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Add hash2curve to ProjectiveMontgomeryXpoint 
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-3
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2 files changed

+142
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‎ed448-goldilocks/src/field/element.rs

Lines changed: 19 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -425,6 +425,25 @@ impl FieldElement {
425425
MontgomeryPoint::new(x, y)
426426
}
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428+
// See https://www.rfc-editor.org/rfc/rfc9380.html#name-curve448-q-3-mod-4-k-1.
429+
// Without y-coordinate.
430+
pub(crate) fn map_to_curve_elligator2_curve448_x(&self) -> FieldElement {
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let mut t1 = self.square(); // 1. t1 = u^2
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t1 *= Self::Z; // 2. t1 = Z * t1 // Z * u^2
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let e1 = t1.ct_eq(&Self::MINUS_ONE); // 3. e1 = t1 == -1 // exceptional case: Z * u^2 == -1
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t1.conditional_assign(&Self::ZERO, e1); // 4. t1 = CMOV(t1, 0, e1) // if t1 == -1, set t1 = 0
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let mut x1 = t1 + Self::ONE; // 5. x1 = t1 + 1
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x1 = x1.invert(); // 6. x1 = inv0(x1)
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x1 *= -Self::J; // 7. x1 = -A * x1 // x1 = -A / (1 + Z * u^2)
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let mut gx1 = x1 + Self::J; // 8. gx1 = x1 + A
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gx1 *= x1; // 9. gx1 = gx1 * x1
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gx1 += Self::ONE; // 10. gx1 = gx1 + B
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gx1 *= x1; // 11. gx1 = gx1 * x1 // gx1 = x1^3 + A * x1^2 + B * x1
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let x2 = -x1 - Self::J; // 12. x2 = -x1 - A
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let e2 = gx1.is_square(); // 14. e2 = is_square(gx1)
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Self::conditional_select(&x2, &x1, e2) // 15. x = CMOV(x2, x1, e2) // If is_square(gx1), x = x1, else x = x2
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}
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// See https://www.shiftleft.org/papers/decaf/decaf.pdf#section.A.3.
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// Implementation copied from <https://sourceforge.net/p/ed448goldilocks/code/ci/e5cc6240690d3ffdfcbdb1e4e851954b789cd5d9/tree/src/per_curve/elligator.tmpl.c#l28>.
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pub(crate) fn map_to_curve_decaf448(&self) -> TwistedExtendedPoint {

‎ed448-goldilocks/src/montgomery/x.rs

Lines changed: 123 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -1,10 +1,17 @@
11
// use crate::constants::A_PLUS_TWO_OVER_FOUR;
2-
use super::{MontgomeryPoint, MontgomeryScalar, ProjectiveMontgomeryPoint};
3-
use crate::AffinePoint;
4-
use crate::field::{ConstMontyType, FieldElement};
2+
use super::{
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DEFAULT_ENCODE_TO_CURVE_SUITE, DEFAULT_HASH_TO_CURVE_SUITE, MontgomeryPoint, MontgomeryScalar,
4+
ProjectiveMontgomeryPoint,
5+
};
6+
use crate::field::{ConstMontyType, FieldElement, FieldElementU84};
7+
use crate::{AffinePoint, Curve448};
58
use core::fmt;
69
use core::ops::Mul;
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use elliptic_curve::array::Array;
711
use elliptic_curve::bigint::U448;
12+
use elliptic_curve::consts::{U28, U84};
13+
use hash2curve::{ExpandMsg, ExpandMsgXof, Expander, FromOkm, MapToCurve};
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use sha3::Shake256;
815
use subtle::{Choice, ConditionallyNegatable, ConditionallySelectable, ConstantTimeEq};
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1017
impl MontgomeryXpoint {
@@ -277,6 +284,67 @@ impl ProjectiveMontgomeryXpoint {
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Self { U, W }
278285
}
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287+
/// Hash a message to a point on the curve
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///
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/// Hash using the default domain separation tag and hash function.
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/// For more control see [`Self::hash()`].
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pub fn hash_with_defaults(msg: &[u8]) -> Self {
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Self::hash::<ExpandMsgXof<Shake256>>(&[msg], &[DEFAULT_HASH_TO_CURVE_SUITE])
293+
}
294+
295+
/// Hash a message to a point on the curve
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///
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/// Implements hash to curve according
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/// see <https://datatracker.ietf.org/doc/rfc9380/>
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pub fn hash<X>(msg: &[&[u8]], dst: &[&[u8]]) -> Self
300+
where
301+
X: ExpandMsg<U28>,
302+
{
303+
let mut expander =
304+
X::expand_message(msg, dst, (84 * 2).try_into().expect("should never fail"))
305+
.expect("should never fail with the given `ExpandMsg` and `dst`");
306+
let mut data = Array::<u8, U84>::default();
307+
expander.fill_bytes(&mut data);
308+
let u0 = FieldElementU84::from_okm(&data).0;
309+
expander.fill_bytes(&mut data);
310+
let u1 = FieldElementU84::from_okm(&data).0;
311+
312+
let q0 = Curve448::map_to_curve(FieldElementU84(u0));
313+
let q1 = Curve448::map_to_curve(FieldElementU84(u1));
314+
315+
Self::from(q0 + q1).double().double()
316+
}
317+
318+
/// Encode a message to a point on the curve
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///
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/// Encode using the default domain separation tag and hash function.
321+
/// For more control see [`Self::encode()`].
322+
pub fn encode_with_defaults(msg: &[u8]) -> Self {
323+
Self::encode::<ExpandMsgXof<Shake256>>(&[msg], &[DEFAULT_ENCODE_TO_CURVE_SUITE])
324+
}
325+
326+
/// Encode a message to a point on the curve
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///
328+
/// Implements encode to curve according
329+
/// see <https://datatracker.ietf.org/doc/rfc9380/>
330+
pub fn encode<X>(msg: &[&[u8]], dst: &[&[u8]]) -> Self
331+
where
332+
X: ExpandMsg<U28>,
333+
{
334+
let mut expander = X::expand_message(msg, dst, 84.try_into().expect("should never fail"))
335+
.expect("should never fail with the given `ExpandMsg` and `dst`");
336+
let mut data = Array::<u8, U84>::default();
337+
expander.fill_bytes(&mut data);
338+
let u = FieldElementU84::from_okm(&data).0;
339+
340+
Self {
341+
U: u.map_to_curve_elligator2_curve448_x(),
342+
W: FieldElement::ONE,
343+
}
344+
.double()
345+
.double()
346+
}
347+
280348
/// Convert the point to affine form
281349
pub fn to_affine(&self) -> MontgomeryXpoint {
282350
let x = self.U * self.W.invert();
@@ -307,6 +375,8 @@ mod tests {
307375
use super::*;
308376
use crate::EdwardsPoint;
309377
use elliptic_curve::CurveGroup;
378+
use hex_literal::hex;
379+
use sha3::Shake256;
310380

311381
#[test]
312382
fn test_montgomery_edwards() {
@@ -338,4 +408,54 @@ mod tests {
338408

339409
assert_eq!(x_identity.to_extended(Choice::from(1)), identity);
340410
}
411+
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#[test]
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fn hash_with_test_vectors() {
414+
const DST: &[u8] = b"QUUX-V01-CS02-with-curve448_XOF:SHAKE256_ELL2_RO_";
415+
const MSGS: &[(&[u8], [u8; 56], [u8; 56])] = &[
416+
(b"", hex!("5ea5ff623d27c75e73717514134e73e419f831a875ca9e82915fdfc7069d0a9f8b532cfb32b1d8dd04ddeedbe3fa1d0d681c01e825d6a9ea"), hex!("afadd8de789f8f8e3516efbbe313a7eba364c939ecba00dabf4ced5c563b18e70a284c17d8f46b564c4e6ce11784a3825d941116622128c1")),
417+
(b"abc", hex!("9b2f7ce34878d7cebf34c582db14958308ea09366d1ec71f646411d3de0ae564d082b06f40cd30dfc08d9fb7cb21df390cf207806ad9d0e4"), hex!("138a0eef0a4993ea696152ed7db61f7ddb4e8100573591e7466d61c0c568ecaec939e36a84d276f34c402526d8989a96e99760c4869ed633")),
418+
(b"abcdef0123456789", hex!("f54ecd14b85a50eeeee0618452df3a75be7bfba11da5118774ae4ea55ac204e153f77285d780c4acee6c96abe3577a0c0b00be6e790cf194"), hex!("935247a64bf78c107069943c7e3ecc52acb27ce4a3230407c8357341685ea2152e8c3da93f8cd77da1bddb5bb759c6e7ae7d516dced42850")),
419+
(b"q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", hex!("5bd67c4f88adf6beb10f7e0d0054659776a55c97b809ec8b3101729e104fd0f684e103792f267fd87cc4afc25a073956ef4f268fb02824d5"), hex!("da1f5cb16a352719e4cb064cf47ba72aeba7752d03e8ca2c56229f419b4ef378785a5af1a53dd7ab4d467c1f92f7b139b3752faf29c96432")),
420+
(b"a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", hex!("ea441c10b3636ecedd5c0dfcae96384cc40de8390a0ab648765b4508da12c586d55dc981275776507ebca0e4d1bcaa302bb69dcfa31b3451"), hex!("fee0192d49bcc0c28d954763c2cbe739b9265c4bebe3883803c64971220cfda60b9ac99ad986cd908c0534b260b5cfca46f6c2b0f3f21bda")),
421+
];
422+
423+
for (msg, x, y) in MSGS {
424+
let p = ProjectiveMontgomeryXpoint::hash::<ExpandMsgXof<Shake256>>(&[msg], &[DST])
425+
.to_affine();
426+
let mut xx = [0u8; 56];
427+
xx.copy_from_slice(&x[..]);
428+
xx.reverse();
429+
let mut yy = [0u8; 56];
430+
yy.copy_from_slice(&y[..]);
431+
yy.reverse();
432+
assert_eq!(p.0, xx);
433+
assert!(p.y(Choice::from(0)) == yy || p.y(Choice::from(1)) == yy);
434+
}
435+
}
436+
437+
#[test]
438+
fn encode_with_test_vectors() {
439+
const DST: &[u8] = b"QUUX-V01-CS02-with-curve448_XOF:SHAKE256_ELL2_NU_";
440+
const MSGS: &[(&[u8], [u8; 56], [u8; 56])] = &[
441+
(b"", hex!("b65e8dbb279fd656f926f68d463b13ca7a982b32f5da9c7cc58afcf6199e4729863fb75ca9ae3c95c6887d95a5102637a1c5c40ff0aafadc"), hex!("ea1ea211cf29eca11c057fe8248181591a19f6ac51d45843a65d4bb8b71bc83a64c771ed7686218a278ef1c5d620f3d26b53162188645453")),
442+
(b"abc", hex!("51aceca4fa95854bbaba58d8a5e17a86c07acadef32e1188cafda26232131800002cc2f27c7aec454e5e0c615bddffb7df6a5f7f0f14793f"), hex!("c590c9246eb28b08dee816d608ef233ea5d76e305dc458774a1e1bd880387e6734219e2018e4aa50a49486dce0ba8740065da37e6cf5212c")),
443+
(b"abcdef0123456789", hex!("c6d65987f146b8d0cb5d2c44e1872ac3af1f458f6a8bd8c232ffe8b9d09496229a5a27f350eb7d97305bcc4e0f38328718352e8e3129ed71"), hex!("4d2f901bf333fdc4135b954f20d59207e9f6a4ecf88ce5af11c892b44f79766ec4ecc9f60d669b95ca8940f39b1b7044140ac2040c1bf659")),
444+
(b"q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq", hex!("9b8d008863beb4a02fb9e4efefd2eba867307fb1c7ce01746115d32e1db551bb254e8e3e4532d5c74a83949a69a60519ecc9178083cbe943"), hex!("346a1fca454d1e67c628437c270ec0f0c4256bb774fe6c0e49de7004ff6d9199e2cd99d8f7575a96aafc4dc8db1811ba0a44317581f41371")),
445+
(b"a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", hex!("8746dc34799112d1f20acda9d7f722c9abb29b1fb6b7e9e566983843c20bd7c9bfad21b45c5166b808d2f5d44e188f1fdaf29cdee8a72e4c"), hex!("7c1293484c9287c298a1a0600c64347eee8530acf563cd8705e05728274d8cd8101835f8003b6f3b78b5beb28f5be188a3d7bce1ec5a36b1")),
446+
];
447+
448+
for (msg, x, y) in MSGS {
449+
let p = ProjectiveMontgomeryXpoint::encode::<ExpandMsgXof<Shake256>>(&[msg], &[DST])
450+
.to_affine();
451+
let mut xx = [0u8; 56];
452+
xx.copy_from_slice(&x[..]);
453+
xx.reverse();
454+
let mut yy = [0u8; 56];
455+
yy.copy_from_slice(&y[..]);
456+
yy.reverse();
457+
assert_eq!(p.0, xx);
458+
assert!(p.y(Choice::from(0)) == yy || p.y(Choice::from(1)) == yy);
459+
}
460+
}
341461
}

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