From 6db30c6db355e621374308cdfed34414d5ae7d42 Mon Sep 17 00:00:00 2001
From: Daniel Lubarov <daniel@lubarov.com>
Date: Wed, 28 Apr 2021 14:42:21 -0700
Subject: [PATCH] Precomputed MDS matrix for CrandallField

---
 src/field/crandall_field.rs | 95 +++++++++++++++++++++++++++++++++++++
 src/field/field.rs          |  2 +-
 2 files changed, 96 insertions(+), 1 deletion(-)

diff --git a/src/field/crandall_field.rs b/src/field/crandall_field.rs
index 1ff8d9d4..b874578d 100644
--- a/src/field/crandall_field.rs
+++ b/src/field/crandall_field.rs
@@ -11,6 +11,90 @@ use std::iter::{Product, Sum};
 /// EPSILON = 9 * 2**28 - 1
 const EPSILON: u64 = 2415919103;
 
+/// A precomputed 8*8 Cauchy matrix, generated with `Field::mds_8`.
+const CAUCHY_MDS_8: [[CrandallField; 8]; 8] = [
+    [
+        CrandallField(16140901062381928449),
+        CrandallField(2635249153041947502),
+        CrandallField(3074457345215605419),
+        CrandallField(11068046442776179508),
+        CrandallField(13835058053470224385),
+        CrandallField(6148914690431210838),
+        CrandallField(9223372035646816257),
+        CrandallField(1),
+    ],
+    [
+        CrandallField(2049638230143736946),
+        CrandallField(16140901062381928449),
+        CrandallField(2635249153041947502),
+        CrandallField(3074457345215605419),
+        CrandallField(11068046442776179508),
+        CrandallField(13835058053470224385),
+        CrandallField(6148914690431210838),
+        CrandallField(9223372035646816257),
+    ],
+    [
+        CrandallField(5534023221388089754),
+        CrandallField(2049638230143736946),
+        CrandallField(16140901062381928449),
+        CrandallField(2635249153041947502),
+        CrandallField(3074457345215605419),
+        CrandallField(11068046442776179508),
+        CrandallField(13835058053470224385),
+        CrandallField(6148914690431210838),
+    ],
+    [
+        CrandallField(16769767337539665921),
+        CrandallField(5534023221388089754),
+        CrandallField(2049638230143736946),
+        CrandallField(16140901062381928449),
+        CrandallField(2635249153041947502),
+        CrandallField(3074457345215605419),
+        CrandallField(11068046442776179508),
+        CrandallField(13835058053470224385),
+    ],
+    [
+        CrandallField(10760600708254618966),
+        CrandallField(16769767337539665921),
+        CrandallField(5534023221388089754),
+        CrandallField(2049638230143736946),
+        CrandallField(16140901062381928449),
+        CrandallField(2635249153041947502),
+        CrandallField(3074457345215605419),
+        CrandallField(11068046442776179508),
+    ],
+    [
+        CrandallField(5675921252705733081),
+        CrandallField(10760600708254618966),
+        CrandallField(16769767337539665921),
+        CrandallField(5534023221388089754),
+        CrandallField(2049638230143736946),
+        CrandallField(16140901062381928449),
+        CrandallField(2635249153041947502),
+        CrandallField(3074457345215605419),
+    ],
+    [
+        CrandallField(1317624576520973751),
+        CrandallField(5675921252705733081),
+        CrandallField(10760600708254618966),
+        CrandallField(16769767337539665921),
+        CrandallField(5534023221388089754),
+        CrandallField(2049638230143736946),
+        CrandallField(16140901062381928449),
+        CrandallField(2635249153041947502),
+    ],
+    [
+        CrandallField(15987178195121148178),
+        CrandallField(1317624576520973751),
+        CrandallField(5675921252705733081),
+        CrandallField(10760600708254618966),
+        CrandallField(16769767337539665921),
+        CrandallField(5534023221388089754),
+        CrandallField(2049638230143736946),
+        CrandallField(16140901062381928449),
+    ],
+];
+
 /// A field designed for use with the Crandall reduction algorithm.
 ///
 /// Its order is
@@ -224,6 +308,17 @@ impl Field for CrandallField {
         let x74 = x73 * x39;
         x74
     }
+
+    fn mds_8(vec: [Self; 8]) -> [Self; 8] {
+        let mut result = [Self::ZERO; 8];
+        for r in 0..8 {
+            for c in 0..8 {
+                let entry = CAUCHY_MDS_8[r][c];
+                result[r] += entry * vec[c];
+            }
+        }
+        result
+    }
 }
 
 impl Neg for CrandallField {
diff --git a/src/field/field.rs b/src/field/field.rs
index 181b6ac8..8497861f 100644
--- a/src/field/field.rs
+++ b/src/field/field.rs
@@ -5,8 +5,8 @@ use std::iter::{Product, Sum};
 use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
 
 use num::Integer;
-use rand::Rng;
 use rand::rngs::OsRng;
+use rand::Rng;
 
 use crate::util::bits_u64;