feat: implement a radix sort in MPC and use it for range checks in co…

…-noir (#290)

co-noir/co-acvm/src/mpc/rep3.rs

@@ -3,8 +3,8 @@ use std::marker::PhantomData;
 use ark_ff::PrimeField;
 use co_brillig::mpc::{Rep3BrilligDriver, Rep3BrilligType};
 use itertools::{izip, Itertools};
-use mpc_core::protocols::rep3::gadgets::sort::batcher_odd_even_merge_sort_yao;
 use mpc_core::protocols::rep3::{arithmetic, yao};
+use mpc_core::protocols::rep3_ring::gadgets::sort::radix_sort_fields;
 use mpc_core::{
     lut::LookupTableProvider,
     protocols::rep3::{
@@ -496,6 +496,6 @@ impl<F: PrimeField, N: Rep3Network> NoirWitnessExtensionProtocol<F> for Rep3Acvm
         inputs: &[Self::ArithmeticShare],
         bitsize: usize,
     ) -> std::io::Result<Vec<Self::ArithmeticShare>> {
-        batcher_odd_even_merge_sort_yao(inputs, &mut self.io_context, bitsize)
+        radix_sort_fields(inputs, &mut self.io_context, bitsize)
     }
 }

mpc-core/src/protocols/rep3/rngs.rs

@@ -8,7 +8,9 @@ use ark_ec::CurveGroup;
 use ark_ff::{One, PrimeField};
 use fancy_garbling::WireMod2;
 use num_bigint::BigUint;
-use rand::{distributions::Standard, prelude::Distribution, Rng, RngCore, SeedableRng};
+use rand::{
+    distributions::Standard, prelude::Distribution, seq::SliceRandom, Rng, RngCore, SeedableRng,
+};
 use rayon::prelude::*;
 
 #[derive(Debug)]
@@ -208,6 +210,16 @@ impl Rep3Rand {
         val & &mask
     }
 
+    /// Generate a random field_element from rng1
+    pub fn random_field_element_rng1<F: PrimeField>(&mut self) -> F {
+        F::rand(&mut self.rng1)
+    }
+
+    /// Generate a random field_element from rng2
+    pub fn random_field_element_rng2<F: PrimeField>(&mut self) -> F {
+        F::rand(&mut self.rng2)
+    }
+
     /// Generate a random `T` from rng1
     pub fn random_element_rng1<T>(&mut self) -> T
     where
@@ -230,6 +242,15 @@ impl Rep3Rand {
         let seed2 = self.rng2.gen();
         (seed1, seed2)
     }
+
+    /// Generate a random shared permutation
+    pub(crate) fn random_perm<T: Clone>(&mut self, input: Vec<T>) -> (Vec<T>, Vec<T>) {
+        let mut a = input.to_owned();
+        let mut b = input;
+        a.shuffle(&mut self.rng1);
+        b.shuffle(&mut self.rng2);
+        (a, b)
+    }
 }
 
 /// This struct is responsible for creating random shares for the Binary to Arithmetic conversion. The approach is the following: for a final sharing x = x1 + x2 + x3, we want to have random values x2, x3 and subtract these from the original value x using a binary circuit to get the share x1. Hence, we need to sample random x2 and x3 and share them amongst the parties. One RandBitComp struct is responsible for either sampling x2 or x3. For sampling x2, parties 1 and 2 will get x2 in plain (since this is the final share of x), so they need to have a PRF key from all parties. party 3, however, will not get x2 in plain and must thus only be able to sample its shares of x2, requiring two PRF keys.

mpc-core/src/protocols/rep3_ring.rs

@@ -10,6 +10,7 @@ pub mod binary;
 pub mod casts;
 pub mod conversion;
 mod detail;
+pub mod gadgets;
 pub mod ring;
 pub mod yao;
 

mpc-core/src/protocols/rep3_ring/gadgets/mod.rs

@@ -0,0 +1,5 @@
+//! Gadgets
+//!
+//! This module contains some commonly used gadgets for the Rep3 protocol.
+
+pub mod sort;