Implement elligator2 tranform from point to representative, compatible

with agl/ed25519/extra25519 and the kleshni C implementation.

Author: jmwample

curve25519-dalek/Cargo.toml

@@ -27,13 +27,14 @@ rustdoc-args = [
     "--html-in-header", "docs/assets/rustdoc-include-katex-header.html",
     "--cfg", "docsrs",
 ]
-features = ["serde", "rand_core", "digest", "legacy_compatibility", "group-bits"]
+features = ["serde", "rand_core", "elligator2", "digest", "legacy_compatibility", "group-bits"]
 
 [dev-dependencies]
 sha2 = { version = "0.10", default-features = false }
 bincode = "1"
 criterion = { version = "0.5", features = ["html_reports"] }
 hex = "0.4.2"
+json = "0.12.4"
 rand = "0.8"
 rand_core = { version = "0.6", default-features = false, features = ["getrandom"] }
 
@@ -69,6 +70,8 @@ precomputed-tables = []
 legacy_compatibility = []
 group = ["dep:group", "rand_core"]
 group-bits = ["group", "ff/bits"]
+elligator2 = []
+digest = ["dep:digest", "elligator2"]
 
 [target.'cfg(all(not(curve25519_dalek_backend = "fiat"), not(curve25519_dalek_backend = "serial"), target_arch = "x86_64"))'.dependencies]
 curve25519-dalek-derive = { version = "0.1", path = "../curve25519-dalek-derive" }

curve25519-dalek/README.md

@@ -56,6 +56,7 @@ curve25519-dalek = ">= 4.0, < 4.2"
 | `serde`            |          | Enables `serde` serialization/deserialization for all the point and scalar types. |
 | `legacy_compatibility`|       | Enables `Scalar::from_bits`, which allows the user to build unreduced scalars whose arithmetic is broken. Do not use this unless you know what you're doing. |
 | `group`            |          | Enables external `group` and `ff` crate traits |
+| `elligator2`       |          | Enables elligator2 functionality for supported types. This allows curve points to be encoded to uniform random representatives, and 32 byte values to be mapped (back) to curve points. |
 
 To disable the default features when using `curve25519-dalek` as a dependency,
 add `default-features = false` to the dependency in your `Cargo.toml`. To

curve25519-dalek/src/backend/serial/u32/constants.rs

@@ -71,12 +71,14 @@ pub(crate) const SQRT_M1: FieldElement2625 = FieldElement2625::from_limbs([
 pub(crate) const APLUS2_OVER_FOUR: FieldElement2625 =
     FieldElement2625::from_limbs([121666, 0, 0, 0, 0, 0, 0, 0, 0, 0]);
 
+#[cfg(feature = "elligator2")]
 /// `MONTGOMERY_A` is equal to 486662, which is a constant of the curve equation
 /// for Curve25519 in its Montgomery form. (This is used internally within the
 /// Elligator map.)
 pub(crate) const MONTGOMERY_A: FieldElement2625 =
     FieldElement2625::from_limbs([486662, 0, 0, 0, 0, 0, 0, 0, 0, 0]);
 
+#[cfg(feature = "elligator2")]
 /// `MONTGOMERY_A_NEG` is equal to -486662. (This is used internally within the
 /// Elligator map.)
 pub(crate) const MONTGOMERY_A_NEG: FieldElement2625 = FieldElement2625::from_limbs([

curve25519-dalek/src/backend/serial/u32/field.rs

@@ -601,4 +601,24 @@ impl FieldElement2625 {
         }
         FieldElement2625::reduce(coeffs)
     }
+
+    /// Returns 1 if self is greater than the other and 0 otherwise
+    // implementation based on C libgmp -> mpn_sub_n
+    pub(crate) fn gt(&self, other: &Self) -> Choice {
+        let mut _ul = 0_u32;
+        let mut _vl = 0_u32;
+        let mut _rl = 0_u32;
+
+        let mut cy = 0_u32;
+        for i in 0..10 {
+            _ul = self.0[i];
+            _vl = other.0[i];
+
+            let (_sl, _cy1) = _ul.overflowing_sub(_vl);
+            let (_rl, _cy2) = _sl.overflowing_sub(cy);
+            cy = _cy1 as u64 | _cy2 as u64;
+        }
+
+        Choice::from((cy != 0_u32) as u8)
+    }
 }

curve25519-dalek/src/backend/serial/u64/constants.rs

@@ -98,11 +98,13 @@ pub(crate) const SQRT_M1: FieldElement51 = FieldElement51::from_limbs([
 pub(crate) const APLUS2_OVER_FOUR: FieldElement51 =
     FieldElement51::from_limbs([121666, 0, 0, 0, 0]);
 
+#[cfg(feature = "elligator2")]
 /// `MONTGOMERY_A` is equal to 486662, which is a constant of the curve equation
 /// for Curve25519 in its Montgomery form. (This is used internally within the
 /// Elligator map.)
 pub(crate) const MONTGOMERY_A: FieldElement51 = FieldElement51::from_limbs([486662, 0, 0, 0, 0]);
 
+#[cfg(feature = "elligator2")]
 /// `MONTGOMERY_A_NEG` is equal to -486662. (This is used internally within the
 /// Elligator map.)
 pub(crate) const MONTGOMERY_A_NEG: FieldElement51 = FieldElement51::from_limbs([

curve25519-dalek/src/backend/serial/u64/field.rs

@@ -572,4 +572,24 @@ impl FieldElement51 {
 
         square
     }
+
+    /// Returns 1 if self is greater than the other and 0 otherwise
+    // implementation based on C libgmp -> mpn_sub_n
+    pub(crate) fn gt(&self, other: &Self) -> Choice {
+        let mut _ul = 0_u64;
+        let mut _vl = 0_u64;
+        let mut _rl = 0_u64;
+
+        let mut cy = 0_u64;
+        for i in 0..5 {
+            _ul = self.0[i];
+            _vl = other.0[i];
+
+            let (_sl, _cy1) = _ul.overflowing_sub(_vl);
+            let (_rl, _cy2) = _sl.overflowing_sub(cy);
+            cy = _cy1 as u64 | _cy2 as u64;
+        }
+
+        Choice::from((cy != 0_u64) as u8)
+    }
 }

curve25519-dalek/src/edwards.rs

@@ -106,6 +106,9 @@ use cfg_if::cfg_if;
 
 #[cfg(feature = "digest")]
 use digest::{generic_array::typenum::U64, Digest};
+#[cfg(feature = "digest")]
+use crate::elligator2::map_to_point;
+
 
 #[cfg(feature = "group")]
 use {
@@ -595,9 +598,7 @@ impl EdwardsPoint {
 
         let sign_bit = (res[31] & 0x80) >> 7;
 
-        let fe = FieldElement::from_bytes(&res);
-
-        let M1 = crate::montgomery::elligator_encode(&fe);
+        let M1 = map_to_point(&res);
         let E1_opt = M1.to_edwards(sign_bit);
 
         E1_opt