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https://github.com/saymrwulf/curve25519-dalek-source.git
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Move Montgomery code to a montgomery.rs module
This commit is contained in:
Henry de Valence
parent
8ad02e2f57
commit
3dddecb4a8
3 changed files with 204 additions and 168 deletions
169
src/edwards.rs
169
src/edwards.rs
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@ -90,6 +90,7 @@ use core::ops::Index;
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use constants;
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use field::FieldElement;
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use scalar::Scalar;
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use montgomery::CompressedMontgomeryU;
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use subtle::slices_equal;
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use subtle::bytes_equal;
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@ -151,133 +152,6 @@ impl CompressedEdwardsY {
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}
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}
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/// In "Montgomery u" format, as used in X25519, a point `(u,v)` on
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/// the Montgomery curve
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///
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/// v^2 = u * (u^2 + 486662*u + 1)
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///
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/// is represented just by `u`. Note that we use `(u,v)` instead of
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/// `(x,y)` for Montgomery coordinates to avoid confusion with Edwards
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/// coordinates. For Montgomery curves, it is possible to compute the
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/// `u`-coordinate of `n(u,v)` just from `n` and `u`, so it is not
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/// necessary to use `v` for a Diffie-Hellman key exchange.
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///
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/// XXX add note on monty, twist security, edwards impl of x25519, rfc7748
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#[derive(Copy, Clone, Debug, PartialEq, Eq)]
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pub struct CompressedMontgomeryU(pub [u8; 32]);
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impl CompressedMontgomeryU {
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/// View this `CompressedMontgomeryU` as an array of bytes.
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pub fn to_bytes(&self) -> [u8; 32] {
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self.0
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}
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/// Attempt to decompress to an `ExtendedPoint`.
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///
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/// # Note
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///
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/// Since there are two curve points with the same
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/// `u`-coordinate, the `u`-coordinate does not fully specify a
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/// point. That is, roundtripping between an `ExtendedPoint` and
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/// a `CompressedMontgomeryU` discards its sign bit.
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///
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/// # Warning
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///
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/// This function is *not* constant time.
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///
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/// # Return
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///
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/// An `Option<ExtendedPoint>`, which will be `None` if either condition holds:
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///
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/// * `u = -1`, or
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/// * `v` is not square.
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//
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// XXX any other exceptional points for the birational map?
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pub fn decompress(&self) -> Option<ExtendedPoint> {
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let u: FieldElement = FieldElement::from_bytes(&self.0);
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// If u = -1, then v^2 = u*(u^2+486662*u+1) = 486660.
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// But 486660 is nonsquare mod p, so this is not a curve point.
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//
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// Note: currently, without this check, u = -1 will accidentally
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// decode to a valid (but incorrect) point, since 0.invert() = 0.
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if u == FieldElement::minus_one() {
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return None;
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}
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let y: FieldElement = CompressedMontgomeryU::to_edwards_y(&u); // y = (u-1)/(u+1)
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// XXX this does two inversions: the above + one in .decompress()
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// is it possible to do one?
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CompressedEdwardsY(y.to_bytes()).decompress()
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}
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/// Given a Montgomery `u` coordinate, compute an Edwards `y` via
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/// `y = (u-1)/(u+1)`.
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///
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/// # Return
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///
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/// A `FieldElement` corresponding to this coordinate, but in Edwards form.
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pub fn to_edwards_y(u: &FieldElement) -> FieldElement {
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// Since `u = (1+y)/(1-y)` and `v = √(u(u²+Au+1))`, so `y = (u-1)/(u+1)`.
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&(u - &FieldElement::one()) * &(u + &FieldElement::one()).invert()
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}
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/// Given a Montgomery `u` coordinate, compute the corresponding
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/// Montgomery `v` coordinate by computing the right-hand side of
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/// the Montgomery field equation, `v² = u(u² + Au +1)`.
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///
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/// # Return
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///
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/// A tuple of (`u8`, `FieldElement`), where the `u8` is `1` if the v² was
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/// actually a square and `0` if otherwise, along with a `FieldElement`: the
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/// Montgomery `v` corresponding to this `u`.
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pub fn to_montgomery_v(u: &FieldElement) -> (u8, FieldElement) {
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let one: FieldElement = FieldElement::one();
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let v_squared: FieldElement = u * &(&u.square() + &(&(&constants::A * u) + &one));
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let (okay, v_inv) = v_squared.invsqrt();
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let v = &v_inv * &v_squared;
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(okay, v)
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}
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/// Given Montgomery coordinates `(u, v)`, recover the Edwards `x` coordinate.
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///
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/// # Inputs
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///
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/// * `u` and `v` are both `&FieldElement`s, corresponding the the `(u, v)`
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/// coordinates of this `CompressedMontgomeryU`.
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/// * `sign` is an &u8.
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///
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/// ## Explanation of choice of `sign`
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///
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/// ### Original Signal behaviour:
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///
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/// - `1u8` will leave `x` negative if it is negative, and will negate
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/// `x` if it is positive, and
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/// - `0u8` will leave `x` positive if it is positive, and will negate
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/// `x` if it is negative.
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///
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/// Hence, if `sign` is `1u8`, the returned `x` will be negative.
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/// Otherwise, if `sign` is `0u8`, the returned `x` will be positive.
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///
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/// # Return
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///
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/// A `FieldElement`, the Edwards `x` coordinate, by using `(u, v)` to
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/// convert from Montgomery to Edwards form via the right-hand side of the
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/// equation: `x=(u/v)*sqrt(-A-2)`.
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pub fn to_edwards_x(u: &FieldElement, v: &FieldElement, sign: &u8) -> FieldElement {
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let mut x: FieldElement = &(u * &v.invert()) * &constants::SQRT_MINUS_APLUS2;
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let neg_x: FieldElement = -(&x);
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let current_sign: u8 = x.is_negative_ed25519();
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// Negate x to match the sign:
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x.conditional_assign(&neg_x, current_sign ^ sign);
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x
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}
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}
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// ------------------------------------------------------------------------
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// Serde support
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// ------------------------------------------------------------------------
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@ -1376,13 +1250,6 @@ mod test {
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use constants;
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use super::*;
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/// The X25519 basepoint, in compressed Montgomery form.
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static BASE_CMPRSSD_MONTY: CompressedMontgomeryU =
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CompressedMontgomeryU([0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
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/// X coordinate of the basepoint.
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/// = 15112221349535400772501151409588531511454012693041857206046113283949847762202
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static BASE_X_COORD_BYTES: [u8; 32] =
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@ -1432,40 +1299,6 @@ mod test {
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0xc0, 0x46, 0x83, 0x43, 0xde, 0x70, 0x4b, 0x85,
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0x09, 0x6f, 0xfe, 0x35, 0x4f, 0x13, 0x2b, 0x42]);
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/// Test Montgomery conversion against the X25519 basepoint.
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#[test]
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fn basepoint_to_montgomery() {
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assert_eq!(constants::ED25519_BASEPOINT.compress_montgomery().unwrap(),
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BASE_CMPRSSD_MONTY);
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}
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/// Test Montgomery conversion against the X25519 basepoint.
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#[test]
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fn basepoint_from_montgomery() {
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assert_eq!(BASE_CMPRSSD_MONTY.decompress().unwrap().compress_edwards(),
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constants::BASE_CMPRSSD);
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}
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/// If u = -1, then v^2 = u*(u^2+486662*u+1) = 486660.
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/// But 486660 is nonsquare mod p, so this should fail.
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///
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/// XXX what does Signal do here?
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#[test]
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fn u_minus_one_monty() {
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let minus_one = FieldElement::minus_one();
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let minus_one_bytes = minus_one.to_bytes();
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let div_by_zero_u = CompressedMontgomeryU(minus_one_bytes);
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assert!(div_by_zero_u.decompress().is_none());
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}
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/// Montgomery compression of the identity point should
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/// fail (it's sent to infinity).
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#[test]
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fn identity_to_monty() {
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let id = ExtendedPoint::identity();
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assert!(id.compress_montgomery().is_none());
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}
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/// Test round-trip decompression for the basepoint.
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#[test]
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fn basepoint_decompression_compression() {
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@ -73,6 +73,7 @@ mod field_64bit;
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pub mod scalar;
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pub mod edwards;
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pub mod montgomery;
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// Feature gate decaf while our implementation is unfinished and probably incorrect.
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#[cfg(feature = "yolocrypto")]
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202
src/montgomery.rs
Normal file
202
src/montgomery.rs
Normal file
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@ -0,0 +1,202 @@
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// -*- mode: rust; -*-
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//
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// To the extent possible under law, the authors have waived all copyright and
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// related or neighboring rights to curve25519-dalek, using the Creative
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// Commons "CC0" public domain dedication. See
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// <http://creativecommons.org/publicdomain/zero/.0/> for full details.
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//
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// Authors:
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// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
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// - Henry de Valence <hdevalence@hdevalence.ca>
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//! Montgomery arithmetic prototype, subject to revision.
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// We allow non snake_case names because coordinates in projective space are
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// traditionally denoted by the capitalisation of their respective
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// counterparts in affine space. Yeah, you heard me, rustc, I'm gonna have my
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// affine and projective cakes and eat both of them too.
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#![allow(non_snake_case)]
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use constants;
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use field::FieldElement;
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use edwards::{ExtendedPoint, CompressedEdwardsY};
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use subtle::ConditionallyAssignable;
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/// In "Montgomery u" format, as used in X25519, a point `(u,v)` on
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/// the Montgomery curve
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///
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/// v^2 = u * (u^2 + 486662*u + 1)
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///
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/// is represented just by `u`. Note that we use `(u,v)` instead of
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/// `(x,y)` for Montgomery coordinates to avoid confusion with Edwards
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/// coordinates. For Montgomery curves, it is possible to compute the
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/// `u`-coordinate of `n(u,v)` just from `n` and `u`, so it is not
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/// necessary to use `v` for a Diffie-Hellman key exchange.
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///
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/// XXX add note on monty, twist security, edwards impl of x25519, rfc7748
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#[derive(Copy, Clone, Debug, PartialEq, Eq)]
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pub struct CompressedMontgomeryU(pub [u8; 32]);
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impl CompressedMontgomeryU {
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/// View this `CompressedMontgomeryU` as an array of bytes.
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pub fn to_bytes(&self) -> [u8; 32] {
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self.0
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}
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/// Attempt to decompress to an `ExtendedPoint`.
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///
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/// # Note
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///
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/// Since there are two curve points with the same
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/// `u`-coordinate, the `u`-coordinate does not fully specify a
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/// point. That is, roundtripping between an `ExtendedPoint` and
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/// a `CompressedMontgomeryU` discards its sign bit.
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///
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/// # Warning
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///
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/// This function is *not* constant time.
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///
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/// # Return
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///
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/// An `Option<ExtendedPoint>`, which will be `None` if either condition holds:
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///
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/// * `u = -1`, or
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/// * `v` is not square.
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//
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// XXX any other exceptional points for the birational map?
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pub fn decompress(&self) -> Option<ExtendedPoint> {
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let u: FieldElement = FieldElement::from_bytes(&self.0);
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// If u = -1, then v^2 = u*(u^2+486662*u+1) = 486660.
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// But 486660 is nonsquare mod p, so this is not a curve point.
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//
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// Note: currently, without this check, u = -1 will accidentally
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// decode to a valid (but incorrect) point, since 0.invert() = 0.
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if u == FieldElement::minus_one() {
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return None;
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}
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let y: FieldElement = CompressedMontgomeryU::to_edwards_y(&u); // y = (u-1)/(u+1)
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// XXX this does two inversions: the above + one in .decompress()
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// is it possible to do one?
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CompressedEdwardsY(y.to_bytes()).decompress()
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}
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/// Given a Montgomery `u` coordinate, compute an Edwards `y` via
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/// `y = (u-1)/(u+1)`.
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///
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/// # Return
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///
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/// A `FieldElement` corresponding to this coordinate, but in Edwards form.
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pub fn to_edwards_y(u: &FieldElement) -> FieldElement {
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// Since `u = (1+y)/(1-y)` and `v = √(u(u²+Au+1))`, so `y = (u-1)/(u+1)`.
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&(u - &FieldElement::one()) * &(u + &FieldElement::one()).invert()
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}
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/// Given a Montgomery `u` coordinate, compute the corresponding
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/// Montgomery `v` coordinate by computing the right-hand side of
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/// the Montgomery field equation, `v² = u(u² + Au +1)`.
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///
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/// # Return
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///
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/// A tuple of (`u8`, `FieldElement`), where the `u8` is `1` if the v² was
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/// actually a square and `0` if otherwise, along with a `FieldElement`: the
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/// Montgomery `v` corresponding to this `u`.
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pub fn to_montgomery_v(u: &FieldElement) -> (u8, FieldElement) {
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let one: FieldElement = FieldElement::one();
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let v_squared: FieldElement = u * &(&u.square() + &(&(&constants::A * u) + &one));
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let (okay, v_inv) = v_squared.invsqrt();
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let v = &v_inv * &v_squared;
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(okay, v)
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}
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/// Given Montgomery coordinates `(u, v)`, recover the Edwards `x` coordinate.
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///
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/// # Inputs
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///
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/// * `u` and `v` are both `&FieldElement`s, corresponding the the `(u, v)`
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/// coordinates of this `CompressedMontgomeryU`.
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/// * `sign` is an &u8.
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///
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/// ## Explanation of choice of `sign`
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///
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/// ### Original Signal behaviour:
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///
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/// - `1u8` will leave `x` negative if it is negative, and will negate
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/// `x` if it is positive, and
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/// - `0u8` will leave `x` positive if it is positive, and will negate
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/// `x` if it is negative.
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///
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/// Hence, if `sign` is `1u8`, the returned `x` will be negative.
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/// Otherwise, if `sign` is `0u8`, the returned `x` will be positive.
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///
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/// # Return
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///
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/// A `FieldElement`, the Edwards `x` coordinate, by using `(u, v)` to
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/// convert from Montgomery to Edwards form via the right-hand side of the
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/// equation: `x=(u/v)*sqrt(-A-2)`.
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pub fn to_edwards_x(u: &FieldElement, v: &FieldElement, sign: &u8) -> FieldElement {
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let mut x: FieldElement = &(u * &v.invert()) * &constants::SQRT_MINUS_APLUS2;
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let neg_x: FieldElement = -(&x);
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let current_sign: u8 = x.is_negative_ed25519();
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// Negate x to match the sign:
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x.conditional_assign(&neg_x, current_sign ^ sign);
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x
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}
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}
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// ------------------------------------------------------------------------
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// Tests
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// ------------------------------------------------------------------------
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#[cfg(test)]
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mod test {
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use super::*;
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/// The X25519 basepoint, in compressed Montgomery form.
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static BASE_CMPRSSD_MONTY: CompressedMontgomeryU =
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CompressedMontgomeryU([0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
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/// Test Montgomery conversion against the X25519 basepoint.
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#[test]
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fn basepoint_to_montgomery() {
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assert_eq!(constants::ED25519_BASEPOINT.compress_montgomery().unwrap(),
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BASE_CMPRSSD_MONTY);
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}
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/// Test Montgomery conversion against the X25519 basepoint.
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#[test]
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fn basepoint_from_montgomery() {
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assert_eq!(BASE_CMPRSSD_MONTY.decompress().unwrap().compress_edwards(),
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constants::BASE_CMPRSSD);
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}
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/// If u = -1, then v^2 = u*(u^2+486662*u+1) = 486660.
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/// But 486660 is nonsquare mod p, so this should fail.
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///
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/// XXX what does Signal do here?
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#[test]
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fn u_minus_one_monty() {
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let minus_one = FieldElement::minus_one();
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let minus_one_bytes = minus_one.to_bytes();
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let div_by_zero_u = CompressedMontgomeryU(minus_one_bytes);
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assert!(div_by_zero_u.decompress().is_none());
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}
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/// Montgomery compression of the identity point should
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/// fail (it's sent to infinity).
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#[test]
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fn identity_to_monty() {
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let id = ExtendedPoint::identity();
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assert!(id.compress_montgomery().is_none());
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}
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}
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