From 1246d84267a00f5a540473f30fa0b8150e54ac1f Mon Sep 17 00:00:00 2001
From: PlexSheep <PlexSheep@protonmail.com>
Date: Sun, 28 May 2023 10:34:56 +0200
Subject: [PATCH] gallois sucks

---
 src/math/ecc.rs     |  7 ++++---
 src/math/gallois.rs | 40 ++++++++++++++++++++++++++++++++++++++--
 src/math/gcd.rs     |  2 +-
 3 files changed, 43 insertions(+), 6 deletions(-)

diff --git a/src/math/ecc.rs b/src/math/ecc.rs
index 62ae2fa..d690b0f 100644
--- a/src/math/ecc.rs
+++ b/src/math/ecc.rs
@@ -26,16 +26,16 @@ pub const INFINITY_POINT: ElipticCurvePoint = ElipticCurvePoint {
 ///
 /// real curves not supported, only in Gallois Fields
 pub struct ElipticCurve {
-    f: Option<GalloisField>,
+    f: GalloisField,
     a: i128,
     b: i128,
     points: Vec<ElipticCurvePoint>,
     verbose: bool,
-    INFINITY_POINT: ElipticCurvePoint
+    INFINITY_POINT: ElipticCurvePoint,
 }
 
 impl ElipticCurve {
-    pub fn new(f: Option<GalloisField>, a: i128, b: i128, verbose: bool) -> Self {
+    pub fn new(f: GalloisField, a: i128, b: i128, verbose: bool) -> Self {
         let e = ElipticCurve {
             f,
             a,
@@ -48,6 +48,7 @@ impl ElipticCurve {
     }
 }
 
+
 #[derive(Debug, Clone)]
 #[pyclass]
 /// represent a specific eliptic curves point
diff --git a/src/math/gallois.rs b/src/math/gallois.rs
index 38e5cbb..12a74c7 100644
--- a/src/math/gallois.rs
+++ b/src/math/gallois.rs
@@ -2,6 +2,12 @@
 /// calculation in a gallois field
 ///
 /// This module contains functions that can be used to calculate things in a gallois field
+/// TODO I'm not sure how accurate it is to call this stuff a gallois field.
+/// They should normally be based on some relation and not use numbers?
+/// It does also not even come close to statisfying the characteristic of prime powers q = p^k.as
+/// base => p = 0
+///
+/// Something is wrong here.
 ///
 /// Author:     Christoph J. Scherr <software@cscherr.de>
 /// License:    MIT
@@ -15,6 +21,8 @@ use num::Integer;
 
 use pyo3::{prelude::*, exceptions::PyValueError};
 
+use primes::{Sieve, PrimeSet, is_prime};
+
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 #[derive(Debug)]
 /// used when trying to find a root for a number which does not have a root.
@@ -59,9 +67,8 @@ pub struct GalloisField {
 impl GalloisField {
     /// make a new gallois field
     pub fn new(base: u128, verbose: bool) -> Self {
-        let field = GalloisField{
+        let mut field = GalloisField{
             base,
-            // TODO: calculate the characteristic
             cha: 0,
             verbose
         };
@@ -296,6 +303,25 @@ impl GalloisField {
             return Ok((w1, w2));
         }
     }
+
+    /// calculate the characteristic of the field
+    pub fn calc_char(mut self) -> u128 {
+        if self.verbose {
+            seperator();
+            println!("calculating characteristic of F_{}", self.base);
+            seperator();
+        }
+        let mut i = 1u128;
+        while self.reduce(i) > 0 {
+            if self.verbose {
+                println!("{i}.\t {i} = {} (mod {})", self.reduce(i), self.base)
+            }
+            i += 1;
+        }
+        
+        self.cha = i;
+        return i;
+    }
 }
 
 #[pymethods]
@@ -378,3 +404,13 @@ fn test_gallois_inverse() {
 
     // TODO add a test for a field that has a non prime base
 }
+
+#[test]
+fn test_calc_char() {
+    assert_eq!(GalloisField::new(16, true).calc_char(), 2);
+    assert_eq!(GalloisField::new(81, true).calc_char(), 81);
+    assert_eq!(GalloisField::new(1151, true).calc_char(), 1151);
+    assert_eq!(GalloisField::new(8, true).calc_char(), 2);
+    assert_eq!(GalloisField::new(2, true).calc_char(), 2);
+    assert_eq!(GalloisField::new(60, true).calc_char(), 3);
+}
diff --git a/src/math/gcd.rs b/src/math/gcd.rs
index ffc9f91..d91725c 100644
--- a/src/math/gcd.rs
+++ b/src/math/gcd.rs
@@ -35,7 +35,7 @@ pub fn alt_egcd(mut a: i128, mut b: i128, recursion: bool) -> Vec<i128> {
         return vec![b, 0, 1]
     }
     let v = alt_egcd(b % a, a, true);
-    let mut result =  vec![
+    let result =  vec![
         v[0], 
         v[2] - (b.checked_div(a).unwrap()) * v[1], 
         v[1],