mirror of
https://github.com/saymrwulf/curve25519-dalek-source.git
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Merge branch 'feature/batch_inversion' into develop
This commit is contained in:
Henry de Valence
commit
ed7345f40b
3 changed files with 531 additions and 72 deletions
94
src/field.rs
94
src/field.rs
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@ -178,6 +178,64 @@ impl FieldElement {
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(t19, t3)
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}
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/// Given a slice of public `FieldElements`, replace each with its inverse.
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///
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/// All input `FieldElements` **MUST** be nonzero.
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///
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/// This function is most efficient when the batch size (slice
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/// length) is a power of 2.
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#[cfg(any(feature = "alloc", feature = "std"))]
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pub fn batch_invert(inputs: &mut [FieldElement]) {
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// First, compute the product of all inputs using a product
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// tree:
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//
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// Inputs: [x_0, x_1, x_2]
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//
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// Tree:
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//
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// x_0*x_1*x_2*1 tree[1]
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// / \
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// x_0*x_1 x_2*1 tree[2,3]
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// / \ / \
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// x_0 x_1 x_2 1 tree[4,5,6,7]
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//
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// The leaves of the tree are the inputs. We store the tree in
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// an array of length 2*n, similar to a binary heap.
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//
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// To initialize the tree, set every node to 1, then fill in
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// the leaf nodes with the input variables. Finally, set every
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// non-leaf node to be the product of its children.
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let n = inputs.len().next_power_of_two();
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let mut tree = vec![FieldElement::one(); 2*n];
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tree[n..n+inputs.len()].copy_from_slice(inputs);
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for i in (1..n).rev() {
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tree[i] = &tree[2*i] * &tree[2*i+1];
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}
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// The root of the tree is the product of all inputs, and is
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// stored at index 1. Compute its inverse.
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let allinv = tree[1].invert();
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// To compute y_i = 1/x_i, start at the i-th leaf node of the
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// tree, and walk up to the root of the tree, multiplying
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// `allinv` by each sibling. This computes
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//
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// y_i = y * (all x_j except x_i)
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//
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// using lg(n) multiplications for each y_i, taking n*lg(n) in
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// total.
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for i in 0..inputs.len() {
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let mut inv = allinv;
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let mut node = n + i;
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while node > 1 {
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inv *= &tree[node ^ 1];
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node = node >> 1;
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}
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inputs[i] = inv;
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}
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}
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/// Given a nonzero field element, compute its inverse.
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///
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/// The inverse is computed as self^(p-2), since
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@ -375,6 +433,21 @@ mod test {
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assert_eq!(FieldElement::one(), &a * &should_be_inverse);
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}
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#[test]
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fn batch_invert_a_matches_nonbatched() {
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let a = FieldElement::from_bytes(&A_BYTES);
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let ap58 = FieldElement::from_bytes(&AP58_BYTES);
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let asq = FieldElement::from_bytes(&ASQ_BYTES);
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let ainv = FieldElement::from_bytes(&AINV_BYTES);
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let a2 = &a + &a;
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let a_list = vec![a, ap58, asq, ainv, a2];
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let mut ainv_list = a_list.clone();
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FieldElement::batch_invert(&mut ainv_list[..]);
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for i in 0..5 {
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assert_eq!(a_list[i].invert(), ainv_list[i]);
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}
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}
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#[test]
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fn a_p58_vs_ap58_constant() {
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let a = FieldElement::from_bytes(&A_BYTES);
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@ -470,4 +543,25 @@ mod bench {
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let a = FieldElement::from_bytes(&A_BYTES);
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b.iter(|| a.invert());
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}
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#[bench]
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fn batch_16_inv(b: &mut Bencher) {
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let a = FieldElement::from_bytes(&A_BYTES);
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let mut a_vec = vec![a; 16];
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b.iter(|| FieldElement::batch_invert(&mut a_vec));
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}
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#[bench]
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fn batch_128_inv(b: &mut Bencher) {
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let a = FieldElement::from_bytes(&A_BYTES);
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let mut a_vec = vec![a; 128];
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b.iter(|| FieldElement::batch_invert(&mut a_vec));
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}
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#[bench]
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fn batch_1024_inv(b: &mut Bencher) {
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let a = FieldElement::from_bytes(&A_BYTES);
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let mut a_vec = vec![a; 1024];
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b.iter(|| FieldElement::batch_invert(&mut a_vec));
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}
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}
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119
src/ristretto.rs
119
src/ristretto.rs
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@ -666,6 +666,87 @@ impl RistrettoPoint {
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CompressedRistretto(s.to_bytes())
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}
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/// Double-and-compress a batch of points.
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#[cfg(any(feature = "alloc", feature = "std"))]
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pub fn double_and_compress_batch<'a, I>(points: I) -> Vec<CompressedRistretto>
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where I: IntoIterator<Item = &'a RistrettoPoint>
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{
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#[derive(Copy, Clone, Debug)]
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struct BatchCompressState {
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e: FieldElement,
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f: FieldElement,
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g: FieldElement,
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h: FieldElement,
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eg: FieldElement,
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fh: FieldElement,
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}
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impl BatchCompressState {
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fn efgh(&self) -> FieldElement {
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&self.eg * &self.fh
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}
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}
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impl<'a> From<&'a RistrettoPoint> for BatchCompressState {
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fn from(P: &'a RistrettoPoint) -> BatchCompressState {
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let XX = P.0.X.square();
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let YY = P.0.Y.square();
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let ZZ = P.0.Z.square();
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let dTT = &P.0.T.square() * &constants::EDWARDS_D;
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let e = &P.0.X * &(&P.0.Y + &P.0.Y); // = 2*X*Y
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let f = &ZZ + &dTT; // = Z^2 + d*T^2
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let g = &YY + &XX; // = Y^2 - a*X^2
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let h = &ZZ - &dTT; // = Z^2 - d*T^2
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let eg = &e * &g;
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let fh = &f * &h;
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BatchCompressState{ e: e, f: f, g: g, h: h, eg: eg, fh: fh }
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}
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}
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let states: Vec<BatchCompressState> = points.into_iter().map(|P| BatchCompressState::from(P)).collect();
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let mut invs: Vec<FieldElement> = states.iter().map(|state| state.efgh()).collect();
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FieldElement::batch_invert(&mut invs[..]);
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states.iter().zip(invs.iter()).map(|(state, inv): (&BatchCompressState, &FieldElement)| {
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let Zinv = &state.eg * &inv;
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let Tinv = &state.fh * &inv;
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let mut magic = constants::INVSQRT_A_MINUS_D;
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let negcheck1 = (&state.eg * &Zinv).is_negative();
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let mut e = state.e;
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let mut g = state.g;
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let mut h = state.h;
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let minus_e = -&e;
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let f_times_sqrta = &state.f * &constants::SQRT_M1;
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e.conditional_assign(&state.g, negcheck1);
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g.conditional_assign(&minus_e, negcheck1);
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h.conditional_assign(&f_times_sqrta, negcheck1);
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magic.conditional_assign(&constants::SQRT_M1, negcheck1);
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let negcheck2 = (&(&h * &e) * &Zinv).is_negative();
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g.conditional_negate(negcheck2);
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let mut s = &(&h - &g) * &(&magic * &(&g * &Tinv));
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let s_is_negative = s.is_negative();
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s.conditional_negate(s_is_negative);
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CompressedRistretto(s.to_bytes())
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}).collect()
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}
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/// Return the coset self + E[4], for debugging.
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fn coset4(&self) -> [ExtendedPoint; 4] {
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[ self.0
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@ -1216,6 +1297,20 @@ mod test {
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}
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}
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#[test]
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fn double_and_compress_1024_random_points() {
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let mut rng = OsRng::new().unwrap();
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let points: Vec<RistrettoPoint> =
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(0..1024).map(|_| RistrettoPoint::random(&mut rng)).collect();
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let compressed = RistrettoPoint::double_and_compress_batch(&points);
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for (P, P2_compressed) in points.iter().zip(compressed.iter()) {
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assert_eq!(*P2_compressed, (P + P).compress());
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}
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}
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#[test]
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fn random_is_valid() {
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let mut rng = OsRng::new().unwrap();
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@ -1254,4 +1349,28 @@ mod bench {
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let P = B * &Scalar::random(&mut rng);
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b.iter(|| P.compress());
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}
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fn double_and_compress_n_random_points(n: usize, b: &mut Bencher) {
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let mut rng = OsRng::new().unwrap();
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let points: Vec<RistrettoPoint> =
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(0..n).map(|_| RistrettoPoint::random(&mut rng)).collect();
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b.iter(|| RistrettoPoint::double_and_compress_batch(&points) );
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}
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#[bench]
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fn double_and_compress_16_random_points(b: &mut Bencher) {
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double_and_compress_n_random_points(16, b);
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}
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#[bench]
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fn double_and_compress_128_random_points(b: &mut Bencher) {
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double_and_compress_n_random_points(128, b);
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}
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#[bench]
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fn double_and_compress_1024_random_points(b: &mut Bencher) {
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double_and_compress_n_random_points(1024, b);
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}
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}
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390
vendor/ristretto.sage
vendored
390
vendor/ristretto.sage
vendored
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@ -49,7 +49,11 @@ def isqrt(x,exn=InvalidEncodingException("Not on curve")):
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"""Return 1/sqrt(x)"""
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if x==0: return 0
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if not is_square(x): raise exn
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return 1/sqrt(x)
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s = sqrt(x)
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#if negative(s): s=-s
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return 1/s
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def inv0(x): return 1/x if x != 0 else 0
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def isqrt_i(x):
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"""Return 1/sqrt(x) or 1/sqrt(zeta * x)"""
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@ -117,16 +121,20 @@ class QuotientEdwardsPoint(object):
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else:
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return self.__class__(-self.x, -self.y)
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def doubleAndEncodeSpec(self):
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return (self+self).encode()
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# Utility functions
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@classmethod
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def bytesToGf(cls,bytes,mustBeProper=True,mustBePositive=False):
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def bytesToGf(cls,bytes,mustBeProper=True,mustBePositive=False,maskHiBits=False):
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"""Convert little-endian bytes to field element, sanity check length"""
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if len(bytes) != cls.encLen:
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raise InvalidEncodingException("wrong length %d" % len(bytes))
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s = dec_le(bytes)
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if mustBeProper and s >= cls.F.modulus():
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if mustBeProper and s >= cls.F.order():
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raise InvalidEncodingException("%d out of range!" % s)
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bitlen = int(ceil(log(cls.F.order())/log(2)))
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if maskHiBits: s &= 2^bitlen-1
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s = cls.F(s)
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if mustBePositive and negative(s):
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raise InvalidEncodingException("%d is negative!" % s)
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@ -197,7 +205,42 @@ class RistrettoPoint(QuotientEdwardsPoint):
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if negative(isr^2*num*y*t): y = -y
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s = isr*y*(z-y)
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return self.gfToBytes(s,mustBePositive=True)
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@optimized_version_of("doubleAndEncodeSpec")
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def doubleAndEncode(self):
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X,Y,Z,T = self.xyzt()
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a,d,mneg = self.a,self.d,self.mneg
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if self.cofactor==8:
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e = 2*X*Y
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f = Z^2+d*T^2
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g = Y^2-a*X^2
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h = Z^2-d*T^2
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inv1 = 1/(e*f*g*h)
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z_inv = inv1*e*g # 1 / (f*h)
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t_inv = inv1*f*h
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if negative(e*g*z_inv):
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if a==-1: sqrta = self.i
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else: sqrta = -1
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e,f,g,h = g,h,-e,f*sqrta
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factor = self.i
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else:
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factor = self.magic
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if negative(h*e*z_inv): g=-g
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s = (h-g)*factor*g*t_inv
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else:
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foo = Y^2+a*X^2
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bar = X*Y
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den = 1/(foo*bar)
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if negative(2*bar^2*den): tmp = a*X^2
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else: tmp = Y^2
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s = self.magic*(Z^2-tmp)*foo*den
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return self.gfToBytes(s,mustBePositive=True)
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@classmethod
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@ -238,8 +281,9 @@ class RistrettoPoint(QuotientEdwardsPoint):
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@classmethod
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def elligatorSpec(cls,r0):
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a,d = cls.a,cls.d
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r = cls.qnr * cls.bytesToGf(r0)^2
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r = cls.qnr * cls.bytesToGf(r0,mustBeProper=False,maskHiBits=True)^2
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den = (d*r-a)*(a*r-d)
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if den == 0: return cls()
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n1 = cls.a*(r+1)*(a+d)*(d-a)/den
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n2 = r*n1
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if is_square(n1):
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|
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@ -253,7 +297,7 @@ class RistrettoPoint(QuotientEdwardsPoint):
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@optimized_version_of("elligatorSpec")
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def elligator(cls,r0):
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a,d = cls.a,cls.d
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r0 = cls.bytesToGf(r0)
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r0 = cls.bytesToGf(r0,mustBeProper=False,maskHiBits=True)
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r = cls.qnr * r0^2
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den = (d*r-a)*(a*r-d)
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num = cls.a*(r+1)*(a+d)*(d-a)
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|
@ -278,15 +322,11 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
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|
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if self.cofactor==8 and negative(x*y*self.isoMagic):
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x,y = self.torque()
|
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isr2 = isqrt(a*(y^2-1)) * sqrt(a*d-1)
|
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|
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sr = xsqrt(1-a*x^2)
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assert sr in [isr2*x*y,-isr2*x*y]
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altx = 1/isr2*self.isoMagic
|
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if negative(altx): s = (1+x*y*isr2)/(a*x)
|
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else: s = (1-x*y*isr2)/(a*x)
|
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altx = x*y*self.isoMagic / sr
|
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if negative(altx): s = (1+sr)/x
|
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else: s = (1-sr)/x
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|
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return self.gfToBytes(s,mustBePositive=True)
|
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|
||||
|
|
@ -297,52 +337,141 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
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s = cls.bytesToGf(s,mustBePositive=True)
|
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|
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if s==0: return cls()
|
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isr = isqrt(s^4 + 2*(a-2*d)*s^2 + 1)
|
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altx = 2*s*isr*cls.isoMagic
|
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if negative(altx): isr = -isr
|
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t = xsqrt(s^4 + 2*(a-2*d)*s^2 + 1)
|
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altx = 2*s*cls.isoMagic/t
|
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if negative(altx): t = -t
|
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x = 2*s / (1+a*s^2)
|
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y = (1-a*s^2) * isr
|
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y = (1-a*s^2) / t
|
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|
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if cls.cofactor==8 and (negative(x*y*cls.isoMagic) or y==0):
|
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raise InvalidEncodingException("x*y is invalid: %d, %d" % (x,y))
|
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|
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return cls(x,y)
|
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|
||||
@optimized_version_of("encodeSpec")
|
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def encode(self):
|
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"""Encode, optimized version"""
|
||||
def toJacobiQuartic(self,toggle_rotation=False,toggle_altx=False,toggle_s=False):
|
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"Return s,t on jacobi curve"
|
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a,d = self.a,self.d
|
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x,y,z,t = self.xyzt()
|
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|
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if self.cofactor == 8:
|
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# Cofactor 8 version
|
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# Simulate IMAGINE_TWIST because that's how libdecaf does it
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x = self.i*x
|
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t = self.i*t
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a = -a
|
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d = -d
|
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|
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# OK, the actual libdecaf code should be here
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num = (z+y)*(z-y)
|
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den = x*y
|
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tmp = isqrt(num*(a-d)*den^2)
|
||||
|
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if negative(tmp^2*den*num*(a-d)*t^2*self.isoMagic):
|
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den,num = num,den
|
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tmp *= sqrt(a-d) # witness that cofactor is 8
|
||||
yisr = x*sqrt(a)
|
||||
toggle = (a==1)
|
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else:
|
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yisr = y*(a*d-1)
|
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toggle = False
|
||||
isr = isqrt(num*(a-d)*den^2)
|
||||
|
||||
iden = isr * den * self.isoMagic # 1/sqrt((z+y)(z-y)) = 1/sqrt(1-Y^2) / z
|
||||
inum = isr * num # sqrt(1-Y^2) * z / xysqrt(a-d) ~ 1/sqrt(1-ax^2)/z
|
||||
|
||||
tiisr = tmp*num
|
||||
altx = tiisr*t*self.isoMagic
|
||||
if negative(altx) != toggle: tiisr =- tiisr
|
||||
s = tmp*den*yisr*(tiisr*z - 1)
|
||||
if negative(iden*inum*self.i*t^2*(d-a)) != toggle_rotation:
|
||||
iden,inum = inum,iden
|
||||
fac = x*sqrt(a)
|
||||
toggle=(a==-1)
|
||||
else:
|
||||
fac = y
|
||||
toggle=False
|
||||
|
||||
imi = self.isoMagic * self.i
|
||||
altx = inum*t*imi
|
||||
neg_altx = negative(altx) != toggle_altx
|
||||
if neg_altx != toggle: inum =- inum
|
||||
|
||||
tmp = fac*(inum*z + 1)
|
||||
s = iden*tmp*imi
|
||||
|
||||
negm1 = (negative(s) != toggle_s) != neg_altx
|
||||
if negm1: m1 = a*fac + z
|
||||
else: m1 = a*fac - z
|
||||
|
||||
swap = toggle_s
|
||||
|
||||
else:
|
||||
# Much simpler cofactor 4 version
|
||||
num = (x+t)*(x-t)
|
||||
isr = isqrt(num*(a-d)*x^2)
|
||||
ratio = isr*num
|
||||
if negative(ratio*self.isoMagic): ratio=-ratio
|
||||
s = (a-d)*isr*x*(ratio*z - t)
|
||||
ratio = isr*num
|
||||
altx = ratio*self.isoMagic
|
||||
|
||||
neg_altx = negative(altx) != toggle_altx
|
||||
if neg_altx: ratio =- ratio
|
||||
|
||||
tmp = ratio*z - t
|
||||
s = (a-d)*isr*x*tmp
|
||||
|
||||
negx = (negative(s) != toggle_s) != neg_altx
|
||||
if negx: m1 = -a*t + x
|
||||
else: m1 = -a*t - x
|
||||
|
||||
swap = toggle_s
|
||||
|
||||
if negative(s): s = -s
|
||||
|
||||
return self.gfToBytes(s,mustBePositive=True)
|
||||
return s,m1,a*tmp,swap
|
||||
|
||||
def invertElligator(self,toggle_r=False,*args,**kwargs):
|
||||
"Produce preimage of self under elligator, or None"
|
||||
a,d = self.a,self.d
|
||||
|
||||
rets = []
|
||||
|
||||
tr = [False,True] if self.cofactor == 8 else [False]
|
||||
for toggle_rotation in tr:
|
||||
for toggle_altx in [False,True]:
|
||||
for toggle_s in [False,True]:
|
||||
for toggle_r in [False,True]:
|
||||
s,m1,m12,swap = self.toJacobiQuartic(toggle_rotation,toggle_altx,toggle_s)
|
||||
|
||||
#print
|
||||
#print toggle_rotation,toggle_altx,toggle_s
|
||||
#print m1
|
||||
#print m12
|
||||
|
||||
|
||||
if self == self.__class__():
|
||||
if self.cofactor == 4:
|
||||
# Hacks for identity!
|
||||
if toggle_altx: m12 = 1
|
||||
elif toggle_s: m1 = 1
|
||||
elif toggle_r: continue
|
||||
## BOTH???
|
||||
|
||||
else:
|
||||
m12 = 1
|
||||
imi = self.isoMagic * self.i
|
||||
if toggle_rotation:
|
||||
if toggle_altx: m1 = -imi
|
||||
else: m1 = +imi
|
||||
else:
|
||||
if toggle_altx: m1 = 0
|
||||
else: m1 = a-d
|
||||
|
||||
rnum = (d*a*m12-m1)
|
||||
rden = ((d*a-1)*m12+m1)
|
||||
if swap: rnum,rden = rden,rnum
|
||||
|
||||
ok,sr = isqrt_i(rnum*rden*self.qnr)
|
||||
if not ok: continue
|
||||
sr *= rnum
|
||||
#print "Works! %d %x" % (swap,sr)
|
||||
|
||||
if negative(sr) != toggle_r: sr = -sr
|
||||
ret = self.gfToBytes(sr)
|
||||
if self.elligator(ret) != self and self.elligator(ret) != -self:
|
||||
print "WRONG!",[toggle_rotation,toggle_altx,toggle_s]
|
||||
if self.elligator(ret) == -self and self != -self: print "Negated!",[toggle_rotation,toggle_altx,toggle_s]
|
||||
rets.append(bytes(ret))
|
||||
return rets
|
||||
|
||||
@optimized_version_of("encodeSpec")
|
||||
def encode(self):
|
||||
"""Encode, optimized version"""
|
||||
return self.gfToBytes(self.toJacobiQuartic()[0])
|
||||
|
||||
@classmethod
|
||||
@optimized_version_of("decodeSpec")
|
||||
|
|
@ -351,7 +480,7 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
|
|||
a,d = cls.a,cls.d
|
||||
s = cls.bytesToGf(s,mustBePositive=True)
|
||||
|
||||
if s==0: return cls()
|
||||
#if s==0: return cls()
|
||||
s2 = s^2
|
||||
den = 1+a*s2
|
||||
num = den^2 - 4*d*s2
|
||||
|
|
@ -374,13 +503,63 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
|
|||
x = 2*s / (1+a*s^2)
|
||||
y = (1-a*s^2) / t
|
||||
return cls(x,sgn*y)
|
||||
|
||||
@optimized_version_of("doubleAndEncodeSpec")
|
||||
def doubleAndEncode(self):
|
||||
X,Y,Z,T = self.xyzt()
|
||||
a,d = self.a,self.d
|
||||
|
||||
if self.cofactor == 8:
|
||||
# Cofactor 8 version
|
||||
# Simulate IMAGINE_TWIST because that's how libdecaf does it
|
||||
X = self.i*X
|
||||
T = self.i*T
|
||||
a = -a
|
||||
d = -d
|
||||
# TODO: This is only being called for a=-1, so could
|
||||
# be wrong for a=1
|
||||
|
||||
e = 2*X*Y
|
||||
f = Y^2+a*X^2
|
||||
g = Y^2-a*X^2
|
||||
h = Z^2-d*T^2
|
||||
|
||||
eim = e*self.isoMagic
|
||||
inv = 1/(eim*g*f*h)
|
||||
fh_inv = eim*g*inv*self.i
|
||||
|
||||
if negative(eim*g*fh_inv):
|
||||
idf = g*self.isoMagic*self.i
|
||||
bar = f
|
||||
foo = g
|
||||
test = eim*f
|
||||
else:
|
||||
idf = eim
|
||||
bar = h
|
||||
foo = -eim
|
||||
test = g*h
|
||||
|
||||
if negative(test*fh_inv): bar =- bar
|
||||
s = idf*(foo+bar)*inv*f*h
|
||||
|
||||
else:
|
||||
xy = X*Y
|
||||
h = Z^2-d*T^2
|
||||
inv = 1/(xy*h)
|
||||
if negative(inv*2*xy^2*self.isoMagic): tmp = Y
|
||||
else: tmp = X
|
||||
s = tmp^2*h*inv # = X/Y or Y/X, interestingly
|
||||
|
||||
return self.gfToBytes(s,mustBePositive=True)
|
||||
|
||||
@classmethod
|
||||
def elligatorSpec(cls,r0):
|
||||
def elligatorSpec(cls,r0,fromR=False):
|
||||
a,d = cls.a,cls.d
|
||||
r = cls.qnr * cls.bytesToGf(r0)^2
|
||||
if fromR: r = r0
|
||||
else: r = cls.qnr * cls.bytesToGf(r0,mustBeProper=False,maskHiBits=True)^2
|
||||
|
||||
den = (d*r-(d-a))*((d-a)*r-d)
|
||||
if den == 0: return cls()
|
||||
n1 = (r+1)*(a-2*d)/den
|
||||
n2 = r*n1
|
||||
if is_square(n1):
|
||||
|
|
@ -394,7 +573,7 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
|
|||
@optimized_version_of("elligatorSpec")
|
||||
def elligator(cls,r0):
|
||||
a,d = cls.a,cls.d
|
||||
r0 = cls.bytesToGf(r0)
|
||||
r0 = cls.bytesToGf(r0,mustBeProper=False,maskHiBits=True)
|
||||
r = cls.qnr * r0^2
|
||||
den = (d*r-(d-a))*((d-a)*r-d)
|
||||
num = (r+1)*(a-2*d)
|
||||
|
|
@ -408,6 +587,40 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
|
|||
if negative(s) == iss: s = -s
|
||||
return cls.fromJacobiQuartic(s,t)
|
||||
|
||||
def elligatorInverseBruteForce(self):
|
||||
"""Invert Elligator using SAGE's polynomial solver"""
|
||||
a,d = self.a,self.d
|
||||
R.<r0> = self.F[]
|
||||
r = self.qnr * r0^2
|
||||
den = (d*r-(d-a))*((d-a)*r-d)
|
||||
n1 = (r+1)*(a-2*d)/den
|
||||
n2 = r*n1
|
||||
ret = set()
|
||||
for s2,t in [(n1, -(r-1)*(a-2*d)^2 / den - 1),
|
||||
(n2,r*(r-1)*(a-2*d)^2 / den - 1)]:
|
||||
x2 = 4*s2/(1+a*s2)^2
|
||||
y = (1-a*s2) / t
|
||||
|
||||
selfT = self
|
||||
for i in xrange(self.cofactor/2):
|
||||
xT,yT = selfT
|
||||
polyX = xT^2-x2
|
||||
polyY = yT-y
|
||||
sx = set(r for r,_ in polyX.numerator().roots())
|
||||
sy = set(r for r,_ in polyY.numerator().roots())
|
||||
ret = ret.union(sx.intersection(sy))
|
||||
|
||||
selfT = selfT.torque()
|
||||
|
||||
ret = [self.gfToBytes(r) for r in ret]
|
||||
|
||||
for r in ret:
|
||||
assert self.elligator(r) in [self,-self]
|
||||
|
||||
ret = [r for r in ret if self.elligator(r) == self]
|
||||
|
||||
return ret
|
||||
|
||||
class Ed25519Point(RistrettoPoint):
|
||||
F = GF(2^255-19)
|
||||
d = F(-121665/121666)
|
||||
|
|
@ -455,7 +668,7 @@ class IsoEd448Point(RistrettoPoint):
|
|||
@classmethod
|
||||
def base(cls):
|
||||
return cls( # RFC has it wrong
|
||||
-345397493039729516374008604150537410266655260075183290216406970281645695073672344430481787759340633221708391583424041788924124567700732,
|
||||
345397493039729516374008604150537410266655260075183290216406970281645695073672344430481787759340633221708391583424041788924124567700732,
|
||||
-363419362147803445274661903944002267176820680343659030140745099590306164083365386343198191849338272965044442230921818680526749009182718
|
||||
)
|
||||
|
||||
|
|
@ -464,7 +677,6 @@ class TwistedEd448GoldilocksPoint(Decaf_1_1_Point):
|
|||
d = F(-39082)
|
||||
a = F(-1)
|
||||
qnr = -1
|
||||
magic = isqrt(a*d-1)
|
||||
cofactor = 4
|
||||
encLen = 56
|
||||
isoMagic = IsoEd448Point.magic
|
||||
|
|
@ -478,14 +690,13 @@ class Ed448GoldilocksPoint(Decaf_1_1_Point):
|
|||
d = F(-39081)
|
||||
a = F(1)
|
||||
qnr = -1
|
||||
magic = isqrt(a*d-1)
|
||||
cofactor = 4
|
||||
encLen = 56
|
||||
isoMagic = IsoEd448Point.magic
|
||||
|
||||
@classmethod
|
||||
def base(cls):
|
||||
return -2*cls( # FIXME: make not negative
|
||||
return 2*cls(
|
||||
224580040295924300187604334099896036246789641632564134246125461686950415467406032909029192869357953282578032075146446173674602635247710, 298819210078481492676017930443930673437544040154080242095928241372331506189835876003536878655418784733982303233503462500531545062832660
|
||||
)
|
||||
|
||||
|
|
@ -532,19 +743,29 @@ def test(cls,n):
|
|||
|
||||
|
||||
P = cls.base()
|
||||
print "base", list(P.encode())
|
||||
for i in xrange(16):
|
||||
Q = P*i
|
||||
print i, list(Q.encode())
|
||||
|
||||
Q = cls()
|
||||
for i in xrange(n):
|
||||
#print i, binascii.hexlify(Q.encode())
|
||||
QQ = cls.decode(Q.encode())
|
||||
#print binascii.hexlify(Q.encode())
|
||||
QE = Q.encode()
|
||||
QQ = cls.decode(QE)
|
||||
if QQ != Q: raise TestFailedException("Round trip %s != %s" % (str(QQ),str(Q)))
|
||||
|
||||
# Testing s -> 1/s: encodes -point on cofactor
|
||||
s = cls.bytesToGf(QE)
|
||||
if s != 0:
|
||||
ss = cls.gfToBytes(1/s,mustBePositive=True)
|
||||
try:
|
||||
QN = cls.decode(ss)
|
||||
if cls.cofactor == 8:
|
||||
raise TestFailedException("1/s shouldnt work for cofactor 8")
|
||||
if QN != -Q:
|
||||
raise TestFailedException("s -> 1/s should negate point for cofactor 4")
|
||||
except InvalidEncodingException as e:
|
||||
# Should be raised iff cofactor==8
|
||||
if cls.cofactor == 4:
|
||||
raise TestFailedException("s -> 1/s should work for cofactor 4")
|
||||
|
||||
QT = Q
|
||||
QE = Q.encode()
|
||||
for h in xrange(cls.cofactor):
|
||||
QT = QT.torque()
|
||||
if QT.encode() != QE:
|
||||
|
|
@ -559,27 +780,26 @@ def test(cls,n):
|
|||
Q2 = Q0*(r+1)
|
||||
if Q1 + Q0 != Q2: raise TestFailedException("Scalarmul doesn't work")
|
||||
Q = Q1
|
||||
|
||||
test(Ed25519Point,100)
|
||||
#test(NegEd25519Point,100)
|
||||
#test(IsoEd25519Point,100)
|
||||
#test(IsoEd448Point,100)
|
||||
#test(TwistedEd448GoldilocksPoint,100)
|
||||
#test(Ed448GoldilocksPoint,100)
|
||||
|
||||
|
||||
def testElligator(cls,n):
|
||||
print "Testing elligator on %s" % cls.__name__
|
||||
for i in xrange(n):
|
||||
r = randombytes(cls.encLen)
|
||||
Q = cls.elligator(r)
|
||||
print list(r), list(Q.encode())
|
||||
|
||||
testElligator(Ed25519Point,100)
|
||||
#testElligator(NegEd25519Point,100)
|
||||
#testElligator(IsoEd448Point,100)
|
||||
#testElligator(Ed448GoldilocksPoint,100)
|
||||
#testElligator(TwistedEd448GoldilocksPoint,100)
|
||||
P = cls.elligator(r)
|
||||
if hasattr(P,"invertElligator"):
|
||||
iv = P.invertElligator()
|
||||
modr = bytes(cls.gfToBytes(cls.bytesToGf(r,mustBeProper=False,maskHiBits=True)))
|
||||
iv2 = P.torque().invertElligator()
|
||||
if modr not in iv: print "Failed to invert Elligator!"
|
||||
if len(iv) != len(set(iv)):
|
||||
print "Elligator inverses not unique!", len(set(iv)), len(iv)
|
||||
if iv != iv2:
|
||||
print "Elligator is untorqueable!"
|
||||
#print [binascii.hexlify(j) for j in iv]
|
||||
#print [binascii.hexlify(j) for j in iv2]
|
||||
#break
|
||||
else:
|
||||
pass # TODO
|
||||
|
||||
def gangtest(classes,n):
|
||||
print "Gang test",[cls.__name__ for cls in classes]
|
||||
|
|
@ -607,5 +827,31 @@ def gangtest(classes,n):
|
|||
for c,ret in zip(classes,rets):
|
||||
print c,binascii.hexlify(ret)
|
||||
print
|
||||
gangtest([IsoEd448Point,TwistedEd448GoldilocksPoint,Ed448GoldilocksPoint],100)
|
||||
gangtest([Ed25519Point,IsoEd25519Point],100)
|
||||
|
||||
def testDoubleAndEncode(cls,n):
|
||||
print "Testing doubleAndEncode on %s" % cls.__name__
|
||||
for i in xrange(n):
|
||||
r1 = randombytes(cls.encLen)
|
||||
r2 = randombytes(cls.encLen)
|
||||
u = cls.elligator(r1) + cls.elligator(r2)
|
||||
u.doubleAndEncode()
|
||||
|
||||
testDoubleAndEncode(Ed25519Point,100)
|
||||
testDoubleAndEncode(NegEd25519Point,100)
|
||||
testDoubleAndEncode(IsoEd25519Point,100)
|
||||
testDoubleAndEncode(IsoEd448Point,100)
|
||||
testDoubleAndEncode(TwistedEd448GoldilocksPoint,100)
|
||||
#test(Ed25519Point,100)
|
||||
#test(NegEd25519Point,100)
|
||||
#test(IsoEd25519Point,100)
|
||||
#test(IsoEd448Point,100)
|
||||
#test(TwistedEd448GoldilocksPoint,100)
|
||||
#test(Ed448GoldilocksPoint,100)
|
||||
#testElligator(Ed25519Point,100)
|
||||
#testElligator(NegEd25519Point,100)
|
||||
#testElligator(IsoEd25519Point,100)
|
||||
#testElligator(IsoEd448Point,100)
|
||||
#testElligator(Ed448GoldilocksPoint,100)
|
||||
#testElligator(TwistedEd448GoldilocksPoint,100)
|
||||
#gangtest([IsoEd448Point,TwistedEd448GoldilocksPoint,Ed448GoldilocksPoint],100)
|
||||
#gangtest([Ed25519Point,IsoEd25519Point],100)
|
||||
|
|
|
|||
Loading…
Reference in a new issue