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lookup_range_check.rs: Add short range check lookup. 

Also introduce a "strict" mode for the full-length lookup, where
"true" requires the field element to be within num_words * K bits,
whereas "false" does not.
This commit is contained in:
therealyingtong 2021-06-24 18:23:01 +08:00
parent af335ff7de
commit 3840f280d7
1 changed files with 420 additions and 108 deletions
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528
src/circuit/gadget/utilities/lookup_range_check.rs
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@ -3,8 +3,8 @@
use crate::spec::lebs2ip;
use halo2::{
circuit::Region,
plonk::{Advice, Column, ConstraintSystem, Error, Fixed, Permutation},
circuit::{Layouter, Region},
plonk::{Advice, Column, ConstraintSystem, Error, Fixed, Permutation, Selector},
poly::Rotation,
};
use std::{convert::TryInto, marker::PhantomData};
@ -13,19 +13,19 @@ use ff::PrimeFieldBits;
use super::*;
#[derive(Debug, Clone)]
#[derive(Eq, PartialEq, Debug, Clone)]
pub struct LookupRangeCheckConfig<F: FieldExt + PrimeFieldBits, const K: usize> {
q_lookup: Column<Fixed>,
running_sum: Column<Advice>,
pub q_lookup: Selector,
pub q_lookup_short: Selector,
pub short_lookup_bitshift: Column<Fixed>,
pub running_sum: Column<Advice>,
constants: Column<Fixed>,
table_idx: Column<Fixed>,
perm: Permutation,
_marker: PhantomData<F>,
}
impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K> {
/// The `q_lookup` column toggles the lookup on or off. It MUST be assigned
/// outside of this helper at the appropriate offsets.
///
/// The `running_sum` advice column breaks the field element into `K`-bit
/// words. It is used to construct the input expression to the lookup
/// argument.
@ -35,21 +35,28 @@ impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K>
/// can be loaded outside this helper.
pub fn configure(
meta: &mut ConstraintSystem<F>,
q_lookup: Column<Fixed>,
running_sum: Column<Advice>,
constants: Column<Fixed>,
table_idx: Column<Fixed>,
perm: Permutation,
) -> Self {
let q_lookup = meta.selector();
let q_lookup_short = meta.selector();
let short_lookup_bitshift = meta.fixed_column();
let config = LookupRangeCheckConfig {
q_lookup,
q_lookup_short,
short_lookup_bitshift,
running_sum,
constants,
table_idx,
perm,
_marker: PhantomData,
};
// Lookup for range checks K bits and above.
meta.lookup(|meta| {
let q_lookup = meta.query_fixed(config.q_lookup, Rotation::cur());
let q_lookup = meta.query_selector(config.q_lookup);
let z_cur = meta.query_advice(config.running_sum, Rotation::cur());
let z_next = meta.query_advice(config.running_sum, Rotation::next());
// z_i = 2^{K}⋅z_{i + 1} + a_i
@ -60,6 +67,28 @@ impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K>
vec![(q_lookup * word, table)]
});
// Lookup for range checks up to S bits, where S < K.
meta.lookup(|meta| {
let q_lookup_short = meta.query_selector(config.q_lookup_short);
let word = meta.query_advice(config.running_sum, Rotation::cur());
let table = meta.query_fixed(config.table_idx, Rotation::cur());
vec![(q_lookup_short * word, table)]
});
// For short lookups, check that the word has been shifted by the correct number of bits.
meta.create_gate("Short lookup bitshift", |meta| {
let inv_two_pow_s = meta.query_fixed(config.short_lookup_bitshift, Rotation::cur());
let word = meta.query_advice(config.running_sum, Rotation::prev());
let shifted_word = meta.query_advice(config.running_sum, Rotation::cur());
let two_pow_k = F::from_u64(1 << K);
// shifted_word = word * 2^{K-s}
// = word * 2^K * inv_two_pow_s
vec![inv_two_pow_s.clone() * (word * two_pow_k * inv_two_pow_s - shifted_word)]
});
config
}
@ -67,7 +96,7 @@ impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K>
// Loads the values [0..2^K) into `table_idx`. This is only used in testing
// for now, since the Sinsemilla chip provides a pre-loaded table in the
// Orchard context.
fn load(&self, layouter: &mut impl Layouter<F>) -> Result<(), Error> {
pub fn load(&self, layouter: &mut impl Layouter<F>) -> Result<(), Error> {
layouter.assign_region(
|| "table_idx",
|mut gate| {
@ -85,19 +114,73 @@ impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K>
)
}
/// Only the lower `num_words * K` bits of the field element are constrained
/// by this function. If the field element does not fit into this range, then
/// the final cumulative sum `z_{num_words}` will be nonzero.
//
/// It is up to the caller to constrain `z_{num_words}` == 0` outside this
/// helper, or otherwise constrain upper bits not covered within the
/// `num_words * K` range.
pub fn lookup_range_check(
/// Range check on an existing cell that is copied into this helper.
pub fn copy_check(
&self,
region: &mut Region<'_, F>,
offset: usize,
mut layouter: impl Layouter<F>,
element: CellValue<F>,
num_words: usize,
strict: bool,
) -> Result<Vec<CellValue<F>>, Error> {
layouter.assign_region(
|| format!("{:?} words range check", num_words),
|mut region| {
// Copy `element` and initialize running sum `z_0 = element` to decompose it.
let z_0 = copy(
&mut region,
|| "z_0",
self.running_sum,
0,
&element,
&self.perm,
)?;
self.range_check(&mut region, z_0, num_words, strict)
},
)
}
/// Range check on a value that is witnessed in this helper.
pub fn witness_check(
&self,
mut layouter: impl Layouter<F>,
value: Option<F>,
num_words: usize,
strict: bool,
) -> Result<(CellValue<F>, Vec<CellValue<F>>), Error> {
layouter.assign_region(
|| "Witness element",
|mut region| {
let z_0 = {
let cell = region.assign_advice(
|| "Witness element",
self.running_sum,
0,
|| value.ok_or(Error::SynthesisError),
)?;
CellValue::new(cell, value)
};
let zs = self.range_check(&mut region, z_0, num_words, strict)?;
Ok((z_0, zs))
},
)
}
/// If `strict` is set to "true", the field element must fit into
/// `num_words * K` bits. In other words, the the final cumulative sum `z_{num_words}`
/// must be zero.
///
/// If `strict` is set to "false", the final `z_{num_words}` is not constrained.
///
/// `element` must have been assigned to `self.running_sum` at offset 0.
fn range_check(
&self,
region: &mut Region<'_, F>,
element: CellValue<F>,
num_words: usize,
strict: bool,
) -> Result<Vec<CellValue<F>>, Error> {
// `num_words` must fit into a single field element.
assert!(num_words * K <= F::CAPACITY as usize);
@ -126,17 +209,7 @@ impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K>
}
};
// Copy `element` and initialize running sum `z_0 = element` to decompose it.
let z_0 = copy(
region,
|| "z_0",
self.running_sum,
offset,
&element,
&self.perm,
)?;
let mut zs = vec![z_0];
let mut zs = vec![element];
// Assign cumulative sum such that
// z_i = 2^{K}⋅z_{i + 1} + a_i
@ -144,21 +217,24 @@ impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K>
//
// For `element` = a_0 + 2^10 a_1 + ... + 2^{120} a_{12}}, initialize z_0 = `element`.
// If `element` fits in 130 bits, we end up with z_{13} = 0.
let mut z = z_0;
let mut z = element;
let inv_two_pow_k = F::from_u64(1u64 << K).invert().unwrap();
for (idx, word) in words.into_iter().enumerate() {
for (idx, word) in words.iter().enumerate() {
// Enable lookup on this row
self.q_lookup.enable(region, idx)?;
// z_next = (z_cur - m_cur) / 2^K
z = {
let z_val = z
.value()
.zip(word)
.zip(*word)
.map(|(z, word)| (z - word) * inv_two_pow_k);
// Assign z_next
let z_cell = region.assign_advice(
|| format!("z_{:?}", idx + 1),
self.running_sum,
offset + idx + 1,
idx + 1,
|| z_val.ok_or(Error::SynthesisError),
)?;
@ -167,21 +243,136 @@ impl<F: FieldExt + PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K>
zs.push(z);
}
if strict {
// Constrain the final `z` to be zero.
let cell =
region.assign_fixed(|| "zero", self.constants, words.len(), || Ok(F::zero()))?;
region.constrain_equal(&self.perm, z.cell(), cell)?;
}
Ok(zs)
}
/// Short range check on an existing cell that is copied into this helper.
///
/// # Panics
///
/// Panics if NUM_BITS is equal to or larger than K.
pub fn copy_short_check(
&self,
mut layouter: impl Layouter<F>,
element: CellValue<F>,
num_bits: usize,
) -> Result<(), Error> {
assert!(num_bits < K);
layouter.assign_region(
|| format!("Range check {:?} bits", num_bits),
|mut region| {
// Copy `element` to use in the k-bit lookup.
let element = copy(
&mut region,
|| "element",
self.running_sum,
0,
&element,
&self.perm,
)?;
self.short_range_check(&mut region, element, num_bits)
},
)
}
/// Short range check on value that is witnessed in this helper.
///
/// # Panics
///
/// Panics if num_bits is larger than K.
pub fn witness_short_check(
&self,
mut layouter: impl Layouter<F>,
element: Option<F>,
num_bits: usize,
) -> Result<CellValue<F>, Error> {
assert!(num_bits <= K);
layouter.assign_region(
|| format!("Range check {:?} bits", num_bits),
|mut region| {
// Witness `element` to use in the k-bit lookup.
let element = {
let cell = region.assign_advice(
|| "Witness element",
self.running_sum,
0,
|| element.ok_or(Error::SynthesisError),
)?;
CellValue::new(cell, element)
};
self.short_range_check(&mut region, element, num_bits)?;
Ok(element)
},
)
}
/// Constrain `x` to be a NUM_BITS word.
///
/// `element` must have been assigned to `self.running_sum` at offset 0.
fn short_range_check(
&self,
region: &mut Region<'_, F>,
element: CellValue<F>,
num_bits: usize,
) -> Result<(), Error> {
// Enable lookup for `element`, to constrain it to 10 bits.
self.q_lookup_short.enable(region, 0)?;
// Assign 2^{-num_bits} in a fixed column.
{
// 2^{-num_bits}
let inv_two_pow_s = F::from_u64(1 << num_bits).invert().unwrap();
region.assign_fixed(
|| format!("2^(-{})", num_bits),
self.short_lookup_bitshift,
1,
|| Ok(inv_two_pow_s),
)?;
}
// Assign shifted `element * 2^{K - num_bits}`
let shifted = element.value().map(|element| {
let shift = F::from_u64(1 << (K - num_bits));
element * shift
});
print!("element: {:?}", element.value());
print!("shifted: {:?}", shifted);
region.assign_advice(
|| format!("element * 2^({}-{})", K, num_bits),
self.running_sum,
1,
|| shifted.ok_or(Error::SynthesisError),
)?;
// Enable lookup for shifted element, to constrain it to 10 bits.
self.q_lookup_short.enable(region, 1)?;
Ok(())
}
}
#[cfg(test)]
mod tests {
use super::super::{CellValue, UtilitiesInstructions, Var};
use super::super::Var;
use super::LookupRangeCheckConfig;
use crate::primitives::sinsemilla::{INV_TWO_POW_K, K};
use crate::spec::lebs2ip;
use ff::PrimeFieldBits;
use ff::{Field, PrimeFieldBits};
use halo2::{
circuit::{layouter::SingleChipLayouter, Layouter},
dev::MockProver,
dev::{MockProver, VerifyFailure},
plonk::{Assignment, Circuit, ConstraintSystem, Error},
};
use pasta_curves::{arithmetic::FieldExt, pallas};
@ -191,27 +382,23 @@ mod tests {
#[test]
fn lookup_range_check() {
struct MyCircuit<F: FieldExt + PrimeFieldBits> {
num_words: usize,
_marker: PhantomData<F>,
}
impl<F: FieldExt + PrimeFieldBits> UtilitiesInstructions<F> for MyCircuit<F> {
type Var = CellValue<F>;
}
impl<F: FieldExt + PrimeFieldBits> Circuit<F> for MyCircuit<F> {
type Config = LookupRangeCheckConfig<F, K>;
fn configure(meta: &mut ConstraintSystem<F>) -> Self::Config {
let running_sum = meta.advice_column();
let constants = meta.fixed_column();
let table_idx = meta.fixed_column();
let q_lookup = meta.fixed_column();
let perm = meta.permutation(&[running_sum.into()]);
let perm = meta.permutation(&[running_sum.into(), constants.into()]);
LookupRangeCheckConfig::<F, K>::configure(
meta,
q_lookup,
running_sum,
constants,
table_idx,
perm,
)
@ -227,45 +414,51 @@ mod tests {
// Load table_idx
config.load(&mut layouter)?;
let num_words = 6;
// Lookup constraining element to be no longer than num_words * K bits.
let elements_and_expected_final_zs = [
(F::from_u64((1 << (num_words * K)) - 1), F::zero()), // a word that is within num_words * K bits long
(F::from_u64(1 << (num_words * K)), F::one()), // a word that is just over num_words * K bits long
(
F::from_u64((1 << (self.num_words * K)) - 1),
F::zero(),
true,
), // a word that is within self.num_words * K bits long
(F::from_u64(1 << (self.num_words * K)), F::one(), false), // a word that is just over self.num_words * K bits long
];
for (element, expected_final_z) in elements_and_expected_final_zs.iter() {
let expected_zs = expected_zs::<F, K>(*element, num_words);
fn expected_zs<F: FieldExt + PrimeFieldBits, const K: usize>(
element: F,
num_words: usize,
) -> Vec<F> {
let chunks = {
element
.to_le_bits()
.iter()
.by_val()
.take(num_words * K)
.collect::<Vec<_>>()
.chunks_exact(K)
.map(|chunk| F::from_u64(lebs2ip::<K>(chunk.try_into().unwrap())))
.collect::<Vec<_>>()
};
let expected_zs = {
let inv_two_pow_k = F::from_bytes(&INV_TWO_POW_K).unwrap();
chunks.iter().fold(vec![element], |mut zs, a_i| {
// z_{i + 1} = (z_i - a_i) / 2^{K}
let z = (zs[zs.len() - 1] - a_i) * inv_two_pow_k;
zs.push(z);
zs
})
};
expected_zs
}
// Load the value to be decomposed into the circuit.
let element = self.load_private(
layouter.namespace(|| "element"),
config.running_sum,
for (element, expected_final_z, strict) in elements_and_expected_final_zs.iter() {
let expected_zs = expected_zs::<F, K>(*element, self.num_words);
let (_, zs) = config.witness_check(
layouter.namespace(|| format!("Lookup {:?}", self.num_words)),
Some(*element),
)?;
// Although this fixed column assignment can be done
// within the `lookup_range_check` method, in practice
// the information needed to toggle the lookup depends
// on some external business logic (e.g. whether the
// top bit of `element` is set).
//
// Leaving the toggle assignment to the caller gives
// them the freedom to define this business logic.
let zs = layouter.assign_region(
|| "word within range",
|mut region| {
for idx in 0..num_words {
// Assign fixed column to activate lookup.
region.assign_fixed(
|| format!("lookup on row {}", idx),
config.q_lookup,
idx,
|| Ok(F::one()),
)?;
}
config.lookup_range_check(&mut region, 0, element, num_words)
},
self.num_words,
*strict,
)?;
assert_eq!(*expected_zs.last().unwrap(), *expected_final_z);
@ -276,13 +469,13 @@ mod tests {
}
}
}
Ok(())
}
}
{
let circuit: MyCircuit<pallas::Base> = MyCircuit {
num_words: 6,
_marker: PhantomData,
};
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
@ -290,31 +483,150 @@ mod tests {
}
}
#[cfg(test)]
fn expected_zs<F: FieldExt + PrimeFieldBits, const K: usize>(
element: F,
num_words: usize,
) -> Vec<F> {
let chunks = {
element
.to_le_bits()
.iter()
.by_val()
.take(num_words * K)
.collect::<Vec<_>>()
.chunks_exact(K)
.map(|chunk| F::from_u64(lebs2ip::<K>(chunk.try_into().unwrap())))
.collect::<Vec<_>>()
};
let expected_zs = {
let inv_two_pow_k = F::from_bytes(&INV_TWO_POW_K).unwrap();
chunks.iter().fold(vec![element], |mut zs, a_i| {
// z_{i + 1} = (z_i - a_i) / 2^{K}
let z = (zs[zs.len() - 1] - a_i) * inv_two_pow_k;
zs.push(z);
zs
})
};
expected_zs
#[test]
fn short_range_check() {
struct MyCircuit<F: FieldExt + PrimeFieldBits> {
element: Option<F>,
num_bits: usize,
_marker: PhantomData<F>,
}
impl<F: FieldExt + PrimeFieldBits> Circuit<F> for MyCircuit<F> {
type Config = LookupRangeCheckConfig<F, K>;
fn configure(meta: &mut ConstraintSystem<F>) -> Self::Config {
let running_sum = meta.advice_column();
let constants = meta.fixed_column();
let table_idx = meta.fixed_column();
let perm = meta.permutation(&[running_sum.into()]);
LookupRangeCheckConfig::<F, K>::configure(
meta,
running_sum,
constants,
table_idx,
perm,
)
}
fn synthesize(
&self,
cs: &mut impl Assignment<F>,
config: Self::Config,
) -> Result<(), Error> {
let mut layouter = SingleChipLayouter::new(cs)?;
// Load table_idx
config.load(&mut layouter)?;
// Lookup constraining element to be no longer than num_bits.
config.witness_short_check(
layouter.namespace(|| format!("Lookup {:?} bits", self.num_bits)),
self.element,
self.num_bits,
)?;
Ok(())
}
}
// Edge case: zero bits
{
let circuit: MyCircuit<pallas::Base> = MyCircuit {
element: Some(pallas::Base::zero()),
num_bits: 0,
_marker: PhantomData,
};
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
assert_eq!(prover.verify(), Ok(()));
}
// Edge case: K bits
{
let circuit: MyCircuit<pallas::Base> = MyCircuit {
element: Some(pallas::Base::from_u64((1 << K) - 1)),
num_bits: K,
_marker: PhantomData,
};
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
assert_eq!(prover.verify(), Ok(()));
}
// Element within `num_bits`
{
let circuit: MyCircuit<pallas::Base> = MyCircuit {
element: Some(pallas::Base::from_u64((1 << 6) - 1)),
num_bits: 6,
_marker: PhantomData,
};
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
assert_eq!(prover.verify(), Ok(()));
}
// Element larger than `num_bits` but within K bits
{
let circuit: MyCircuit<pallas::Base> = MyCircuit {
element: Some(pallas::Base::from_u64(1 << 6)),
num_bits: 6,
_marker: PhantomData,
};
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
assert_eq!(
prover.verify(),
Err(vec![VerifyFailure::Lookup {
lookup_index: 1,
row: 1
}])
);
}
// Element larger than K bits
{
let circuit: MyCircuit<pallas::Base> = MyCircuit {
element: Some(pallas::Base::from_u64(1 << K)),
num_bits: 6,
_marker: PhantomData,
};
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
assert_eq!(
prover.verify(),
Err(vec![
VerifyFailure::Lookup {
lookup_index: 1,
row: 0
},
VerifyFailure::Lookup {
lookup_index: 1,
row: 1
},
])
);
}
// Element which is not within `num_bits`, but which has a shifted value within
// num_bits
{
let num_bits = 6;
let shifted = pallas::Base::from_u64((1 << num_bits) - 1);
// Recall that shifted = element * 2^{K-s}
// => element = shifted * 2^{s-K}
let element = shifted
* pallas::Base::from_u64(1 << (K as u64 - num_bits))
.invert()
.unwrap();
let circuit: MyCircuit<pallas::Base> = MyCircuit {
element: Some(element),
num_bits: num_bits as usize,
_marker: PhantomData,
};
let prover = MockProver::<pallas::Base>::run(11, &circuit, vec![]).unwrap();
assert_eq!(
prover.verify(),
Err(vec![VerifyFailure::Lookup {
lookup_index: 1,
row: 0
}])
);
}
}
}