mirror of
https://github.com/arnaucube/ark-r1cs-std.git
synced 2026-01-10 16:01:28 +01:00
adds a smaller than gadget
This commit is contained in:
Kobi Gurkan
committed by
Pratyush Mishra
Pratyush Mishra
parent
33f7d3988f
commit
ccbb5ef553
@@ -62,6 +62,7 @@ pub mod pairing;
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pub mod alloc;
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pub mod eq;
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pub mod select;
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pub mod smaller_than;
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pub mod prelude {
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pub use crate::{
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250
r1cs-std/src/smaller_than.rs
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250
r1cs-std/src/smaller_than.rs
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@@ -0,0 +1,250 @@
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use crate::{
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boolean::Boolean,
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fields::{fp::FpGadget, FieldGadget},
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ToBitsGadget,
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};
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use algebra::PrimeField;
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use r1cs_core::{ConstraintSystem, SynthesisError};
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use std::marker::PhantomData;
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pub struct SmallerThanGadget<ConstraintF: PrimeField> {
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constraint_field_type: PhantomData<ConstraintF>,
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}
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impl<ConstraintF: PrimeField> SmallerThanGadget<ConstraintF> {
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// the function assumes a and b are known to be <= (p-1)/2
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pub fn is_smaller_than<CS: ConstraintSystem<ConstraintF>>(
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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) -> Result<Boolean, SynthesisError> {
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let two = ConstraintF::one() + ConstraintF::one();
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let d0 = a.sub(cs.ns(|| "a - b"), b)?;
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let d = d0.mul_by_constant(cs.ns(|| "mul 2"), &two)?;
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let d_bits = d.to_bits_strict(cs.ns(|| "d to bits"))?;
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let d_bits_len = d_bits.len();
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Ok(d_bits[d_bits_len - 1])
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}
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// the function assumes a and b are known to be <= (p-1)/2
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pub fn is_smaller_than_or_equal_to<CS: ConstraintSystem<ConstraintF>>(
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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) -> Result<Boolean, SynthesisError> {
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let b_plus_one = b.add_constant(cs.ns(|| "plus one"), &ConstraintF::one())?;
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Self::is_smaller_than(cs.ns(|| "is smaller than"), a, &b_plus_one)
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}
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// the function assumes a and b are known to be <= (p-1)/2
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pub fn enforce_smaller_than<CS: ConstraintSystem<ConstraintF>>(
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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) -> Result<(), SynthesisError> {
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let is_smaller_than = Self::is_smaller_than(cs.ns(|| "is smaller than"), a, b)?;
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cs.enforce(
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|| "enforce smaller than",
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|_| is_smaller_than.lc(CS::one(), ConstraintF::one()),
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|lc| lc + (ConstraintF::one(), CS::one()),
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|lc| lc + (ConstraintF::one(), CS::one()),
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);
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Ok(())
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}
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// the function assumes a and b are known to be <= (p-1)/2
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pub fn enforce_smaller_than_or_equal_to<CS: ConstraintSystem<ConstraintF>>(
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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) -> Result<(), SynthesisError> {
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let b_plus_one = b.add_constant(cs.ns(|| "plus one"), &ConstraintF::one())?;
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Self::enforce_smaller_than(cs.ns(|| "enforce smaller than"), a, &b_plus_one)
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}
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pub fn enforce_smaller_than_strict<CS: ConstraintSystem<ConstraintF>>(
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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) -> Result<(), SynthesisError> {
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let a_bits = a.to_bits(cs.ns(|| "a to bits"))?;
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Boolean::enforce_smaller_or_equal_than::<_, _, ConstraintF, _>(
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cs.ns(|| "enforce a smaller than modulus minus one div two"),
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&a_bits,
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ConstraintF::modulus_minus_one_div_two(),
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)?;
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let b_bits = b.to_bits(cs.ns(|| "b to bits"))?;
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Boolean::enforce_smaller_or_equal_than::<_, _, ConstraintF, _>(
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cs.ns(|| "enforce b smaller than modulus minus one div two"),
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&b_bits,
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ConstraintF::modulus_minus_one_div_two(),
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)?;
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let is_smaller_than = Self::is_smaller_than(cs.ns(|| "is smaller than"), a, b)?;
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cs.enforce(
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|| "enforce smaller than",
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|_| is_smaller_than.lc(CS::one(), ConstraintF::one()),
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|lc| lc + (ConstraintF::one(), CS::one()),
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|lc| lc + (ConstraintF::one(), CS::one()),
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);
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Ok(())
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}
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pub fn enforce_smaller_than_or_equal_to_strict<CS: ConstraintSystem<ConstraintF>>(
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mut cs: CS,
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a: &FpGadget<ConstraintF>,
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b: &FpGadget<ConstraintF>,
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) -> Result<(), SynthesisError> {
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let b_plus_one = b.add_constant(cs.ns(|| "plus one"), &ConstraintF::one())?;
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Self::enforce_smaller_than_strict(cs.ns(|| "enforce smaller than strict"), a, &b_plus_one)
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}
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}
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#[cfg(test)]
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mod test {
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use rand::{Rng, SeedableRng};
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use rand_xorshift::XorShiftRng;
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use std::cmp::Ordering;
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use super::SmallerThanGadget;
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use crate::{
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alloc::AllocGadget, fields::fp::FpGadget, test_constraint_system::TestConstraintSystem,
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};
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use algebra::{bls12_381::Fr, PrimeField, UniformRand};
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use r1cs_core::ConstraintSystem;
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#[test]
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fn test_smaller_than() {
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let mut rng = &mut XorShiftRng::from_seed([
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0x5d, 0xbe, 0x62, 0x59, 0x8d, 0x31, 0x3d, 0x76, 0x32, 0x37, 0xdb, 0x17, 0xe5, 0xbc,
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0x06, 0x54,
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]);
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fn rand_in_range<R: Rng>(rng: &mut R) -> Fr {
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let pminusonedivtwo = Fr::from_repr(Fr::modulus_minus_one_div_two());
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let mut r;
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loop {
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r = Fr::rand(rng);
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if r <= pminusonedivtwo {
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break;
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}
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}
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r
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}
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for i in 0..10 {
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let mut cs = TestConstraintSystem::<Fr>::new();
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let a = rand_in_range(&mut rng);
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let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
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let b = rand_in_range(&mut rng);
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let b_var = FpGadget::<Fr>::alloc(cs.ns(|| "b"), || Ok(b)).unwrap();
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match a.cmp(&b) {
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Ordering::Less => {
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SmallerThanGadget::<Fr>::enforce_smaller_than_strict(
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cs.ns(|| "smaller than test"),
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&a_var,
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&b_var,
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)
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.unwrap();
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SmallerThanGadget::<Fr>::enforce_smaller_than_or_equal_to_strict(
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cs.ns(|| "smaller than test 2"),
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&a_var,
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&b_var,
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)
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.unwrap();
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},
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Ordering::Greater => {
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SmallerThanGadget::<Fr>::enforce_smaller_than_strict(
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cs.ns(|| "smaller than test"),
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&b_var,
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&a_var,
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)
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.unwrap();
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SmallerThanGadget::<Fr>::enforce_smaller_than_or_equal_to_strict(
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cs.ns(|| "smaller than test 2"),
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&b_var,
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&a_var,
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)
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.unwrap();
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},
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_ => {},
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}
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if i == 0 {
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println!("number of constraints: {}", cs.num_constraints());
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}
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assert!(cs.is_satisfied());
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}
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for _i in 0..10 {
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let mut cs = TestConstraintSystem::<Fr>::new();
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let a = rand_in_range(&mut rng);
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let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
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let b = rand_in_range(&mut rng);
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let b_var = FpGadget::<Fr>::alloc(cs.ns(|| "b"), || Ok(b)).unwrap();
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match b.cmp(&a) {
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Ordering::Less => {
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SmallerThanGadget::<Fr>::enforce_smaller_than_strict(
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cs.ns(|| "smaller than test"),
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&a_var,
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&b_var,
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)
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.unwrap();
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SmallerThanGadget::<Fr>::enforce_smaller_than_or_equal_to_strict(
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cs.ns(|| "smaller than test 2"),
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&a_var,
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&b_var,
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)
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.unwrap();
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},
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Ordering::Greater => {
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SmallerThanGadget::<Fr>::enforce_smaller_than_strict(
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cs.ns(|| "smaller than test"),
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&b_var,
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&a_var,
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)
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.unwrap();
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SmallerThanGadget::<Fr>::enforce_smaller_than_or_equal_to(
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cs.ns(|| "smaller than test 2"),
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&b_var,
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&a_var,
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)
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.unwrap();
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},
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_ => {},
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}
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assert!(!cs.is_satisfied());
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}
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for _i in 0..10 {
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let mut cs = TestConstraintSystem::<Fr>::new();
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let a = rand_in_range(&mut rng);
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let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
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SmallerThanGadget::<Fr>::enforce_smaller_than_strict(
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cs.ns(|| "smaller than test"),
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&a_var,
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&a_var,
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)
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.unwrap();
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assert!(!cs.is_satisfied());
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}
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for _i in 0..10 {
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let mut cs = TestConstraintSystem::<Fr>::new();
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let a = rand_in_range(&mut rng);
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let a_var = FpGadget::<Fr>::alloc(cs.ns(|| "a"), || Ok(a)).unwrap();
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SmallerThanGadget::<Fr>::enforce_smaller_than_or_equal_to(
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cs.ns(|| "smaller than or equal to test"),
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&a_var,
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&a_var,
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)
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.unwrap();
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assert!(cs.is_satisfied());
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}
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}
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}
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