Curve instantiation on base field

src/fields/fp.rs

@@ -181,7 +181,12 @@ impl<'a, P: PrimeFieldParams> From<&'a str> for Fp<P> {
 }
 
 impl<P: PrimeFieldParams> Clone for Fp<P> {
-    fn clone(&self) -> Self { unimplemented!() }
+    fn clone(&self) -> Self {
+        Fp {
+            value: self.value.clone(),
+            _marker: PhantomData
+        }
+    }
 }
 
 forward_ops_to_field_ops!(impl(P: PrimeFieldParams) Fp<P>);

src/fields/mod.rs

@@ -1,3 +1,6 @@
+#[macro_use]
+mod macros;
+
 pub mod fp;
 
 #[cfg(test)]
@@ -5,8 +8,9 @@ pub mod tests;
 
 use rand::Rng;
 use self::fp::{Fp, PrimeFieldParams};
+use std::fmt::Debug;
 
-pub trait Field: Sized + Clone {
+pub trait Field: Sized + Clone + Debug {
 	fn zero() -> Self;
 	fn one() -> Self;
     fn random<R: Rng>(rng: &mut R) -> Self;

src/groups/macros.rs

@@ -0,0 +1,107 @@
+macro_rules! forward_val_val_binop {
+    (impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
+        impl<$($t: $p),*> $imp<$rhs> for $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: $rhs) -> $res {
+                $imp::$method(&self, &other)
+            }
+        }
+    }
+}
+
+macro_rules! forward_ref_val_binop {
+    (impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
+        impl<'a, $($t: $p),*> $imp<$rhs> for &'a $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: $rhs) -> $res {
+                $imp::$method(self, &other)
+            }
+        }
+    }
+}
+
+macro_rules! forward_val_ref_binop {
+    (impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
+        impl<'a, $($t: $p),*> $imp<&'a $rhs> for $res {
+            type Output = $res;
+
+            #[inline]
+            fn $method(self, other: &$rhs) -> $res {
+                $imp::$method(&self, other)
+            }
+        }
+    }
+}
+
+macro_rules! forward_all_binop_to_ref_ref {
+    (impl($($t:ident: $p:ident),*) $imp:ident for $res:ty, $method:ident, $rhs:ty) => {
+        forward_val_val_binop!(impl($($t: $p),*) $imp for $res, $method, $rhs);
+        forward_ref_val_binop!(impl($($t: $p),*) $imp for $res, $method, $rhs);
+        forward_val_ref_binop!(impl($($t: $p),*) $imp for $res, $method, $rhs);
+    };
+}
+
+macro_rules! forward_ops_to_group_ops {
+    (impl($($t:ident: $p:ident),*) $res:ty) => {
+        impl<'a, 'b, $($t: $p),*> Add<&'a $res> for &'b $res {
+            type Output = $res;
+
+            #[inline]
+            fn add(self, other: &'a $res) -> $res {
+                Jacobian::add(self, other)
+            }
+        }
+
+        impl<'a, 'b, $($t: $p),*> Mul<&'a Fr> for &'b $res {
+            type Output = $res;
+
+            #[inline]
+            fn mul(self, other: &'a Fr) -> $res {
+                Jacobian::mul(self, other)
+            }
+        }
+
+        impl<'a, 'b, $($t: $p),*> Sub<&'a $res> for &'b $res {
+            type Output = $res;
+
+            #[inline]
+            fn sub(self, other: &'a $res) -> $res {
+                Jacobian::sub(self, other)
+            }
+        }
+
+        impl<'a, $($t: $p),*> Neg for &'a $res {
+            type Output = $res;
+
+            #[inline]
+            fn neg(self) -> $res {
+                Jacobian::neg(self)
+            }
+        }
+
+        impl<$($t: $p),*> Neg for $res {
+            type Output = $res;
+
+            #[inline]
+            fn neg(self) -> $res {
+                Jacobian::neg(&self)
+            }
+        }
+
+        impl<$($t: $p),*> PartialEq for $res {
+            fn eq(&self, other: &Self) -> bool {
+                Jacobian::eq(self, other)
+            }
+        }
+
+        impl<$($t: $p),*> Eq for $res {}
+
+        forward_all_binop_to_ref_ref!(impl($($t: $p),*) Add for $res, add, $res);
+        forward_all_binop_to_ref_ref!(impl($($t: $p),*) Sub for $res, sub, $res);
+        forward_all_binop_to_ref_ref!(impl($($t: $p),*) Mul for $res, mul, Fr);
+    }
+}

src/groups/mod.rs

@@ -0,0 +1,255 @@
+use fields::Field;
+use fields::fp::{PrimeFieldParams, Fp};
+use super::Fr;
+use rand::Rng;
+use std::ops::{Add,Mul,Sub,Neg};
+use std::fmt;
+
+#[cfg(test)]
+pub mod tests;
+
+#[macro_use]
+mod macros;
+
+pub trait GroupParams: Sized {
+    type Base: Field;
+
+    fn zero() -> Jacobian<Self>;
+    fn one() -> Jacobian<Self>;
+    fn coeff_b() -> Self::Base;
+    fn name() -> &'static str;
+}
+
+pub struct Jacobian<P: GroupParams> {
+    x: P::Base,
+    y: P::Base,
+    z: P::Base
+}
+
+impl<P: GroupParams> fmt::Debug for Jacobian<P> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{}({:?}, {:?}, {:?})", P::name(), self.x, self.y, self.z)
+    }
+}
+
+impl<P: GroupParams> Clone for Jacobian<P> {
+    fn clone(&self) -> Self {
+        Jacobian {
+            x: self.x.clone(),
+            y: self.y.clone(),
+            z: self.z.clone()
+        }
+    }
+}
+pub enum Affine<P: GroupParams> {
+    Zero,
+    Point{x: P::Base, y: P::Base}
+}
+
+impl<P: GroupParams> Clone for Affine<P> {
+    fn clone(&self) -> Self {
+        match *self {
+            Affine::Zero => Affine::Zero,
+            Affine::Point{ref x, ref y} => Affine::Point{x: x.clone(), y: y.clone()}
+        }
+    }
+}
+
+impl<P: GroupParams> Affine<P> {
+/*
+    fn to_jacobian(self) -> Jacobian<P> {
+        match self {
+            Affine::Zero => P::zero(),
+            Affine::Point{x, y} => Jacobian {
+                x: x,
+                y: y,
+                z: P::Base::one()
+            }
+        }
+    }
+*/
+}
+
+impl<P: GroupParams> Jacobian<P> {
+    pub fn new(x: P::Base, y: P::Base, z: P::Base) -> Option<Self> {
+        let tmp = Jacobian {
+            x: x,
+            y: y,
+            z: z
+        };
+
+        if tmp.is_well_formed() {
+            Some(tmp)
+        } else {
+            None
+        }
+    }
+
+    pub fn random<R: Rng>(rng: &mut R) -> Self {
+        Self::one() * &Fr::random(rng)
+    }
+
+    pub fn is_well_formed(&self) -> bool {
+        if self.is_zero() {
+            true
+        } else {
+            let x2 = self.x.squared();
+            let y2 = self.y.squared();
+            let z2 = self.z.squared();
+
+            let x3 = self.x.mul(&x2);
+            let z3 = self.z.mul(&z2);
+            let z6 = z3.squared();
+
+            (y2.eq(&z6.mul(&P::coeff_b()).add(&x3)))
+        }
+    }
+
+    pub fn to_affine(&self) -> Affine<P> {
+        if self.is_zero() {
+            Affine::Zero
+        } else {
+            let z_inv = self.z.inverse();
+            let z2_inv = z_inv.squared();
+            let z3_inv = z2_inv.mul(&z_inv);
+
+            Affine::Point {
+                x: self.x.mul(&z2_inv),
+                y: self.y.mul(&z3_inv)
+            }
+        }
+    }
+
+    pub fn zero() -> Self {
+        P::zero()
+    }
+
+    pub fn one() -> Self {
+        P::one()
+    }
+
+    pub fn add(&self, other: &Self) -> Self {
+        if self.is_zero() {
+            return other.clone()
+        }
+
+        if other.is_zero() {
+            return self.clone()
+        }
+
+        let z1_squared = self.z.squared();
+        let z2_squared = other.z.squared();
+        let u1 = self.x.mul(&z2_squared);
+        let u2 = other.x.mul(&z1_squared);
+        let z1_cubed = self.z.mul(&z1_squared);
+        let z2_cubed = other.z.mul(&z2_squared);
+        let s1 = self.y.mul(&z2_cubed);
+        let s2 = other.y.mul(&z1_cubed);
+
+        if u1.eq(&u2) && s1.eq(&s2) {
+            self.double()
+        } else {
+            let h = u2.sub(&u1);
+            let s2_minus_s1 = s2.sub(&s1);
+            let i = h.add(&h).squared();
+            let j = h.mul(&i);
+            let r = s2_minus_s1.add(&s2_minus_s1);
+            let v = u1.mul(&i);
+            let s1_j = s1.mul(&j);
+            let x3 = r.squared().sub(&j).sub(&v.add(&v));
+            let y3 = r.mul(&v.sub(&x3)).sub(&s1_j.add(&s1_j));
+
+            Jacobian {
+                x: x3,
+                y: y3,
+                z: self.z.add(&other.z).squared().sub(&z1_squared).sub(&z2_squared).mul(&h)
+            }
+        }
+    }
+
+    pub fn double(&self) -> Self {
+        let a = self.x.squared();
+        let b = self.y.squared();
+        let c = b.squared();
+        let mut d = self.x.add(&b).squared().sub(&a).sub(&c);
+        d = d.add(&d);
+        let e = a.add(&a).add(&a);
+        let f = e.squared();
+        let x3 = f.sub(&d.add(&d));
+        let mut eight_c = c.add(&c);
+        eight_c = eight_c.add(&eight_c);
+        eight_c = eight_c.add(&eight_c);
+        let y3 = e.mul(&d.sub(&x3)).sub(&eight_c);
+        let y1z1 = self.y.mul(&self.z);
+        let z3 = y1z1.add(&y1z1);
+
+        Jacobian {
+            x: x3,
+            y: y3,
+            z: z3
+        }
+    }
+
+    pub fn eq(&self, other: &Self) -> bool {
+        if self.is_zero() {
+            return other.is_zero()
+        }
+
+        if other.is_zero() {
+            return false;
+        }
+
+        let z1_squared = self.z.squared();
+        let z2_squared = other.z.squared();
+
+        if self.x.mul(&z2_squared).ne(&other.x.mul(&z1_squared)) {
+            return false;
+        }
+
+        let z1_cubed = self.z.mul(&z1_squared);
+        let z2_cubed = other.z.mul(&z2_squared);
+
+        if self.y.mul(&z2_cubed).ne(&other.y.mul(&z1_cubed)) {
+            return false;
+        }
+
+        return true;
+    }
+
+    pub fn neg(&self) -> Self {
+        Jacobian {
+            x: self.x.clone(),
+            y: self.y.neg(),
+            z: self.z.clone()
+        }
+    }
+
+    #[inline]
+    pub fn is_zero(&self) -> bool {
+        self.z.is_zero()
+    }
+
+    pub fn mul<S: PrimeFieldParams>(&self, other: &Fp<S>) -> Jacobian<P> {
+        let mut result = Jacobian::<P>::zero();
+        let mut found_one = false;
+        for i in (0..S::bits()).rev() {
+            if found_one {
+                result = result.double();
+            }
+
+            if other.test_bit(i) {
+                found_one = true;
+                result = &result + self;
+            }
+        }
+
+        result
+    }
+
+    #[inline]
+    pub fn sub(&self, other: &Self) -> Jacobian<P> {
+        self.add(&other.neg())
+    }
+}
+
+forward_ops_to_group_ops!(impl(P: GroupParams) Jacobian<P>);

src/groups/tests.rs

@@ -0,0 +1,76 @@
+use super::*;
+use ::Fr;
+use fields::Field;
+
+use rand::Rng;
+
+pub fn group_trials<P: GroupParams>() {
+    fn test_doubling<P: GroupParams>() {
+        type G<P> = Jacobian<P>;
+
+        let one = G::<P>::one();
+        let two = one.add(&one);
+        let three = two.add(&one);
+        let four = three.add(&one);
+
+        assert_eq!(one.double(), two);
+        assert_eq!(two.double(), four);
+    }
+
+    fn random_test_addition<P: GroupParams, R: Rng>(rng: &mut R) {
+        type G<P> = Jacobian<P>;
+
+        for _ in 0..50 {
+            let r1 = &G::<P>::random(rng);
+            let r2 = &G::<P>::random(rng);
+            let r3 = &G::<P>::random(rng);
+
+            let s1 = (r1 + r2) + r3;
+            let s2 = (r2 + r3) + r1;
+
+            assert_eq!(s1, s2);
+        }
+    }
+    
+    fn random_test_doubling<P: GroupParams, R: Rng>(rng: &mut R) {
+        type G<P> = Jacobian<P>;
+
+        for _ in 0..50 {
+            let r1 = &G::<P>::random(rng);
+            let r2 = &G::<P>::random(rng);
+
+            let a = (r1 + r2) + r1;
+            let b = r1.double() + r2;
+
+            assert!(a.eq(&b));
+        }
+    }
+
+    fn random_test_dh<P: GroupParams, R: Rng>(rng: &mut R) {
+        type G<P> = Jacobian<P>;
+
+        for _ in 0..50 {
+            let alice_sk = Fr::random(rng);
+            let bob_sk = Fr::random(rng);
+
+            let alice_pk = G::<P>::one() * &alice_sk;
+            let bob_pk = G::<P>::one() * &bob_sk;
+
+            let alice_shared = &bob_pk * &alice_sk;
+            let bob_shared = &alice_pk * &bob_sk;
+
+            assert_eq!(alice_shared, bob_shared);
+        }
+    }
+
+    test_doubling::<P>();
+
+    use rand::{SeedableRng,StdRng};
+    let seed: [usize; 4] = [103245, 191922, 1293, 192103];
+    let mut rng = StdRng::from_seed(&seed);
+
+    random_test_addition::<P, _>(&mut rng);
+    random_test_doubling::<P, _>(&mut rng);
+    random_test_dh::<P, _>(&mut rng);
+}
+

src/lib.rs

@@ -1,7 +1,18 @@
 extern crate num;
 extern crate rand;
 
-#[macro_use]
-mod macros;
 mod fields;
 mod params;
+
+mod groups;
+
+pub use fields::fp::Fp;
+pub use params::{FrParams,FqParams,G1Params};
+pub use fields::Field;
+pub use groups::Jacobian;
+
+pub type Fr = Fp<FrParams>;
+pub type Fq = Fp<FqParams>;
+
+pub type Scalar = Fr;
+pub type G1 = Jacobian<G1Params>;

src/params.rs

@@ -1,5 +1,8 @@
 use num::{Num,BigUint};
+use fields::Field;
 use fields::fp::PrimeFieldParams;
+use super::{Fr,Fq,G1};
+use groups::*;
 
 pub struct FrParams;
 
@@ -25,12 +28,53 @@ impl PrimeFieldParams for FqParams {
 fn test_fr() {
     use fields;
 
-    fields::tests::field_trials::<fields::fp::Fp<FrParams>>();
+    fields::tests::field_trials::<super::Fr>();
 }
 
 #[test]
 fn test_fq() {
     use fields;
 
-    fields::tests::field_trials::<fields::fp::Fp<FqParams>>();
+    fields::tests::field_trials::<super::Fq>();
+}
+
+pub struct G1Params;
+
+impl GroupParams for G1Params {
+    type Base = super::Fq;
+
+    fn name() -> &'static str {
+        "G1"
+    }
+    fn zero() -> Jacobian<Self> {
+        Jacobian::new(Fq::zero(), Fq::one(), Fq::zero()).unwrap()
+    }
+    fn one() -> Jacobian<Self> {
+        Jacobian::new(Fq::from("1"), Fq::from("2"), Fq::one()).unwrap()
+    }
+    fn coeff_b() -> Self::Base {
+        Fq::from("3")
+    }
+}
+
+#[test]
+fn test_g1() {
+    use groups;
+
+    groups::tests::group_trials::<G1Params>();
+}
+
+#[test]
+fn g1_test_vector() {
+    let a = G1::one() * &Fr::from("19797905000333868150253315089095386158892526856493194078073564469188852136946");
+    let b = G1::one() * &Fr::from("2730506433347642574983433139433778984782882168213690554721050571242082865799");
+    let e = &a + &b;
+
+    let expect = G1::new(
+        Fq::from("18450621724990678172567114131642278789161361170999664461184794604011563728206"),
+        Fq::from("21329688341674583036384007811166435666174342925504675855816423131698588368496"),
+        Fq::one()
+    ).unwrap();
+
+    assert!(expect.eq(&e));
 }