2021-02-26 09:33:59 -08:00
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#![allow(clippy::many_single_char_names)]
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#![allow(clippy::op_ref)]
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2021-02-25 12:29:25 -08:00
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use group::Curve;
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use halo2::arithmetic::FieldExt;
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use halo2::dev::MockProver;
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use halo2::pasta::{EqAffine, Fp};
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use halo2::plonk::{
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create_proof, keygen_pk, keygen_vk, verify_proof, Advice, Assignment, Circuit, Column,
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ConstraintSystem, Error, Fixed, Permutation, VerifyingKey,
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};
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use halo2::poly::{
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commitment::{Blind, Params},
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Rotation,
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};
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2021-04-30 18:28:50 -07:00
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use halo2::transcript::{Blake2bRead, Blake2bWrite, Challenge255};
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2021-02-25 12:29:25 -08:00
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use std::marker::PhantomData;
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#[test]
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fn plonk_api() {
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const K: u32 = 5;
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/// This represents an advice column at a certain row in the ConstraintSystem
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#[derive(Copy, Clone, Debug)]
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pub struct Variable(Column<Advice>, usize);
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// Initialize the polynomial commitment parameters
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let params: Params<EqAffine> = Params::new(K);
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#[derive(Clone)]
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struct PLONKConfig {
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a: Column<Advice>,
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b: Column<Advice>,
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c: Column<Advice>,
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d: Column<Advice>,
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e: Column<Advice>,
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sa: Column<Fixed>,
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sb: Column<Fixed>,
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sc: Column<Fixed>,
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sm: Column<Fixed>,
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sp: Column<Fixed>,
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sl: Column<Fixed>,
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sl2: Column<Fixed>,
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perm: Permutation,
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perm2: Permutation,
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}
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trait StandardCS<FF: FieldExt> {
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fn raw_multiply<F>(&mut self, f: F) -> Result<(Variable, Variable, Variable), Error>
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where
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F: FnOnce() -> Result<(FF, FF, FF), Error>;
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fn raw_add<F>(&mut self, f: F) -> Result<(Variable, Variable, Variable), Error>
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where
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F: FnOnce() -> Result<(FF, FF, FF), Error>;
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fn copy(&mut self, a: Variable, b: Variable) -> Result<(), Error>;
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fn public_input<F>(&mut self, f: F) -> Result<Variable, Error>
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where
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F: FnOnce() -> Result<FF, Error>;
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fn lookup_table(&mut self, values: &[Vec<FF>]) -> Result<(), Error>;
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}
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#[derive(Clone)]
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struct MyCircuit<F: FieldExt> {
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a: Option<F>,
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lookup_tables: Vec<Vec<F>>,
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}
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struct StandardPLONK<'a, F: FieldExt, CS: Assignment<F> + 'a> {
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cs: &'a mut CS,
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config: PLONKConfig,
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current_gate: usize,
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_marker: PhantomData<F>,
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}
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impl<'a, FF: FieldExt, CS: Assignment<FF>> StandardPLONK<'a, FF, CS> {
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fn new(cs: &'a mut CS, config: PLONKConfig) -> Self {
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StandardPLONK {
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cs,
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config,
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current_gate: 0,
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_marker: PhantomData,
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}
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}
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}
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impl<'a, FF: FieldExt, CS: Assignment<FF>> StandardCS<FF> for StandardPLONK<'a, FF, CS> {
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fn raw_multiply<F>(&mut self, f: F) -> Result<(Variable, Variable, Variable), Error>
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where
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F: FnOnce() -> Result<(FF, FF, FF), Error>,
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{
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let index = self.current_gate;
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self.current_gate += 1;
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let mut value = None;
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self.cs.assign_advice(
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|| "lhs",
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self.config.a,
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index,
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|| {
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value = Some(f()?);
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Ok(value.ok_or(Error::SynthesisError)?.0)
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},
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)?;
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self.cs.assign_advice(
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|| "lhs^4",
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self.config.d,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.0.square().square()),
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)?;
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self.cs.assign_advice(
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|| "rhs",
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self.config.b,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.1),
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)?;
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self.cs.assign_advice(
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|| "rhs^4",
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self.config.e,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.1.square().square()),
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)?;
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self.cs.assign_advice(
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|| "out",
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self.config.c,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.2),
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)?;
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self.cs
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.assign_fixed(|| "a", self.config.sa, index, || Ok(FF::zero()))?;
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self.cs
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.assign_fixed(|| "b", self.config.sb, index, || Ok(FF::zero()))?;
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self.cs
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.assign_fixed(|| "c", self.config.sc, index, || Ok(FF::one()))?;
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self.cs
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.assign_fixed(|| "a * b", self.config.sm, index, || Ok(FF::one()))?;
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Ok((
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Variable(self.config.a, index),
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Variable(self.config.b, index),
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Variable(self.config.c, index),
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))
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}
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fn raw_add<F>(&mut self, f: F) -> Result<(Variable, Variable, Variable), Error>
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where
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F: FnOnce() -> Result<(FF, FF, FF), Error>,
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{
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let index = self.current_gate;
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self.current_gate += 1;
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let mut value = None;
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self.cs.assign_advice(
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|| "lhs",
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self.config.a,
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index,
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|| {
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value = Some(f()?);
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Ok(value.ok_or(Error::SynthesisError)?.0)
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},
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)?;
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self.cs.assign_advice(
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|| "lhs^4",
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self.config.d,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.0.square().square()),
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)?;
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self.cs.assign_advice(
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|| "rhs",
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self.config.b,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.1),
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)?;
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self.cs.assign_advice(
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|| "rhs^4",
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self.config.e,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.1.square().square()),
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)?;
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self.cs.assign_advice(
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|| "out",
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self.config.c,
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index,
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|| Ok(value.ok_or(Error::SynthesisError)?.2),
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)?;
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self.cs
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.assign_fixed(|| "a", self.config.sa, index, || Ok(FF::one()))?;
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self.cs
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.assign_fixed(|| "b", self.config.sb, index, || Ok(FF::one()))?;
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self.cs
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.assign_fixed(|| "c", self.config.sc, index, || Ok(FF::one()))?;
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self.cs
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.assign_fixed(|| "a * b", self.config.sm, index, || Ok(FF::zero()))?;
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Ok((
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Variable(self.config.a, index),
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Variable(self.config.b, index),
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Variable(self.config.c, index),
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))
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}
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fn copy(&mut self, left: Variable, right: Variable) -> Result<(), Error> {
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self.cs.copy(
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&self.config.perm,
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left.0.into(),
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left.1,
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right.0.into(),
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right.1,
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)?;
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self.cs.copy(
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&self.config.perm2,
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left.0.into(),
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left.1,
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right.0.into(),
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right.1,
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)
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}
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fn public_input<F>(&mut self, f: F) -> Result<Variable, Error>
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where
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F: FnOnce() -> Result<FF, Error>,
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{
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let index = self.current_gate;
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self.current_gate += 1;
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self.cs
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.assign_advice(|| "value", self.config.a, index, || f())?;
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self.cs
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.assign_fixed(|| "public", self.config.sp, index, || Ok(FF::one()))?;
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Ok(Variable(self.config.a, index))
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}
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fn lookup_table(&mut self, values: &[Vec<FF>]) -> Result<(), Error> {
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for (&value_0, &value_1) in values[0].iter().zip(values[1].iter()) {
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let index = self.current_gate;
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self.current_gate += 1;
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self.cs
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.assign_fixed(|| "table col 1", self.config.sl, index, || Ok(value_0))?;
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self.cs
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.assign_fixed(|| "table col 2", self.config.sl2, index, || Ok(value_1))?;
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}
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Ok(())
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}
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}
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impl<F: FieldExt> Circuit<F> for MyCircuit<F> {
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type Config = PLONKConfig;
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fn configure(meta: &mut ConstraintSystem<F>) -> PLONKConfig {
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let e = meta.advice_column();
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let a = meta.advice_column();
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let b = meta.advice_column();
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let sf = meta.fixed_column();
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let c = meta.advice_column();
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let d = meta.advice_column();
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let p = meta.instance_column();
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let perm = meta.permutation(&[a.into(), b.into(), c.into()]);
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let perm2 = meta.permutation(&[a.into(), b.into(), c.into()]);
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let sm = meta.fixed_column();
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let sa = meta.fixed_column();
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let sb = meta.fixed_column();
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let sc = meta.fixed_column();
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let sp = meta.fixed_column();
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let sl = meta.fixed_column();
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let sl2 = meta.fixed_column();
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/*
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* A B ... sl sl2
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* [
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* instance 0 ... 0 0
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* a a ... 0 0
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* a a^2 ... 0 0
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* a a ... 0 0
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* a a^2 ... 0 0
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* ... ... ... ... ...
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* ... ... ... instance 0
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* ... ... ... a a
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* ... ... ... a a^2
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* ... ... ... 0 0
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* ]
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*/
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2021-05-26 16:37:32 -07:00
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meta.lookup(|meta| {
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let a_ = meta.query_any(a.into(), Rotation::cur());
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let sl_ = meta.query_any(sl.into(), Rotation::cur());
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vec![(a_, sl_)]
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});
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meta.lookup(|meta| {
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let a_ = meta.query_any(a.into(), Rotation::cur());
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let b_ = meta.query_any(b.into(), Rotation::cur());
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let sl_ = meta.query_any(sl.into(), Rotation::cur());
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let sl2_ = meta.query_any(sl2.into(), Rotation::cur());
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vec![(a_ * b_, sl_ * sl2_)]
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});
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2021-02-25 12:29:25 -08:00
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meta.create_gate("Combined add-mult", |meta| {
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let d = meta.query_advice(d, Rotation::next());
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let a = meta.query_advice(a, Rotation::cur());
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let sf = meta.query_fixed(sf, Rotation::cur());
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let e = meta.query_advice(e, Rotation::prev());
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let b = meta.query_advice(b, Rotation::cur());
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let c = meta.query_advice(c, Rotation::cur());
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let sa = meta.query_fixed(sa, Rotation::cur());
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let sb = meta.query_fixed(sb, Rotation::cur());
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let sc = meta.query_fixed(sc, Rotation::cur());
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let sm = meta.query_fixed(sm, Rotation::cur());
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2021-05-27 06:44:02 -07:00
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vec![
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a.clone() * sa
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+ b.clone() * sb
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+ a * b * sm
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+ (c * sc * (-F::one()))
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+ sf * (d * e),
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]
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2021-02-25 12:29:25 -08:00
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});
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meta.create_gate("Public input", |meta| {
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let a = meta.query_advice(a, Rotation::cur());
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let p = meta.query_instance(p, Rotation::cur());
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let sp = meta.query_fixed(sp, Rotation::cur());
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2021-05-27 06:44:02 -07:00
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vec![sp * (a + p * (-F::one()))]
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2021-02-25 12:29:25 -08:00
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});
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PLONKConfig {
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a,
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b,
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c,
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d,
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e,
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sa,
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sb,
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sc,
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sm,
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sp,
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sl,
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sl2,
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perm,
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perm2,
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}
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}
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fn synthesize(
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&self,
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cs: &mut impl Assignment<F>,
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config: PLONKConfig,
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) -> Result<(), Error> {
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let mut cs = StandardPLONK::new(cs, config);
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let _ = cs.public_input(|| Ok(F::one() + F::one()))?;
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for _ in 0..10 {
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let mut a_squared = None;
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let (a0, _, c0) = cs.raw_multiply(|| {
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a_squared = self.a.map(|a| a.square());
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Ok((
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self.a.ok_or(Error::SynthesisError)?,
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self.a.ok_or(Error::SynthesisError)?,
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a_squared.ok_or(Error::SynthesisError)?,
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))
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})?;
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let (a1, b1, _) = cs.raw_add(|| {
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let fin = a_squared.and_then(|a2| self.a.map(|a| a + a2));
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|
|
Ok((
|
|
|
|
self.a.ok_or(Error::SynthesisError)?,
|
|
|
|
a_squared.ok_or(Error::SynthesisError)?,
|
|
|
|
fin.ok_or(Error::SynthesisError)?,
|
|
|
|
))
|
|
|
|
})?;
|
|
|
|
cs.copy(a0, a1)?;
|
|
|
|
cs.copy(b1, c0)?;
|
|
|
|
}
|
|
|
|
|
|
|
|
cs.lookup_table(&self.lookup_tables)?;
|
|
|
|
|
|
|
|
Ok(())
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
let a = Fp::from_u64(2834758237) * Fp::ZETA;
|
|
|
|
let a_squared = a * &a;
|
|
|
|
let instance = Fp::one() + Fp::one();
|
|
|
|
let lookup_table = vec![instance, a, a, Fp::zero()];
|
|
|
|
let lookup_table_2 = vec![Fp::zero(), a, a_squared, Fp::zero()];
|
|
|
|
|
|
|
|
let empty_circuit: MyCircuit<Fp> = MyCircuit {
|
|
|
|
a: None,
|
|
|
|
lookup_tables: vec![lookup_table.clone(), lookup_table_2.clone()],
|
|
|
|
};
|
|
|
|
|
|
|
|
let circuit: MyCircuit<Fp> = MyCircuit {
|
|
|
|
a: Some(a),
|
|
|
|
lookup_tables: vec![lookup_table, lookup_table_2],
|
|
|
|
};
|
|
|
|
|
|
|
|
// Initialize the proving key
|
|
|
|
let vk = keygen_vk(¶ms, &empty_circuit).expect("keygen_vk should not fail");
|
|
|
|
let pk = keygen_pk(¶ms, vk, &empty_circuit).expect("keygen_pk should not fail");
|
|
|
|
|
|
|
|
let mut pubinputs = pk.get_vk().get_domain().empty_lagrange();
|
|
|
|
pubinputs[0] = instance;
|
|
|
|
let pubinput = params
|
|
|
|
.commit_lagrange(&pubinputs, Blind::default())
|
|
|
|
.to_affine();
|
|
|
|
|
|
|
|
// Check this circuit is satisfied.
|
|
|
|
let prover = match MockProver::run(K, &circuit, vec![pubinputs.to_vec()]) {
|
|
|
|
Ok(prover) => prover,
|
|
|
|
Err(e) => panic!("{:?}", e),
|
|
|
|
};
|
|
|
|
assert_eq!(prover.verify(), Ok(()));
|
|
|
|
|
|
|
|
for _ in 0..10 {
|
2021-05-07 07:21:54 -07:00
|
|
|
let mut transcript = Blake2bWrite::<_, _, Challenge255<_>>::init(vec![]);
|
2021-02-25 12:29:25 -08:00
|
|
|
// Create a proof
|
|
|
|
create_proof(
|
|
|
|
¶ms,
|
|
|
|
&pk,
|
|
|
|
&[circuit.clone(), circuit.clone()],
|
|
|
|
&[&[pubinputs.clone()], &[pubinputs.clone()]],
|
|
|
|
&mut transcript,
|
|
|
|
)
|
|
|
|
.expect("proof generation should not fail");
|
|
|
|
let proof: Vec<u8> = transcript.finalize();
|
|
|
|
|
|
|
|
let pubinput_slice = &[pubinput];
|
|
|
|
let pubinput_slice_copy = &[pubinput];
|
|
|
|
let msm = params.empty_msm();
|
2021-05-07 07:21:54 -07:00
|
|
|
let mut transcript = Blake2bRead::<_, _, Challenge255<_>>::init(&proof[..]);
|
2021-02-25 12:29:25 -08:00
|
|
|
let guard = verify_proof(
|
|
|
|
¶ms,
|
|
|
|
pk.get_vk(),
|
|
|
|
msm,
|
|
|
|
&[pubinput_slice, pubinput_slice_copy],
|
|
|
|
&mut transcript,
|
|
|
|
)
|
|
|
|
.unwrap();
|
|
|
|
{
|
|
|
|
let msm = guard.clone().use_challenges();
|
|
|
|
assert!(msm.eval());
|
|
|
|
}
|
|
|
|
{
|
|
|
|
let g = guard.compute_g();
|
|
|
|
let (msm, _) = guard.clone().use_g(g);
|
|
|
|
assert!(msm.eval());
|
|
|
|
}
|
|
|
|
let msm = guard.clone().use_challenges();
|
|
|
|
assert!(msm.clone().eval());
|
2021-05-07 07:21:54 -07:00
|
|
|
let mut transcript = Blake2bRead::<_, _, Challenge255<_>>::init(&proof[..]);
|
2021-02-25 12:29:25 -08:00
|
|
|
let mut vk_buffer = vec![];
|
|
|
|
pk.get_vk().write(&mut vk_buffer).unwrap();
|
|
|
|
let vk = VerifyingKey::<EqAffine>::read::<_, MyCircuit<Fp>>(&mut &vk_buffer[..], ¶ms)
|
|
|
|
.unwrap();
|
|
|
|
let guard = verify_proof(
|
|
|
|
¶ms,
|
|
|
|
&vk,
|
|
|
|
msm,
|
|
|
|
&[pubinput_slice, pubinput_slice_copy],
|
|
|
|
&mut transcript,
|
|
|
|
)
|
|
|
|
.unwrap();
|
|
|
|
{
|
|
|
|
let msm = guard.clone().use_challenges();
|
|
|
|
assert!(msm.eval());
|
|
|
|
}
|
|
|
|
{
|
|
|
|
let g = guard.compute_g();
|
|
|
|
let (msm, _) = guard.clone().use_g(g);
|
|
|
|
assert!(msm.eval());
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Check that the verification key has not changed unexpectedly
|
|
|
|
{
|
|
|
|
assert_eq!(
|
|
|
|
format!("{:#?}", pk.get_vk().pinned()),
|
|
|
|
r#####"PinnedVerificationKey {
|
|
|
|
base_modulus: "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001",
|
|
|
|
scalar_modulus: "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001",
|
|
|
|
domain: PinnedEvaluationDomain {
|
|
|
|
k: 5,
|
|
|
|
extended_k: 7,
|
|
|
|
omega: 0x0cc3380dc616f2e1daf29ad1560833ed3baea3393eceb7bc8fa36376929b78cc,
|
|
|
|
},
|
|
|
|
cs: PinnedConstraintSystem {
|
|
|
|
num_fixed_columns: 8,
|
|
|
|
num_advice_columns: 5,
|
|
|
|
num_instance_columns: 1,
|
|
|
|
gates: [
|
|
|
|
Sum(
|
|
|
|
Sum(
|
|
|
|
Sum(
|
|
|
|
Sum(
|
|
|
|
Product(
|
|
|
|
Advice(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
Fixed(
|
|
|
|
3,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
Product(
|
|
|
|
Advice(
|
|
|
|
1,
|
|
|
|
),
|
|
|
|
Fixed(
|
|
|
|
4,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
),
|
|
|
|
Product(
|
|
|
|
Product(
|
|
|
|
Advice(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
Advice(
|
|
|
|
1,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
Fixed(
|
|
|
|
6,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
),
|
|
|
|
Scaled(
|
|
|
|
Product(
|
|
|
|
Advice(
|
|
|
|
2,
|
|
|
|
),
|
|
|
|
Fixed(
|
|
|
|
5,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
Product(
|
|
|
|
Fixed(
|
|
|
|
2,
|
|
|
|
),
|
|
|
|
Product(
|
|
|
|
Advice(
|
|
|
|
3,
|
|
|
|
),
|
|
|
|
Advice(
|
|
|
|
4,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
),
|
|
|
|
),
|
|
|
|
Product(
|
|
|
|
Fixed(
|
|
|
|
7,
|
|
|
|
),
|
|
|
|
Sum(
|
|
|
|
Advice(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
Scaled(
|
|
|
|
Instance(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
),
|
|
|
|
],
|
|
|
|
advice_queries: [
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 1,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 2,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 3,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 4,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
1,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 0,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
-1,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
],
|
|
|
|
instance_queries: [
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 0,
|
|
|
|
column_type: Instance,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
],
|
|
|
|
fixed_queries: [
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 6,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 7,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 0,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 2,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 3,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 4,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 1,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
(
|
|
|
|
Column {
|
|
|
|
index: 5,
|
|
|
|
column_type: Fixed,
|
|
|
|
},
|
|
|
|
Rotation(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
],
|
|
|
|
permutations: [
|
|
|
|
Argument {
|
|
|
|
columns: [
|
|
|
|
Column {
|
|
|
|
index: 1,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Column {
|
|
|
|
index: 2,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Column {
|
|
|
|
index: 3,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
],
|
|
|
|
},
|
|
|
|
Argument {
|
|
|
|
columns: [
|
|
|
|
Column {
|
|
|
|
index: 1,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Column {
|
|
|
|
index: 2,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
Column {
|
|
|
|
index: 3,
|
|
|
|
column_type: Advice,
|
|
|
|
},
|
|
|
|
],
|
|
|
|
},
|
|
|
|
],
|
|
|
|
lookups: [
|
|
|
|
Argument {
|
|
|
|
input_expressions: [
|
|
|
|
Advice(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
],
|
|
|
|
table_expressions: [
|
|
|
|
Fixed(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
],
|
|
|
|
},
|
|
|
|
Argument {
|
|
|
|
input_expressions: [
|
|
|
|
Product(
|
|
|
|
Advice(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
Advice(
|
|
|
|
1,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
],
|
|
|
|
table_expressions: [
|
|
|
|
Product(
|
|
|
|
Fixed(
|
|
|
|
0,
|
|
|
|
),
|
|
|
|
Fixed(
|
|
|
|
1,
|
|
|
|
),
|
|
|
|
),
|
|
|
|
],
|
|
|
|
},
|
|
|
|
],
|
|
|
|
},
|
|
|
|
fixed_commitments: [
|
2021-04-23 02:32:09 -07:00
|
|
|
(0x2bbc94ef7b22aebef24f9a4b0cc1831882548b605171366017d45c3e6fd92075, 0x082b801a6e176239943bfb759fb02138f47a5c8cc4aa7fa0af559fde4e3abd97),
|
|
|
|
(0x2bf5082b105b2156ed0e9c5b8e42bf2a240b058f74a464d080e9585274dd1e84, 0x222ad83cee7777e7a160585e212140e5e770dd8d1df788d869b5ee483a5864fb),
|
|
|
|
(0x374a656456a0aae7429b23336f825752b575dd5a44290ff614946ee59d6a20c0, 0x054491e187e6e3460e7601fb54ae10836d34d420026f96316f0c5c62f86db9b8),
|
|
|
|
(0x374a656456a0aae7429b23336f825752b575dd5a44290ff614946ee59d6a20c0, 0x054491e187e6e3460e7601fb54ae10836d34d420026f96316f0c5c62f86db9b8),
|
|
|
|
(0x02e62cd68370b13711139a08cbcdd889e800a272b9ea10acc90880fff9d89199, 0x1a96c468cb0ce77065d3a58f1e55fea9b72d15e44c01bba1e110bd0cbc6e9bc6),
|
|
|
|
(0x224ef42758215157d3ee48fb8d769da5bddd35e5929a90a4a89736f5c4b5ae9b, 0x11bc3a1e08eb320cde764f1492ecef956d71e996e2165f7a9a30ad2febb511c1),
|
|
|
|
(0x0009ccc670d8d139c168165a3bdffc9b06620c8440df66c2b35757572763a04f, 0x3e12747aa6df89dd554200e592026cc43dd529fb32de6fc6f252128d1e596a8a),
|
|
|
|
(0x12ed9a5b874da7ed995fcff158687dad0d642a4f1af67a6524078bb6fb8754b0, 0x097ac5730034c8fa454dac57d700af4b92d82691ef76c0bf9e6e6fa719a936c2),
|
2021-02-25 12:29:25 -08:00
|
|
|
],
|
|
|
|
permutations: [
|
|
|
|
VerifyingKey {
|
|
|
|
commitments: [
|
2021-04-23 02:32:09 -07:00
|
|
|
(0x1347b4b385837977a96b87f199c6a9a81520015539d1e8fa79429bb4ca229a00, 0x2168e404cabef513654d6ff516cde73f0ba87e3dc84e4b940ed675b5f66f3884),
|
|
|
|
(0x0e6d69cd2455ec43be640f6397ed65c9e51b1d8c0fd2216339314ff37ade122a, 0x222ed6dc8cfc9ea26dcc10b9d4add791ada60f2b5a63ee1e4635f88aa0c96654),
|
|
|
|
(0x13c447846f48c41a5e0675ccf88ebc0cdef2c96c51446d037acb866d24255785, 0x1f0b5414fc5e8219dbfab996eed6129d831488b2386a8b1a63663938903bd63a),
|
2021-02-25 12:29:25 -08:00
|
|
|
],
|
|
|
|
},
|
|
|
|
VerifyingKey {
|
|
|
|
commitments: [
|
2021-04-23 02:32:09 -07:00
|
|
|
(0x1347b4b385837977a96b87f199c6a9a81520015539d1e8fa79429bb4ca229a00, 0x2168e404cabef513654d6ff516cde73f0ba87e3dc84e4b940ed675b5f66f3884),
|
|
|
|
(0x0e6d69cd2455ec43be640f6397ed65c9e51b1d8c0fd2216339314ff37ade122a, 0x222ed6dc8cfc9ea26dcc10b9d4add791ada60f2b5a63ee1e4635f88aa0c96654),
|
|
|
|
(0x13c447846f48c41a5e0675ccf88ebc0cdef2c96c51446d037acb866d24255785, 0x1f0b5414fc5e8219dbfab996eed6129d831488b2386a8b1a63663938903bd63a),
|
2021-02-25 12:29:25 -08:00
|
|
|
],
|
|
|
|
},
|
|
|
|
],
|
|
|
|
}"#####
|
|
|
|
);
|
|
|
|
}
|
|
|
|
}
|