[FIX] m31 exp (#96)

* chore: test vectors for M31

* fix: M31 exponentiation

---------

Co-authored-by: enpsi <[email protected]>

.gitignore

@@ -19,6 +19,9 @@ Cargo.lock
 # Project data
 notes.md
 
+# Generated by SageMath
+*.sage.py
+
 # Programming env
 .vscode/
 perf.data

arith/src/field/m31.rs

@@ -131,7 +131,7 @@ impl Field for M31 {
         while !e.is_zero() {
             let b = e & 1;
             if b == 1 {
-                res *= self;
+                res *= t;
             }
             t = t * t;
             e >>= 1;

arith/src/tests/m31.rs

@@ -2,7 +2,7 @@ use std::io::Cursor;
 
 use ark_std::test_rng;
 
-use crate::{FieldSerde, M31x16, M31};
+use crate::{Field, FieldSerde, M31x16, M31};
 
 use super::{
     field::{random_field_tests, random_inversion_tests},
@@ -32,3 +32,15 @@ fn test_custom_serde_vectorize_m31() {
     let b = b.unwrap();
     assert_eq!(a, b);
 }
+
+/// Compare to test vectors generated in SageMath
+#[test]
+fn test_vectors() {
+    // M31 inversion
+    let a = M31::from(3);
+    let a_inv = M31::from(1431655765);
+    assert_eq!(a_inv, a.inv().unwrap());
+    // M31 exponentiation
+    let a_pow_11 = M31::from(177147);
+    assert_eq!(a_pow_11, a.exp(11));
+}

arith/src/tests/m31_ext.rs

@@ -13,3 +13,36 @@ fn test_field() {
     random_extension_field_tests::<M31Ext3x16>("Simd M31 Ext3".to_string());
     random_simd_field_tests::<M31Ext3x16>("Simd M31 Ext3".to_string());
 }
+
+/// Compare to test vectors generated in SageMath
+#[test]
+fn test_vectors() {
+    use crate::{Field, M31};
+    let a = M31Ext3 {
+        v: [M31::from(1), M31::from(2), M31::from(3)],
+    };
+    let b = M31Ext3 {
+        v: [M31::from(4), M31::from(5), M31::from(6)],
+    };
+    let expected_prod = M31Ext3 {
+        v: [M31::from(139), M31::from(103), M31::from(28)],
+    };
+    assert_eq!(expected_prod, a * b);
+
+    let expected_inv = M31Ext3 {
+        v: [
+            M31::from(1279570927),
+            M31::from(2027416670),
+            M31::from(696388467),
+        ],
+    };
+    assert_eq!(expected_inv, a.inv().unwrap());
+    let a_pow_11 = M31Ext3 {
+        v: [
+            M31::from(2145691179),
+            M31::from(1848238717),
+            M31::from(1954563431),
+        ],
+    };
+    assert_eq!(a_pow_11, a.exp(11));
+}

arith/src/tests/test_vectors.sage

@@ -0,0 +1,24 @@
+# Generate test vectors for the field implementations using SageMath
+# Usage: sage test_vectors.sage
+
+# M31 Field
+p = 2**31 - 1
+print("M31 Field")
+print(f"p = {p}")
+F = GF(p)
+a = F(3)
+print(f"a = {a}")
+print(f"a^(-1) = {a^(-1)}")
+print(f"a^(11) = {a^(11)}")
+
+# Degree 3 extension
+R.<x> = F[]
+K.<a> = F.extension(x^3 - 5)
+print("M31 Degree 3 Extension")
+b = 1 + 2*a + 3*a^2
+c = 4 + 5*a + 6*a^2
+print(f"b = {b}")
+print(f"c = {c}")
+print(f"b*c = {b*c}")
+print(f"b^(-1) = {b^(-1)}")
+print(f"b^(11) = {b^(11)}")