✨ Less Than

mpc-algebra/examples/algebra.rs

@@ -3,10 +3,11 @@ use std::path::PathBuf;
 use ark_ff::{BigInteger, BigInteger256, Field, FpParameters, PrimeField, UniformRand};
 use ark_ff::{One, Zero};
 use ark_poly::reveal;
+use ark_std::{end_timer, start_timer};
 use log::debug;
 use mpc_algebra::{
     AdditiveFieldShare, BitAdd, BitDecomposition, BitwiseLessThan, EqualityZero,
-    IntervalTestHalfModulus, LogicalOperations, MpcField, Reveal, UniformBitRand,
+    LessThan, LogicalOperations, MpcField, Reveal, UniformBitRand,
 };
 use mpc_net::{MpcMultiNet as Net, MpcNet};
 
@@ -178,6 +179,20 @@ fn test_interval_test_half_modulus() {
     }
 }
 
+fn test_less_than() {
+    let mut rng = ark_std::test_rng();
+
+    for _ in 0..5 {
+        let timer = start_timer!(|| "less_than test");
+        let a = MF::bit_rand(&mut rng);
+        let b = MF::bit_rand(&mut rng);
+
+        let res = a.less_than(&b);
+        assert_eq!(res.reveal().is_one(), a.reveal() < b.reveal());
+        end_timer!(timer)
+    }
+}
+
 fn test_and() {
     let mut rng = ark_std::test_rng();
 
@@ -352,6 +367,8 @@ fn main() {
 
     test_bit_rand();
     println!("Test bit_rand passed");
+    test_less_than();
+    println!("Test less_than passed");
     test_interval_test_half_modulus();
     println!("Test interval_test_half_modulus passed");
     test_rand_number_bitwise();

mpc-algebra/src/mpc_primitives.rs

@@ -13,10 +13,11 @@ pub trait BitwiseLessThan {
     fn bitwise_lt(&self, other: &Self) -> Self::Output;
 }
 
-pub trait IntervalTestHalfModulus {
+pub trait LessThan : UniformBitRand {
     type Output;
-
+    
     fn interval_test_half_modulus(&self) -> Self::Output;
+    fn less_than(&self, other: &Self) -> Self::Output;
 }
 
 pub trait LogicalOperations {

mpc-algebra/src/wire/field.rs

@@ -3,6 +3,7 @@ use derivative::Derivative;
 use mpc_trait::MpcWire;
 use num_bigint::BigUint;
 use rand::Rng;
+use core::panic;
 use std::fmt::{self, Debug, Display};
 use std::io::{self, Read, Write};
 use std::iter::{Product, Sum};
@@ -22,7 +23,7 @@ use ark_serialize::{
 
 // use crate::channel::MpcSerNet;
 use crate::share::field::FieldShare;
-use crate::{BeaverSource, BitAdd, BitDecomposition, BitwiseLessThan, IntervalTestHalfModulus, LogicalOperations, Reveal};
+use crate::{BeaverSource, BitAdd, BitDecomposition, BitwiseLessThan, LessThan, LogicalOperations, Reveal};
 use crate::{EqualityZero, UniformBitRand};
 use mpc_net::{MpcMultiNet as Net, MpcNet};
 
@@ -301,9 +302,8 @@ impl<F: PrimeField, S: FieldShare<F>> BitwiseLessThan for Vec<MpcField<F, S>> {
 }
 
 
-impl<F: PrimeField + SquareRootField, S: FieldShare<F>> IntervalTestHalfModulus for MpcField<F,S> {
+impl<F: PrimeField + SquareRootField, S: FieldShare<F>> LessThan for MpcField<F,S> {
     type Output = Self;
-
     // check if shared value a is in the interval [0, modulus/2)
     fn interval_test_half_modulus(&self) -> Self::Output {
         // define double self as x
@@ -334,6 +334,15 @@ impl<F: PrimeField + SquareRootField, S: FieldShare<F>> IntervalTestHalfModulus
         // return 1 - lsb_x
         one - lsb_x
     }
+
+    fn less_than(&self, other: &Self) -> Self::Output {
+        // [z]=[b−a<p/2],[x]=[a<p/2],[y]=[b>p/2]
+        // ([z]∧[x])∨([z]∧[y])∨(¬[z]∧[x]∧[y])=[z(x+y)+(1−2z)xy].
+        let z = (*other-self).interval_test_half_modulus();
+        let x = self.interval_test_half_modulus();
+        let y = Self::one() - other.interval_test_half_modulus();
+        z*(x+y)+(Self::one()-Self::from_public(F::from(2u8))*z)*x*y
+    }
 }
 
 impl<F: Field, S: FieldShare<F>> LogicalOperations for Vec<MpcField<F, S>> {