeyVisitor {
type Value = VerifyingKey;
fn expecting(&self, formatter: &mut ::core::fmt::Formatter<'_>) -> ::core::fmt::Result {
write!(formatter, concat!("An ed25519 verifying (public) key"))
}
fn visit_bytes<E: serde::de::Error>(self, bytes: &[u8]) -> Result<Self::Value, E> {
VerifyingKey::try_from(bytes).map_err(E::custom)
}
fn visit_seq<A>(self, mut seq: A) -> Result<Self::Value, A::Error>
where
A: serde::de::SeqAccess<'de>,
{
let mut bytes = [0u8; 32];
#[allow(clippy::needless_range_loop)]
for i in 0..32 {
bytes[i] = seq
.next_element()?
.ok_or_else(|| serde::de::Error::invalid_length(i, &"expected 32 bytes"))?;
}
let remaining = (0..)
.map(|_| seq.next_element::<u8>())
.take_while(|el| matches!(el, Ok(Some(_))))
.count();
if remaining > 0 {
return Err(serde::de::Error::invalid_length(
32 + remaining,
&"expected 32 bytes",
));
}
VerifyingKey::try_from(&bytes[..]).map_err(serde::de::Error::custom)
}
}
deserializer.deserialize_bytes(VerifyingKeyVisitor)
}
}