mirror of
https://github.com/Qortal/pirate-librustzcash.git
synced 2025-08-01 12:51:30 +00:00
941 lines
30 KiB
Rust
941 lines
30 KiB
Rust
use pairing::{
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Engine,
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Field,
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PrimeField
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};
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use bellman::{
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SynthesisError,
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ConstraintSystem,
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LinearCombination
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};
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use super::{
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Assignment
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};
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use super::num::AllocatedNum;
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use super::boolean::{
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Boolean
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};
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use super::blake2s::blake2s;
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use ::jubjub::{
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JubjubEngine,
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JubjubParams,
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montgomery
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};
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pub struct EdwardsPoint<E: Engine, Var> {
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pub x: AllocatedNum<E, Var>,
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pub y: AllocatedNum<E, Var>
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}
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impl<E: JubjubEngine, Var: Copy> EdwardsPoint<E, Var> {
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/// This extracts the x-coordinate, which is an injective
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/// encoding for elements of the prime order subgroup.
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pub fn into_num(&self) -> AllocatedNum<E, Var> {
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self.x.clone()
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}
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/// Perform addition between any two points
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pub fn add<CS>(
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&self,
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mut cs: CS,
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other: &Self,
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params: &E::Params
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) -> Result<Self, SynthesisError>
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where CS: ConstraintSystem<E, Variable=Var>
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{
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// Compute U = (x1 + y1) * (x2 + y2)
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let u = AllocatedNum::alloc(cs.namespace(|| "U"), || {
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let mut t0 = *self.x.get_value().get()?;
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t0.add_assign(self.y.get_value().get()?);
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let mut t1 = *other.x.get_value().get()?;
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t1.add_assign(other.y.get_value().get()?);
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t0.mul_assign(&t1);
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Ok(t0)
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})?;
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cs.enforce(
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|| "U computation",
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LinearCombination::<Var, E>::zero() + self.x.get_variable()
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+ self.y.get_variable(),
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LinearCombination::<Var, E>::zero() + other.x.get_variable()
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+ other.y.get_variable(),
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LinearCombination::<Var, E>::zero() + u.get_variable()
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);
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// Compute A = y2 * x1
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let a = other.y.mul(cs.namespace(|| "A computation"), &self.x)?;
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// Compute B = x2 * y1
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let b = other.x.mul(cs.namespace(|| "B computation"), &self.y)?;
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// Compute C = d*A*B
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let c = AllocatedNum::alloc(cs.namespace(|| "C"), || {
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let mut t0 = *a.get_value().get()?;
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t0.mul_assign(b.get_value().get()?);
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t0.mul_assign(params.edwards_d());
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Ok(t0)
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})?;
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cs.enforce(
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|| "C computation",
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LinearCombination::<Var, E>::zero() + (*params.edwards_d(), a.get_variable()),
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LinearCombination::<Var, E>::zero() + b.get_variable(),
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LinearCombination::<Var, E>::zero() + c.get_variable()
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);
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// Compute x3 = (A + B) / (1 + C)
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let x3 = AllocatedNum::alloc(cs.namespace(|| "x3"), || {
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let mut t0 = *a.get_value().get()?;
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t0.add_assign(b.get_value().get()?);
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let mut t1 = E::Fr::one();
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t1.add_assign(c.get_value().get()?);
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match t1.inverse() {
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Some(t1) => {
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t0.mul_assign(&t1);
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Ok(t0)
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},
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None => {
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Err(SynthesisError::AssignmentMissing)
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}
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}
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})?;
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let one = cs.one();
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cs.enforce(
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|| "x3 computation",
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LinearCombination::<Var, E>::zero() + one + c.get_variable(),
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LinearCombination::<Var, E>::zero() + x3.get_variable(),
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LinearCombination::<Var, E>::zero() + a.get_variable()
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+ b.get_variable()
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);
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// Compute y3 = (U - A - B) / (1 - C)
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let y3 = AllocatedNum::alloc(cs.namespace(|| "y3"), || {
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let mut t0 = *u.get_value().get()?;
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t0.sub_assign(a.get_value().get()?);
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t0.sub_assign(b.get_value().get()?);
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let mut t1 = E::Fr::one();
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t1.sub_assign(c.get_value().get()?);
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match t1.inverse() {
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Some(t1) => {
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t0.mul_assign(&t1);
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Ok(t0)
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},
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None => {
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Err(SynthesisError::AssignmentMissing)
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}
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}
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})?;
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cs.enforce(
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|| "y3 computation",
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LinearCombination::<Var, E>::zero() + one - c.get_variable(),
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LinearCombination::<Var, E>::zero() + y3.get_variable(),
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LinearCombination::<Var, E>::zero() + u.get_variable()
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- a.get_variable()
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- b.get_variable()
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);
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Ok(EdwardsPoint {
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x: x3,
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y: y3
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})
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}
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}
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pub struct MontgomeryPoint<E: Engine, Var> {
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x: AllocatedNum<E, Var>,
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y: AllocatedNum<E, Var>
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}
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impl<E: JubjubEngine, Var: Copy> MontgomeryPoint<E, Var> {
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/// Converts an element in the prime order subgroup into
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/// a point in the birationally equivalent twisted
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/// Edwards curve.
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pub fn into_edwards<CS>(
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&self,
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mut cs: CS,
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params: &E::Params
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) -> Result<EdwardsPoint<E, Var>, SynthesisError>
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where CS: ConstraintSystem<E, Variable=Var>
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{
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// Compute u = (scale*x) / y
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let u = AllocatedNum::alloc(cs.namespace(|| "u"), || {
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let mut t0 = *self.x.get_value().get()?;
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t0.mul_assign(params.scale());
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match self.y.get_value().get()?.inverse() {
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Some(invy) => {
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t0.mul_assign(&invy);
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Ok(t0)
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},
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None => {
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Err(SynthesisError::AssignmentMissing)
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}
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}
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})?;
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cs.enforce(
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|| "u computation",
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LinearCombination::<Var, E>::zero() + self.y.get_variable(),
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LinearCombination::<Var, E>::zero() + u.get_variable(),
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LinearCombination::<Var, E>::zero() + (*params.scale(), self.x.get_variable())
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);
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// Compute v = (x - 1) / (x + 1)
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let v = AllocatedNum::alloc(cs.namespace(|| "v"), || {
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let mut t0 = *self.x.get_value().get()?;
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let mut t1 = t0;
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t0.sub_assign(&E::Fr::one());
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t1.add_assign(&E::Fr::one());
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match t1.inverse() {
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Some(t1) => {
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t0.mul_assign(&t1);
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Ok(t0)
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},
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None => {
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Err(SynthesisError::AssignmentMissing)
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}
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}
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})?;
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let one = cs.one();
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cs.enforce(
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|| "v computation",
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LinearCombination::<Var, E>::zero() + self.x.get_variable()
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+ one,
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LinearCombination::<Var, E>::zero() + v.get_variable(),
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LinearCombination::<Var, E>::zero() + self.x.get_variable()
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- one,
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);
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Ok(EdwardsPoint {
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x: u,
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y: v
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})
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}
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pub fn group_hash<CS>(
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mut cs: CS,
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tag: &[Boolean<Var>],
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params: &E::Params
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) -> Result<Self, SynthesisError>
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where CS: ConstraintSystem<E, Variable=Var>
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{
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// This code is specialized for a field of this size
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assert_eq!(E::Fr::NUM_BITS, 255);
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assert!(tag.len() % 8 == 0);
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// Perform BLAKE2s hash
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let h = blake2s(cs.namespace(|| "blake2s"), tag)?;
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// Read the x-coordinate
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let x = AllocatedNum::from_bits_strict(
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cs.namespace(|| "read x coordinate"),
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&h[1..]
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)?;
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// Allocate the y-coordinate given the first bit
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// of the hash as its parity ("sign bit").
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let y = AllocatedNum::alloc(
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cs.namespace(|| "y-coordinate"),
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|| {
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let s: bool = *h[0].get_value().get()?;
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let x: E::Fr = *x.get_value().get()?;
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let p = montgomery::Point::<E, _>::get_for_x(x, s, params);
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let p = p.get()?;
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let (_, y) = p.into_xy().expect("can't be the point at infinity");
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Ok(y)
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}
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)?;
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// Unpack the y-coordinate
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let ybits = y.into_bits_strict(cs.namespace(|| "y-coordinate unpacking"))?;
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// Enforce that the y-coordinate has the right sign
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Boolean::enforce_equal(
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cs.namespace(|| "correct sign constraint"),
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&h[0],
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&ybits[E::Fr::NUM_BITS as usize - 1]
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)?;
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// interpret the result as a point on the curve
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let mut p = Self::interpret(
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cs.namespace(|| "point interpretation"),
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&x,
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&y,
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params
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)?;
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// Perform three doublings to move the point into the prime
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// order subgroup.
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for i in 0..3 {
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// Assert the y-coordinate is nonzero (the doubling
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// doesn't work for y=0).
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p.y.assert_nonzero(
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cs.namespace(|| format!("nonzero y-coordinate {}", i))
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)?;
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p = p.double(
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cs.namespace(|| format!("doubling {}", i)),
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params
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)?;
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}
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Ok(p)
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}
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/// Interprets an (x, y) pair as a point
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/// in Montgomery, does not check that it's
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/// on the curve. Useful for constants and
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/// window table lookups.
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pub fn interpret_unchecked(
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x: AllocatedNum<E, Var>,
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y: AllocatedNum<E, Var>
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) -> Self
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{
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MontgomeryPoint {
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x: x,
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y: y
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}
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}
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pub fn interpret<CS>(
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mut cs: CS,
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x: &AllocatedNum<E, Var>,
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y: &AllocatedNum<E, Var>,
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params: &E::Params
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) -> Result<Self, SynthesisError>
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where CS: ConstraintSystem<E, Variable=Var>
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{
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// y^2 = x^3 + A.x^2 + x
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let x2 = x.square(cs.namespace(|| "x^2"))?;
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let x3 = x2.mul(cs.namespace(|| "x^3"), x)?;
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cs.enforce(
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|| "on curve check",
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LinearCombination::zero() + y.get_variable(),
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LinearCombination::zero() + y.get_variable(),
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LinearCombination::zero() + x3.get_variable()
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+ (*params.montgomery_a(), x2.get_variable())
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+ x.get_variable()
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);
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Ok(MontgomeryPoint {
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x: x.clone(),
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y: y.clone()
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})
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}
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/// Performs an affine point addition, not defined for
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/// coincident points.
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pub fn add<CS>(
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&self,
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mut cs: CS,
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other: &Self,
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params: &E::Params
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) -> Result<Self, SynthesisError>
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where CS: ConstraintSystem<E, Variable=Var>
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{
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// Compute lambda = (y' - y) / (x' - x)
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let lambda = AllocatedNum::alloc(cs.namespace(|| "lambda"), || {
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let mut n = *other.y.get_value().get()?;
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n.sub_assign(self.y.get_value().get()?);
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let mut d = *other.x.get_value().get()?;
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d.sub_assign(self.x.get_value().get()?);
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match d.inverse() {
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Some(d) => {
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n.mul_assign(&d);
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Ok(n)
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},
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None => {
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Err(SynthesisError::AssignmentMissing)
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}
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}
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})?;
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cs.enforce(
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|| "evaluate lambda",
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LinearCombination::<Var, E>::zero() + other.x.get_variable()
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- self.x.get_variable(),
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LinearCombination::zero() + lambda.get_variable(),
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LinearCombination::<Var, E>::zero() + other.y.get_variable()
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- self.y.get_variable()
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);
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// Compute x'' = lambda^2 - A - x - x'
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let xprime = AllocatedNum::alloc(cs.namespace(|| "xprime"), || {
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let mut t0 = *lambda.get_value().get()?;
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t0.square();
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t0.sub_assign(params.montgomery_a());
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t0.sub_assign(self.x.get_value().get()?);
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t0.sub_assign(other.x.get_value().get()?);
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Ok(t0)
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})?;
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// (lambda) * (lambda) = (A + x + x' + x'')
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let one = cs.one();
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cs.enforce(
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|| "evaluate xprime",
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LinearCombination::zero() + lambda.get_variable(),
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LinearCombination::zero() + lambda.get_variable(),
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LinearCombination::<Var, E>::zero() + (*params.montgomery_a(), one)
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+ self.x.get_variable()
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+ other.x.get_variable()
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+ xprime.get_variable()
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);
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// Compute y' = -(y + lambda(x' - x))
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let yprime = AllocatedNum::alloc(cs.namespace(|| "yprime"), || {
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let mut t0 = *xprime.get_value().get()?;
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t0.sub_assign(self.x.get_value().get()?);
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t0.mul_assign(lambda.get_value().get()?);
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t0.add_assign(self.y.get_value().get()?);
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t0.negate();
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Ok(t0)
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})?;
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// y' + y = lambda(x - x')
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cs.enforce(
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|| "evaluate yprime",
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LinearCombination::zero() + self.x.get_variable()
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- xprime.get_variable(),
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LinearCombination::zero() + lambda.get_variable(),
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LinearCombination::<Var, E>::zero() + yprime.get_variable()
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+ self.y.get_variable()
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);
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Ok(MontgomeryPoint {
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x: xprime,
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y: yprime
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})
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}
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|
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/// Performs an affine point doubling, not defined for
|
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/// the point of order two (0, 0).
|
|
pub fn double<CS>(
|
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&self,
|
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mut cs: CS,
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params: &E::Params
|
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) -> Result<Self, SynthesisError>
|
|
where CS: ConstraintSystem<E, Variable=Var>
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{
|
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// Square x
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let xx = self.x.square(&mut cs)?;
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|
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// Compute lambda = (3.xx + 2.A.x + 1) / 2.y
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let lambda = AllocatedNum::alloc(cs.namespace(|| "lambda"), || {
|
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let mut t0 = *xx.get_value().get()?;
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let mut t1 = t0;
|
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t0.double(); // t0 = 2.xx
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t0.add_assign(&t1); // t0 = 3.xx
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t1 = *self.x.get_value().get()?; // t1 = x
|
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t1.mul_assign(params.montgomery_2a()); // t1 = 2.A.x
|
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t0.add_assign(&t1);
|
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t0.add_assign(&E::Fr::one());
|
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t1 = *self.y.get_value().get()?; // t1 = y
|
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t1.double(); // t1 = 2.y
|
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match t1.inverse() {
|
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Some(t1) => {
|
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t0.mul_assign(&t1);
|
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|
|
Ok(t0)
|
|
},
|
|
None => {
|
|
Err(SynthesisError::AssignmentMissing)
|
|
}
|
|
}
|
|
})?;
|
|
|
|
// (2.y) * (lambda) = (3.xx + 2.A.x + 1)
|
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let one = cs.one();
|
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cs.enforce(
|
|
|| "evaluate lambda",
|
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LinearCombination::<Var, E>::zero() + self.y.get_variable()
|
|
+ self.y.get_variable(),
|
|
|
|
LinearCombination::zero() + lambda.get_variable(),
|
|
|
|
LinearCombination::<Var, E>::zero() + xx.get_variable()
|
|
+ xx.get_variable()
|
|
+ xx.get_variable()
|
|
+ (*params.montgomery_2a(), self.x.get_variable())
|
|
+ one
|
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);
|
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|
|
// Compute x' = (lambda^2) - A - 2.x
|
|
let xprime = AllocatedNum::alloc(cs.namespace(|| "xprime"), || {
|
|
let mut t0 = *lambda.get_value().get()?;
|
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t0.square();
|
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t0.sub_assign(params.montgomery_a());
|
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t0.sub_assign(self.x.get_value().get()?);
|
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t0.sub_assign(self.x.get_value().get()?);
|
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|
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Ok(t0)
|
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})?;
|
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|
|
// (lambda) * (lambda) = (A + 2.x + x')
|
|
cs.enforce(
|
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|| "evaluate xprime",
|
|
LinearCombination::zero() + lambda.get_variable(),
|
|
LinearCombination::zero() + lambda.get_variable(),
|
|
LinearCombination::<Var, E>::zero() + (*params.montgomery_a(), one)
|
|
+ self.x.get_variable()
|
|
+ self.x.get_variable()
|
|
+ xprime.get_variable()
|
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);
|
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|
|
// Compute y' = -(y + lambda(x' - x))
|
|
let yprime = AllocatedNum::alloc(cs.namespace(|| "yprime"), || {
|
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let mut t0 = *xprime.get_value().get()?;
|
|
t0.sub_assign(self.x.get_value().get()?);
|
|
t0.mul_assign(lambda.get_value().get()?);
|
|
t0.add_assign(self.y.get_value().get()?);
|
|
t0.negate();
|
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|
|
Ok(t0)
|
|
})?;
|
|
|
|
// y' + y = lambda(x - x')
|
|
cs.enforce(
|
|
|| "evaluate yprime",
|
|
LinearCombination::zero() + self.x.get_variable()
|
|
- xprime.get_variable(),
|
|
|
|
LinearCombination::zero() + lambda.get_variable(),
|
|
|
|
LinearCombination::<Var, E>::zero() + yprime.get_variable()
|
|
+ self.y.get_variable()
|
|
);
|
|
|
|
Ok(MontgomeryPoint {
|
|
x: xprime,
|
|
y: yprime
|
|
})
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod test {
|
|
use bellman::{ConstraintSystem};
|
|
use rand::{XorShiftRng, SeedableRng, Rng};
|
|
use pairing::bls12_381::{Bls12, Fr};
|
|
use pairing::{Field};
|
|
use ::circuit::test::*;
|
|
use ::jubjub::{
|
|
montgomery,
|
|
edwards,
|
|
JubjubBls12
|
|
};
|
|
use super::{
|
|
MontgomeryPoint,
|
|
EdwardsPoint,
|
|
AllocatedNum,
|
|
Boolean
|
|
};
|
|
use super::super::boolean::AllocatedBit;
|
|
use ::group_hash::group_hash;
|
|
|
|
#[test]
|
|
fn test_into_edwards() {
|
|
let params = &JubjubBls12::new();
|
|
let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
|
|
|
for _ in 0..100 {
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
|
|
let p = montgomery::Point::<Bls12, _>::rand(rng, params);
|
|
let (u, v) = edwards::Point::from_montgomery(&p, params).into_xy();
|
|
let (x, y) = p.into_xy().unwrap();
|
|
|
|
let numx = AllocatedNum::alloc(cs.namespace(|| "mont x"), || {
|
|
Ok(x)
|
|
}).unwrap();
|
|
let numy = AllocatedNum::alloc(cs.namespace(|| "mont y"), || {
|
|
Ok(y)
|
|
}).unwrap();
|
|
|
|
let p = MontgomeryPoint::interpret_unchecked(numx, numy);
|
|
|
|
let q = p.into_edwards(&mut cs, params).unwrap();
|
|
|
|
assert!(cs.is_satisfied());
|
|
assert!(q.x.get_value().unwrap() == u);
|
|
assert!(q.y.get_value().unwrap() == v);
|
|
|
|
cs.set("u/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied().unwrap(), "u computation");
|
|
cs.set("u/num", u);
|
|
assert!(cs.is_satisfied());
|
|
|
|
cs.set("v/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied().unwrap(), "v computation");
|
|
cs.set("v/num", v);
|
|
assert!(cs.is_satisfied());
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_group_hash() {
|
|
let params = &JubjubBls12::new();
|
|
let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
|
|
|
let mut num_errs = 0;
|
|
let mut num_unsatisfied = 0;
|
|
let mut num_satisfied = 0;
|
|
|
|
for _ in 0..100 {
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
|
|
let mut tag_bytes = vec![];
|
|
let mut tag = vec![];
|
|
for i in 0..10 {
|
|
let mut byte = 0;
|
|
for j in 0..8 {
|
|
byte <<= 1;
|
|
let b: bool = rng.gen();
|
|
if b {
|
|
byte |= 1;
|
|
}
|
|
tag.push(Boolean::from(
|
|
AllocatedBit::alloc(
|
|
cs.namespace(|| format!("bit {} {}", i, j)),
|
|
Some(b)
|
|
).unwrap()
|
|
));
|
|
}
|
|
tag_bytes.push(byte);
|
|
}
|
|
|
|
let p = MontgomeryPoint::group_hash(
|
|
cs.namespace(|| "gh"),
|
|
&tag,
|
|
params
|
|
);
|
|
|
|
let expected = group_hash::<Bls12>(&tag_bytes, params);
|
|
|
|
if p.is_err() {
|
|
assert!(expected.is_none());
|
|
num_errs += 1;
|
|
} else {
|
|
if !cs.is_satisfied() {
|
|
assert!(expected.is_none());
|
|
num_unsatisfied += 1;
|
|
} else {
|
|
let p = p.unwrap();
|
|
let (x, y) = expected.unwrap().into_xy().unwrap();
|
|
|
|
assert_eq!(p.x.get_value().unwrap(), x);
|
|
assert_eq!(p.y.get_value().unwrap(), y);
|
|
|
|
num_satisfied += 1;
|
|
}
|
|
}
|
|
}
|
|
|
|
assert_eq!(
|
|
(num_errs, num_unsatisfied, num_satisfied),
|
|
(47, 4, 49)
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn test_interpret() {
|
|
let params = &JubjubBls12::new();
|
|
let rng = &mut XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
|
|
|
for _ in 0..100 {
|
|
let p = montgomery::Point::<Bls12, _>::rand(rng, ¶ms);
|
|
let (mut x, mut y) = p.into_xy().unwrap();
|
|
|
|
{
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
let numx = AllocatedNum::alloc(cs.namespace(|| "x"), || {
|
|
Ok(x)
|
|
}).unwrap();
|
|
let numy = AllocatedNum::alloc(cs.namespace(|| "y"), || {
|
|
Ok(y)
|
|
}).unwrap();
|
|
|
|
let p = MontgomeryPoint::interpret(&mut cs, &numx, &numy, ¶ms).unwrap();
|
|
|
|
assert!(cs.is_satisfied());
|
|
assert_eq!(p.x.get_value().unwrap(), x);
|
|
assert_eq!(p.y.get_value().unwrap(), y);
|
|
|
|
y.negate();
|
|
cs.set("y/num", y);
|
|
assert!(cs.is_satisfied());
|
|
x.negate();
|
|
cs.set("x/num", x);
|
|
assert!(!cs.is_satisfied());
|
|
}
|
|
|
|
{
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
let numx = AllocatedNum::alloc(cs.namespace(|| "x"), || {
|
|
Ok(x)
|
|
}).unwrap();
|
|
let numy = AllocatedNum::alloc(cs.namespace(|| "y"), || {
|
|
Ok(y)
|
|
}).unwrap();
|
|
|
|
MontgomeryPoint::interpret(&mut cs, &numx, &numy, ¶ms).unwrap();
|
|
|
|
assert_eq!(cs.which_is_unsatisfied().unwrap(), "on curve check");
|
|
}
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_doubling_order_2() {
|
|
let params = &JubjubBls12::new();
|
|
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
|
|
let x = AllocatedNum::alloc(cs.namespace(|| "x"), || {
|
|
Ok(Fr::zero())
|
|
}).unwrap();
|
|
let y = AllocatedNum::alloc(cs.namespace(|| "y"), || {
|
|
Ok(Fr::zero())
|
|
}).unwrap();
|
|
|
|
let p = MontgomeryPoint {
|
|
x: x,
|
|
y: y
|
|
};
|
|
|
|
assert!(p.double(&mut cs, params).is_err());
|
|
}
|
|
|
|
#[test]
|
|
fn test_edwards_addition() {
|
|
let params = &JubjubBls12::new();
|
|
let rng = &mut XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
|
|
|
for _ in 0..100 {
|
|
let p1 = edwards::Point::<Bls12, _>::rand(rng, params);
|
|
let p2 = edwards::Point::<Bls12, _>::rand(rng, params);
|
|
|
|
let p3 = p1.add(&p2, params);
|
|
|
|
let (x0, y0) = p1.into_xy();
|
|
let (x1, y1) = p2.into_xy();
|
|
let (x2, y2) = p3.into_xy();
|
|
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
|
|
let num_x0 = AllocatedNum::alloc(cs.namespace(|| "x0"), || {
|
|
Ok(x0)
|
|
}).unwrap();
|
|
let num_y0 = AllocatedNum::alloc(cs.namespace(|| "y0"), || {
|
|
Ok(y0)
|
|
}).unwrap();
|
|
|
|
let num_x1 = AllocatedNum::alloc(cs.namespace(|| "x1"), || {
|
|
Ok(x1)
|
|
}).unwrap();
|
|
let num_y1 = AllocatedNum::alloc(cs.namespace(|| "y1"), || {
|
|
Ok(y1)
|
|
}).unwrap();
|
|
|
|
let p1 = EdwardsPoint {
|
|
x: num_x0,
|
|
y: num_y0
|
|
};
|
|
|
|
let p2 = EdwardsPoint {
|
|
x: num_x1,
|
|
y: num_y1
|
|
};
|
|
|
|
let p3 = p1.add(cs.namespace(|| "addition"), &p2, params).unwrap();
|
|
|
|
assert!(cs.is_satisfied());
|
|
|
|
assert!(p3.x.get_value().unwrap() == x2);
|
|
assert!(p3.y.get_value().unwrap() == y2);
|
|
|
|
let u = cs.get("addition/U/num");
|
|
cs.set("addition/U/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("addition/U computation"));
|
|
cs.set("addition/U/num", u);
|
|
assert!(cs.is_satisfied());
|
|
|
|
let x3 = cs.get("addition/x3/num");
|
|
cs.set("addition/x3/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("addition/x3 computation"));
|
|
cs.set("addition/x3/num", x3);
|
|
assert!(cs.is_satisfied());
|
|
|
|
let y3 = cs.get("addition/y3/num");
|
|
cs.set("addition/y3/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("addition/y3 computation"));
|
|
cs.set("addition/y3/num", y3);
|
|
assert!(cs.is_satisfied());
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_montgomery_addition() {
|
|
let params = &JubjubBls12::new();
|
|
let rng = &mut XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
|
|
|
for _ in 0..100 {
|
|
let p1 = loop {
|
|
let x: Fr = rng.gen();
|
|
let s: bool = rng.gen();
|
|
|
|
if let Some(p) = montgomery::Point::<Bls12, _>::get_for_x(x, s, params) {
|
|
break p;
|
|
}
|
|
};
|
|
|
|
let p2 = loop {
|
|
let x: Fr = rng.gen();
|
|
let s: bool = rng.gen();
|
|
|
|
if let Some(p) = montgomery::Point::<Bls12, _>::get_for_x(x, s, params) {
|
|
break p;
|
|
}
|
|
};
|
|
|
|
let p3 = p1.add(&p2, params);
|
|
|
|
let (x0, y0) = p1.into_xy().unwrap();
|
|
let (x1, y1) = p2.into_xy().unwrap();
|
|
let (x2, y2) = p3.into_xy().unwrap();
|
|
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
|
|
let num_x0 = AllocatedNum::alloc(cs.namespace(|| "x0"), || {
|
|
Ok(x0)
|
|
}).unwrap();
|
|
let num_y0 = AllocatedNum::alloc(cs.namespace(|| "y0"), || {
|
|
Ok(y0)
|
|
}).unwrap();
|
|
|
|
let num_x1 = AllocatedNum::alloc(cs.namespace(|| "x1"), || {
|
|
Ok(x1)
|
|
}).unwrap();
|
|
let num_y1 = AllocatedNum::alloc(cs.namespace(|| "y1"), || {
|
|
Ok(y1)
|
|
}).unwrap();
|
|
|
|
let p1 = MontgomeryPoint {
|
|
x: num_x0,
|
|
y: num_y0
|
|
};
|
|
|
|
let p2 = MontgomeryPoint {
|
|
x: num_x1,
|
|
y: num_y1
|
|
};
|
|
|
|
let p3 = p1.add(cs.namespace(|| "addition"), &p2, params).unwrap();
|
|
|
|
assert!(cs.is_satisfied());
|
|
|
|
assert!(p3.x.get_value().unwrap() == x2);
|
|
assert!(p3.y.get_value().unwrap() == y2);
|
|
|
|
cs.set("addition/yprime/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("addition/evaluate yprime"));
|
|
cs.set("addition/yprime/num", y2);
|
|
assert!(cs.is_satisfied());
|
|
|
|
cs.set("addition/xprime/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("addition/evaluate xprime"));
|
|
cs.set("addition/xprime/num", x2);
|
|
assert!(cs.is_satisfied());
|
|
|
|
cs.set("addition/lambda/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("addition/evaluate lambda"));
|
|
}
|
|
}
|
|
|
|
#[test]
|
|
fn test_doubling() {
|
|
let params = &JubjubBls12::new();
|
|
let rng = &mut XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
|
|
|
for _ in 0..100 {
|
|
let p = loop {
|
|
let x: Fr = rng.gen();
|
|
let s: bool = rng.gen();
|
|
|
|
if let Some(p) = montgomery::Point::<Bls12, _>::get_for_x(x, s, params) {
|
|
break p;
|
|
}
|
|
};
|
|
|
|
let p2 = p.double(params);
|
|
|
|
let (x0, y0) = p.into_xy().unwrap();
|
|
let (x1, y1) = p2.into_xy().unwrap();
|
|
|
|
let mut cs = TestConstraintSystem::<Bls12>::new();
|
|
|
|
let x = AllocatedNum::alloc(cs.namespace(|| "x"), || {
|
|
Ok(x0)
|
|
}).unwrap();
|
|
let y = AllocatedNum::alloc(cs.namespace(|| "y"), || {
|
|
Ok(y0)
|
|
}).unwrap();
|
|
|
|
let p = MontgomeryPoint {
|
|
x: x,
|
|
y: y
|
|
};
|
|
|
|
let p2 = p.double(cs.namespace(|| "doubling"), params).unwrap();
|
|
|
|
assert!(cs.is_satisfied());
|
|
|
|
assert!(p2.x.get_value().unwrap() == x1);
|
|
assert!(p2.y.get_value().unwrap() == y1);
|
|
|
|
cs.set("doubling/yprime/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("doubling/evaluate yprime"));
|
|
cs.set("doubling/yprime/num", y1);
|
|
assert!(cs.is_satisfied());
|
|
|
|
cs.set("doubling/xprime/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("doubling/evaluate xprime"));
|
|
cs.set("doubling/xprime/num", x1);
|
|
assert!(cs.is_satisfied());
|
|
|
|
cs.set("doubling/lambda/num", rng.gen());
|
|
assert_eq!(cs.which_is_unsatisfied(), Some("doubling/evaluate lambda"));
|
|
}
|
|
}
|
|
}
|