From 79c923a08c316569ad0f60faed565ec782245177 Mon Sep 17 00:00:00 2001
From: PlexSheep <PlexSheep@protonmail.com>
Date: Thu, 18 May 2023 01:51:30 +0200
Subject: [PATCH] gallois module

---
 src/math/gallois.rs | 152 ++++++++++++++++++++++++++++++++++++++++++++
 src/math/mod.rs     |   1 +
 src/math/modexp.rs  |  13 ++++
 3 files changed, 166 insertions(+)
 create mode 100644 src/math/gallois.rs

diff --git a/src/math/gallois.rs b/src/math/gallois.rs
new file mode 100644
index 0000000..ff608af
--- /dev/null
+++ b/src/math/gallois.rs
@@ -0,0 +1,152 @@
+#![allow(dead_code)]
+use num::Integer;
+
+/// calculation in a gallois field
+///
+/// This module contains functions that can be used to calculate things in a gallois field
+///
+/// Author:     Christoph J. Scherr <software@cscherr.de>
+/// License:    MIT
+/// Source:     <https://git.cscherr.de/PlexSheep/plexcryptool/>
+
+use crate::math::modexp;
+
+use core::fmt;
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+#[derive(Debug)]
+/// used when trying to find a root for a number which does not have a root.
+pub struct NoInverseError;
+
+impl fmt::Display for NoInverseError {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "inverse for 0 does not exist")
+    }
+}
+///////////////////////////////////////////////////////////////////////////////////////////////////
+#[derive(Debug)]
+/// used when trying to find a root for a number which does not have a root.
+pub struct DivisionByZeroError;
+
+impl fmt::Display for DivisionByZeroError {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "division by zero")
+    }
+}
+///////////////////////////////////////////////////////////////////////////////////////////////////
+#[derive(Debug)]
+/// used when trying to find a root for a number which does not have a root.
+pub struct NoRootError;
+
+impl fmt::Display for NoRootError {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "no root in the specified gallois field")
+    }
+}
+///////////////////////////////////////////////////////////////////////////////////////////////////
+#[derive(Debug, Copy, Clone)]
+/// represent a gallois field
+pub struct GalloisFiled {
+    base: u128,
+    cha: u128,
+    verbose: bool,
+}
+
+/// implementations for the gallois field
+impl GalloisFiled {
+    /// make a new gallois field
+    pub fn new(base: u128, verbose: bool) -> Self {
+        let mut field = GalloisFiled{
+            base,
+            // TODO: calculate the characteristic
+            cha: 0,
+            verbose
+        };
+        if verbose {
+            dbg!(&field);
+        }
+        return field;
+    }
+
+    /// reduce a number to fit into the gallois field
+    pub fn reduce(self, n: u128) -> u128 {
+        let mut n = n;
+        if n < 0 {
+            while n < 0 {
+                n += self.base;
+            }
+        }
+        n %= self.base;
+        return n;
+    }
+
+    /// reduce a negative number to fit into the gallois field
+    pub fn reduce_neg(self, n: i128) -> u128 {
+        let mut n = n;
+        if n < 0 {
+            while n < 0 {
+                n += self.base as i128;
+            }
+        }
+        n %= self.base as i128;
+        return n as u128;
+    }
+
+    /// calculate the exponent of a base in the field
+    pub fn pow(self, base: u128, exp: u128) -> u128 {
+        return modexp::modular_exponentiation_wrapper(base, exp, self.base, false);
+    }
+
+    /// find the additive inverse of a number
+    pub fn a_inverse(self, n: u128) -> u128 {
+        return self.base - self.reduce(n);
+    }
+
+    /// find the multiplicative inverse of a number
+    pub fn inverse(self, n: u128) -> Result<u128, NoInverseError> {
+        if n == 0 {
+            return Err(NoInverseError);
+        }
+        let egcd = (n as i128).extended_gcd(&(self.base as i128));
+        dbg!(n);
+        return Ok(egcd.x as u128);
+    }
+
+    pub fn divide(self, a: u128, b: u128) -> Result<u128, DivisionByZeroError> {
+        let b = self.inverse(b);
+        match b {
+            Ok(r) => {
+                return Ok(self.reduce(a * r));
+            }
+            Err(e) => {
+                dbg!(e);
+                return Err(DivisionByZeroError);
+            }
+        }
+    }
+
+    /// calculate the square root of a number in a field
+    pub fn sqrt(self, n: u128) -> Result<u128, NoRootError> {
+        // TODO implement this
+        panic!("TODO")
+    }
+}
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+#[test]
+fn test_gallois_sqrt() {
+    panic!("TODO")
+}
+
+#[test]
+fn test_gallois_inverse() {
+    let field = GalloisFiled::new(31, true);
+    assert_eq!(field.inverse(12).unwrap(), 13);
+    assert_eq!(field.inverse(28).unwrap(), 10);
+    assert!(field.inverse(0).is_err());
+
+    let field = GalloisFiled::new(83, true);
+    assert_eq!(field.inverse(6).unwrap(), 14);
+    assert_eq!(field.inverse(54).unwrap(), 20);
+    assert!(field.inverse(0).is_err());
+}
diff --git a/src/math/mod.rs b/src/math/mod.rs
index 6beca9c..3c829fa 100644
--- a/src/math/mod.rs
+++ b/src/math/mod.rs
@@ -9,3 +9,4 @@
 pub mod modexp;
 pub mod pm1;
 pub mod modred;
+pub mod gallois;
diff --git a/src/math/modexp.rs b/src/math/modexp.rs
index 4fe4dc5..da39441 100644
--- a/src/math/modexp.rs
+++ b/src/math/modexp.rs
@@ -68,6 +68,19 @@ pub fn modular_exponentiation(
     return res;
 }
 
+/// quick wrapper for modular_exponentiation without BigInts
+pub fn modular_exponentiation_wrapper(
+    base: u128,
+    exp: u128, 
+    field: u128,
+    verbose: bool) -> u128 {
+    
+    let base = BigInt::from(base);
+    let exp = BigInt::from(exp);
+    let field = BigInt::from(field);
+    return modular_exponentiation(base, exp, field, verbose).to_u128().expect("number too big");
+}
+
 #[pyfunction]
 #[pyo3(name="modular_exponentiation")]
 #[pyo3(signature=(base, orig_exp, field, verbose = false))]