change ring for Fp2

README.md

@@ -3,7 +3,7 @@ Implementation of Goldilocks and its extension fields
 
 This repo implements 
 - Goldilocks Field mod `2^64 - 2^32 + 1`
-- Goldilocks quadratic extension over `x^2 + 1`
+- Goldilocks quadratic extension over `x^2 - 7`
 - Goldilocks cubic extension over `x^3 - x - 1`
 
 Traits are compatible with `ff 0.13.0`.

src/fp2.rs

@@ -1,4 +1,4 @@
-//! This module implements Goldilocks quadratic extension field mod x^2 + 1
+//! This module implements Goldilocks quadratic extension field mod x^2 - 7
 
 use crate::Goldilocks;
 use core::iter::{Product, Sum};
@@ -8,15 +8,16 @@ use rand_core::RngCore;
 use serde::{Deserialize, Serialize};
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
-/// Degree 3 Goldilocks extension field mod x^2 + 1
+/// Degree 3 Goldilocks extension field mod x^2 - 7 
 #[derive(Clone, Copy, Debug, Default, PartialEq, Eq, Serialize, Deserialize)]
 pub struct GoldilocksExt2(pub [Goldilocks; 2]);
 
 /// For a = (a1, a2) and b = (b1, b2)
 /// The multiplication is define as
-/// c := a * b = a(x) * b(x) % (x^2 + 1)
-///    = x*a2*b1 + x*a1*b2
-///    + a1*b1 - a2*b2
+/// c := a * b = a(x) * b(x) % (x^2 - 7)
+///    = x*a2*b1 + x*a1*b2 
+///    + a1*b1 + 7*a2*b2
+
 
 /// This requires 9 multiplications and 6 1 additions
 fn mul_internal(a: &GoldilocksExt2, b: &GoldilocksExt2) -> GoldilocksExt2 {
@@ -26,7 +27,7 @@ fn mul_internal(a: &GoldilocksExt2, b: &GoldilocksExt2) -> GoldilocksExt2 {
     let a2b1 = a.0[1] * b.0[0];
     let a2b2 = a.0[1] * b.0[1];
 
-    let c1 = a1b1 - a2b2;
+    let c1 = a1b1 + Goldilocks(7) * a2b2;
     let c2 = a2b1 + a1b2;
     GoldilocksExt2([c1, c2])
 }

src/tests/fp2.rs

@@ -13,6 +13,6 @@ fn test_field() {
 fn known_answer_tests() {
     let a = GoldilocksExt2([Goldilocks::from(1), Goldilocks::from(2)]);
     let b = GoldilocksExt2([Goldilocks::from(3), Goldilocks::from(4)]);
-    let c = GoldilocksExt2([-Goldilocks::from(5), Goldilocks::from(10)]);
+    let c = GoldilocksExt2([Goldilocks::from(59), Goldilocks::from(10)]);
     assert_eq!(a * b, c)
 }