Srinath Setty
2 years ago
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5 changed files with 503 additions and 591 deletions
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+0 -1rustfmt.toml
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+1 -1src/circuit.rs
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+501 -35src/gadgets/ecc.rs
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+0 -552src/gadgets/ecc_circuit.rs
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+1 -2src/gadgets/mod.rs
@ -1,5 +1,4 @@ |
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edition = "2018" |
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tab_spaces = 2 |
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newline_style = "Unix" |
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report_fixme = "Always" |
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use_try_shorthand = true |
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@ -1,552 +0,0 @@ |
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#![allow(non_snake_case)]
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use crate::gadgets::utils::{
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alloc_one, alloc_zero, conditionally_select, conditionally_select2, select_one_or, select_zero_or,
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};
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use bellperson::{
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gadgets::{
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boolean::{AllocatedBit, Boolean},
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num::AllocatedNum,
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Assignment,
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},
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ConstraintSystem, SynthesisError,
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};
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use ff::PrimeField;
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use rand::rngs::OsRng;
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#[derive(Clone)]
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pub struct AllocatedPoint<Fp>
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where
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Fp: PrimeField,
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{
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pub(crate) x: AllocatedNum<Fp>,
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pub(crate) y: AllocatedNum<Fp>,
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pub(crate) is_infinity: AllocatedNum<Fp>,
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}
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impl<Fp> AllocatedPoint<Fp>
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where
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Fp: PrimeField,
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{
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// Creates a new allocated point from allocated nums.
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pub fn new(x: AllocatedNum<Fp>, y: AllocatedNum<Fp>, is_infinity: AllocatedNum<Fp>) -> Self {
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Self { x, y, is_infinity }
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}
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// Check that is infinity is 0/1
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#[allow(dead_code)]
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pub fn check_is_infinity<CS: ConstraintSystem<Fp>>(
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&self,
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mut cs: CS,
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) -> Result<(), SynthesisError> {
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// Check that is_infinity * ( 1 - is_infinity ) = 0
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cs.enforce(
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|| "is_infinity is bit",
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|lc| lc + self.is_infinity.get_variable(),
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|lc| lc + CS::one() - self.is_infinity.get_variable(),
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|lc| lc,
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);
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Ok(())
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}
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#[allow(dead_code)]
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// Allocate a random point. Only used for testing
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pub fn random_vartime<CS: ConstraintSystem<Fp>>(mut cs: CS) -> Result<Self, SynthesisError> {
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loop {
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let x = Fp::random(&mut OsRng);
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let y = (x * x * x + Fp::one() + Fp::one() + Fp::one() + Fp::one() + Fp::one()).sqrt();
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if y.is_some().unwrap_u8() == 1 {
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let x_alloc = AllocatedNum::alloc(cs.namespace(|| "x"), || Ok(x))?;
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let y_alloc = AllocatedNum::alloc(cs.namespace(|| "y"), || Ok(y.unwrap()))?;
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let is_infinity = alloc_zero(cs.namespace(|| "Is Infinity"))?;
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return Ok(Self::new(x_alloc, y_alloc, is_infinity));
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}
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}
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}
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// Make the point io
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#[allow(dead_code)]
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pub fn inputize<CS: ConstraintSystem<Fp>>(&self, mut cs: CS) -> Result<(), SynthesisError> {
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let _ = self.x.inputize(cs.namespace(|| "Input point.x"));
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let _ = self.y.inputize(cs.namespace(|| "Input point.y"));
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let _ = self
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.is_infinity
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.inputize(cs.namespace(|| "Input point.is_infinity"));
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Ok(())
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}
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// Adds other point to this point and returns the result
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// Assumes that both other.is_infinity and this.is_infinty are bits
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pub fn add<CS: ConstraintSystem<Fp>>(
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&self,
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mut cs: CS,
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other: &AllocatedPoint<Fp>,
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) -> Result<Self, SynthesisError> {
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// Allocate the boolean variables that check if either of the points is infinity
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//************************************************************************/
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// lambda = (other.y - self.y) * (other.x - self.x).invert().unwrap();
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//************************************************************************/
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// First compute (other.x - self.x).inverse()
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// If either self or other are 1 then compute bogus values
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// x_diff = other != inf && self != inf ? (other.x - self.x) : 1
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let x_diff_actual = AllocatedNum::alloc(cs.namespace(|| "actual x diff"), || {
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Ok(*other.x.get_value().get()? - *self.x.get_value().get()?)
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})?;
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cs.enforce(
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|| "actual x_diff is correct",
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|lc| lc + other.x.get_variable() - self.x.get_variable(),
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|lc| lc + CS::one(),
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|lc| lc + x_diff_actual.get_variable(),
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);
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// Compute self.is_infinity OR other.is_infinity
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let at_least_one_inf = AllocatedNum::alloc(cs.namespace(|| "at least one inf"), || {
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Ok(*self.is_infinity.get_value().get()? * *other.is_infinity.get_value().get()?)
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})?;
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cs.enforce(
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|| "at least one inf = self.is_infinity * other.is_infinity",
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|lc| lc + self.is_infinity.get_variable(),
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|lc| lc + other.is_infinity.get_variable(),
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|lc| lc + at_least_one_inf.get_variable(),
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);
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// x_diff = 1 if either self.is_infinity or other.is_infinity else x_diff_actual
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let x_diff = select_one_or(
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cs.namespace(|| "Compute x_diff"),
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&x_diff_actual,
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&at_least_one_inf,
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)?;
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let x_diff_inv = AllocatedNum::alloc(cs.namespace(|| "x diff inverse"), || {
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if *at_least_one_inf.get_value().get()? == Fp::one() {
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// Set to default
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Ok(Fp::one())
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} else {
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// Set to the actual inverse
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let inv = (*other.x.get_value().get()? - *self.x.get_value().get()?).invert();
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if inv.is_some().unwrap_u8() == 1 {
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Ok(inv.unwrap())
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} else {
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Err(SynthesisError::DivisionByZero)
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}
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}
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})?;
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cs.enforce(
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|| "Check inverse",
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|lc| lc + x_diff.get_variable(),
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|lc| lc + x_diff_inv.get_variable(),
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|lc| lc + CS::one(),
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);
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let lambda = AllocatedNum::alloc(cs.namespace(|| "lambda"), || {
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Ok(
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(*other.y.get_value().get()? - *self.y.get_value().get()?)
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* x_diff_inv.get_value().get()?,
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)
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})?;
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cs.enforce(
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|| "Check that lambda is correct",
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|lc| lc + other.y.get_variable() - self.y.get_variable(),
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|lc| lc + x_diff_inv.get_variable(),
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|lc| lc + lambda.get_variable(),
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);
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//************************************************************************/
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// x = lambda * lambda - self.x - other.x;
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//************************************************************************/
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let x = AllocatedNum::alloc(cs.namespace(|| "x"), || {
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Ok(
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*lambda.get_value().get()? * lambda.get_value().get()?
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- *self.x.get_value().get()?
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- *other.x.get_value().get()?,
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)
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})?;
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cs.enforce(
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|| "check that x is correct",
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|lc| lc + lambda.get_variable(),
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|lc| lc + lambda.get_variable(),
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|lc| lc + x.get_variable() + self.x.get_variable() + other.x.get_variable(),
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);
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//************************************************************************/
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// y = lambda * (self.x - x) - self.y;
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//************************************************************************/
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let y = AllocatedNum::alloc(cs.namespace(|| "y"), || {
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Ok(
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*lambda.get_value().get()? * (*self.x.get_value().get()? - *x.get_value().get()?)
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- *self.y.get_value().get()?,
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)
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})?;
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cs.enforce(
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|| "Check that y is correct",
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|lc| lc + lambda.get_variable(),
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|lc| lc + self.x.get_variable() - x.get_variable(),
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|lc| lc + y.get_variable() + self.y.get_variable(),
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);
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let is_infinity = AllocatedNum::alloc(cs.namespace(|| "is infinity"), || Ok(Fp::zero()))?;
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//************************************************************************/
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// We only return the computed x, y if neither of the points is infinity.
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// if self.is_infinity return other.clone()
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// elif other.is_infinity return self.clone()
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// Otherwise return the computed points.
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//************************************************************************/
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// Now compute the output x
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let inner_x = conditionally_select2(
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cs.namespace(|| "final x: inner if"),
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&self.x,
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&x,
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&other.is_infinity,
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)?;
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let final_x = conditionally_select2(
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cs.namespace(|| "final x: outer if"),
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&other.x,
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&inner_x,
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&self.is_infinity,
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)?;
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// The output y
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let inner_y = conditionally_select2(
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cs.namespace(|| "final y: inner if"),
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&self.y,
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&y,
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&other.is_infinity,
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)?;
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let final_y = conditionally_select2(
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cs.namespace(|| "final y: outer if"),
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&other.y,
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&inner_y,
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&self.is_infinity,
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)?;
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// The output is_infinity
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let inner_is_infinity = conditionally_select2(
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cs.namespace(|| "final is infinity: inner if"),
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&self.is_infinity,
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&is_infinity,
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&other.is_infinity,
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)?;
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let final_is_infinity = conditionally_select2(
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cs.namespace(|| "final is infinity: outer if"),
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&other.is_infinity,
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&inner_is_infinity,
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&self.is_infinity,
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)?;
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Ok(Self::new(final_x, final_y, final_is_infinity))
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}
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pub fn double<CS: ConstraintSystem<Fp>>(&self, mut cs: CS) -> Result<Self, SynthesisError> {
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//*************************************************************/
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// lambda = (Fp::one() + Fp::one() + Fp::one())
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// * self.x
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// * self.x
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// * ((Fp::one() + Fp::one()) * self.y).invert().unwrap();
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/*************************************************************/
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// Compute tmp = (Fp::one() + Fp::one())* self.y ? self != inf : 1
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let tmp_actual = AllocatedNum::alloc(cs.namespace(|| "tmp_actual"), || {
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Ok(*self.y.get_value().get()? + *self.y.get_value().get()?)
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})?;
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cs.enforce(
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|| "check tmp_actual",
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|lc| lc + CS::one() + CS::one(),
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|lc| lc + self.y.get_variable(),
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|lc| lc + tmp_actual.get_variable(),
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);
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let tmp = select_one_or(cs.namespace(|| "tmp"), &tmp_actual, &self.is_infinity)?;
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// Compute inv = tmp.invert
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let tmp_inv = AllocatedNum::alloc(cs.namespace(|| "tmp inverse"), || {
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if *self.is_infinity.get_value().get()? == Fp::one() {
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// Return default value 1
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Ok(Fp::one())
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} else {
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// Return the actual inverse
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let inv = (*tmp.get_value().get()?).invert();
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if inv.is_some().unwrap_u8() == 1 {
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Ok(inv.unwrap())
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} else {
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Err(SynthesisError::DivisionByZero)
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}
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}
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})?;
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cs.enforce(
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|| "Check inverse",
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|lc| lc + tmp.get_variable(),
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|lc| lc + tmp_inv.get_variable(),
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|lc| lc + CS::one(),
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);
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// Now compute lambda as (Fp::one() + Fp::one + Fp::one()) * self.x * self.x * tmp_inv
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let prod_1 = AllocatedNum::alloc(cs.namespace(|| "alloc prod 1"), || {
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Ok(*tmp_inv.get_value().get()? * self.x.get_value().get()?)
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})?;
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cs.enforce(
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|| "Check prod 1",
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|lc| lc + self.x.get_variable(),
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|lc| lc + tmp_inv.get_variable(),
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|lc| lc + prod_1.get_variable(),
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);
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let prod_2 = AllocatedNum::alloc(cs.namespace(|| "alloc prod 2"), || {
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Ok(*prod_1.get_value().get()? * self.x.get_value().get()?)
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})?;
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cs.enforce(
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|| "Check prod 2",
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|lc| lc + self.x.get_variable(),
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|lc| lc + prod_1.get_variable(),
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|lc| lc + prod_2.get_variable(),
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);
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let lambda = AllocatedNum::alloc(cs.namespace(|| "lambda"), || {
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Ok(*prod_2.get_value().get()? * (Fp::one() + Fp::one() + Fp::one()))
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})?;
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cs.enforce(
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|| "Check lambda",
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|lc| lc + CS::one() + CS::one() + CS::one(),
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|lc| lc + prod_2.get_variable(),
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|lc| lc + lambda.get_variable(),
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);
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/*************************************************************/
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// x = lambda * lambda - self.x - self.x;
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/*************************************************************/
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let x = AllocatedNum::alloc(cs.namespace(|| "x"), || {
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Ok(
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((*lambda.get_value().get()?) * (*lambda.get_value().get()?))
|
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- *self.x.get_value().get()?
|
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- self.x.get_value().get()?,
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)
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})?;
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cs.enforce(
|
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|| "Check x",
|
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|lc| lc + lambda.get_variable(),
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|lc| lc + lambda.get_variable(),
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|lc| lc + x.get_variable() + self.x.get_variable() + self.x.get_variable(),
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);
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/*************************************************************/
|
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// y = lambda * (self.x - x) - self.y;
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/*************************************************************/
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let y = AllocatedNum::alloc(cs.namespace(|| "y"), || {
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Ok(
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(*lambda.get_value().get()?) * (*self.x.get_value().get()? - x.get_value().get()?)
|
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- self.y.get_value().get()?,
|
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)
|
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})?;
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cs.enforce(
|
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|| "Check y",
|
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|lc| lc + lambda.get_variable(),
|
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|lc| lc + self.x.get_variable() - x.get_variable(),
|
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|lc| lc + y.get_variable() + self.y.get_variable(),
|
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);
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|
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/*************************************************************/
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// Only return the computed x and y if the point is not infinity
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/*************************************************************/
|
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|
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// x
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let final_x = select_zero_or(cs.namespace(|| "final x"), &x, &self.is_infinity)?;
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|
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// y
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let final_y = select_zero_or(cs.namespace(|| "final y"), &y, &self.is_infinity)?;
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|
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// is_infinity
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let final_is_infinity = self.is_infinity.clone();
|
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|
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Ok(Self::new(final_x, final_y, final_is_infinity))
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}
|
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|
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#[allow(dead_code)]
|
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pub fn scalar_mul_mont<CS: ConstraintSystem<Fp>>(
|
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&self,
|
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mut cs: CS,
|
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scalar: Vec<AllocatedBit>,
|
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) -> Result<Self, SynthesisError> {
|
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/*************************************************************/
|
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// Initialize RO = Self {
|
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// x: Fp::zero(),
|
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// y: Fp::zero(),
|
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// is_infinity: true,
|
|||
// _p: Default::default(),
|
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//};
|
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/*************************************************************/
|
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|
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let zero = alloc_zero(cs.namespace(|| "Allocate zero"))?;
|
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let one = alloc_one(cs.namespace(|| "Allocate one"))?;
|
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let mut R0 = Self::new(zero.clone(), zero, one);
|
|||
|
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/*************************************************************/
|
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// Initialize R1 and the bits of the scalar
|
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/*************************************************************/
|
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|
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let mut R1 = self.clone();
|
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|
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for i in (0..scalar.len()).rev() {
|
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/*************************************************************/
|
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//if bits[i] {
|
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// R0 = R0.add(&R1);
|
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// R1 = R1.double();
|
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//} else {
|
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// R0 = R0.double();
|
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// R1 = R0.add(&R1);
|
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//}
|
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/*************************************************************/
|
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|
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let R0_and_R1 = R0.add(cs.namespace(|| format!("{}: R0 + R1", i)), &R1)?;
|
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let R0_double = R0.double(cs.namespace(|| format!("{}: 2 * R0", i)))?;
|
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let R1_double = R1.double(cs.namespace(|| format!("{}: 2 * R1", i)))?;
|
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|
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R0 = Self::conditionally_select(
|
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cs.namespace(|| format!("{}: Update R0", i)),
|
|||
&R0_and_R1,
|
|||
&R0_double,
|
|||
&Boolean::from(scalar[i].clone()),
|
|||
)?;
|
|||
|
|||
R1 = Self::conditionally_select(
|
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cs.namespace(|| format!("{}: Update R1", i)),
|
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&R1_double,
|
|||
&R0_and_R1,
|
|||
&Boolean::from(scalar[i].clone()),
|
|||
)?;
|
|||
}
|
|||
Ok(R0)
|
|||
}
|
|||
|
|||
#[allow(dead_code)]
|
|||
pub fn scalar_mul<CS: ConstraintSystem<Fp>>(
|
|||
&self,
|
|||
mut cs: CS,
|
|||
scalar: Vec<AllocatedBit>,
|
|||
) -> Result<Self, SynthesisError> {
|
|||
/*************************************************************/
|
|||
// Initialize res = Self {
|
|||
// x: Fp::zero(),
|
|||
// y: Fp::zero(),
|
|||
// is_infinity: true,
|
|||
// _p: Default::default(),
|
|||
//};
|
|||
/*************************************************************/
|
|||
|
|||
let zero = alloc_zero(cs.namespace(|| "Allocate zero"))?;
|
|||
let one = alloc_one(cs.namespace(|| "Allocate one"))?;
|
|||
let mut res = Self::new(zero.clone(), zero, one);
|
|||
|
|||
for i in (0..scalar.len()).rev() {
|
|||
/*************************************************************/
|
|||
// res = res.double();
|
|||
/*************************************************************/
|
|||
|
|||
res = res.double(cs.namespace(|| format!("{}: double", i)))?;
|
|||
|
|||
/*************************************************************/
|
|||
// if scalar[i] {
|
|||
// res = self.add(&res);
|
|||
// }
|
|||
/*************************************************************/
|
|||
|
|||
let self_and_res = self.add(cs.namespace(|| format!("{}: add", i)), &res)?;
|
|||
res = Self::conditionally_select(
|
|||
cs.namespace(|| format!("{}: Update res", i)),
|
|||
&self_and_res,
|
|||
&res,
|
|||
&Boolean::from(scalar[i].clone()),
|
|||
)?;
|
|||
}
|
|||
Ok(res)
|
|||
}
|
|||
|
|||
/// If condition outputs a otherwise outputs b
|
|||
pub fn conditionally_select<CS: ConstraintSystem<Fp>>(
|
|||
mut cs: CS,
|
|||
a: &Self,
|
|||
b: &Self,
|
|||
condition: &Boolean,
|
|||
) -> Result<Self, SynthesisError> {
|
|||
let x = conditionally_select(cs.namespace(|| "select x"), &a.x, &b.x, condition)?;
|
|||
|
|||
let y = conditionally_select(cs.namespace(|| "select y"), &a.y, &b.y, condition)?;
|
|||
|
|||
let is_infinity = conditionally_select(
|
|||
cs.namespace(|| "select is_infinity"),
|
|||
&a.is_infinity,
|
|||
&b.is_infinity,
|
|||
condition,
|
|||
)?;
|
|||
|
|||
Ok(Self::new(x, y, is_infinity))
|
|||
}
|
|||
}
|
|||
|
|||
#[cfg(test)]
|
|||
mod tests {
|
|||
use super::*;
|
|||
use crate::bellperson::shape_cs::ShapeCS;
|
|||
use crate::bellperson::solver::SatisfyingAssignment;
|
|||
type G = pasta_curves::pallas::Point;
|
|||
type Fp = pasta_curves::pallas::Scalar;
|
|||
type Fq = pasta_curves::vesta::Scalar;
|
|||
use crate::bellperson::r1cs::{NovaShape, NovaWitness};
|
|||
use crate::gadgets::ecc::Point;
|
|||
use ff::PrimeFieldBits;
|
|||
|
|||
fn synthesize_smul<Fp, Fq, CS>(mut cs: CS) -> (AllocatedPoint<Fp>, AllocatedPoint<Fp>, Fq)
|
|||
where
|
|||
Fp: PrimeField,
|
|||
Fq: PrimeField + PrimeFieldBits,
|
|||
CS: ConstraintSystem<Fp>,
|
|||
{
|
|||
let a = AllocatedPoint::<Fp>::random_vartime(cs.namespace(|| "a")).unwrap();
|
|||
let _ = a.inputize(cs.namespace(|| "inputize a")).unwrap();
|
|||
let s = Fq::random(&mut OsRng);
|
|||
// Allocate random bits and only keep 128 bits
|
|||
let bits: Vec<AllocatedBit> = s
|
|||
.to_le_bits()
|
|||
.into_iter()
|
|||
.enumerate()
|
|||
.map(|(i, bit)| AllocatedBit::alloc(cs.namespace(|| format!("bit {}", i)), Some(bit)))
|
|||
.collect::<Result<Vec<AllocatedBit>, SynthesisError>>()
|
|||
.unwrap();
|
|||
let e = a.scalar_mul(cs.namespace(|| "Scalar Mul"), bits).unwrap();
|
|||
let _ = e.inputize(cs.namespace(|| "inputize e")).unwrap();
|
|||
(a, e, s)
|
|||
}
|
|||
|
|||
#[test]
|
|||
fn test_ecc_circuit_ops() {
|
|||
// First create the shape
|
|||
let mut cs: ShapeCS<G> = ShapeCS::new();
|
|||
let _ = synthesize_smul::<Fp, Fq, _>(cs.namespace(|| "synthesize"));
|
|||
println!("Number of constraints: {}", cs.num_constraints());
|
|||
let shape = cs.r1cs_shape();
|
|||
let gens = cs.r1cs_gens();
|
|||
|
|||
// Then the satisfying assignment
|
|||
let mut cs: SatisfyingAssignment<G> = SatisfyingAssignment::new();
|
|||
let (a, e, s) = synthesize_smul::<Fp, Fq, _>(cs.namespace(|| "synthesize"));
|
|||
let (inst, witness) = cs.r1cs_instance_and_witness(&shape, &gens).unwrap();
|
|||
|
|||
let a_p: Point<Fp, Fq> = Point::new(
|
|||
a.x.get_value().unwrap(),
|
|||
a.y.get_value().unwrap(),
|
|||
a.is_infinity.get_value().unwrap() == Fp::one(),
|
|||
);
|
|||
let e_p: Point<Fp, Fq> = Point::new(
|
|||
e.x.get_value().unwrap(),
|
|||
e.y.get_value().unwrap(),
|
|||
e.is_infinity.get_value().unwrap() == Fp::one(),
|
|||
);
|
|||
let e_new = a_p.scalar_mul(&s);
|
|||
assert!(e_p.x == e_new.x && e_p.y == e_new.y);
|
|||
// Make sure that this is satisfiable
|
|||
assert!(shape.is_sat(&gens, &inst, &witness).is_ok());
|
|||
}
|
|||
}
|
|||
@ -1,3 +1,2 @@ |
|||
mod ecc;
|
|||
pub mod ecc_circuit;
|
|||
pub mod ecc;
|
|||
pub mod utils;
|
|||