subtraction and calculating char in GF
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@ -165,14 +165,6 @@ impl ElipticCurve {
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if !self.check_point(p2, false) {
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if !self.check_point(p2, false) {
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return Err(String::from("{p2} is not a valid point"));
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return Err(String::from("{p2} is not a valid point"));
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}
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}
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if self.field.prime_base {
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// verbisity stuff
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//if self.verbose {
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// println!("{} = {}; {} = -{} = {} <=> {}",
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// p1.r, p2.r, p1.s, p2.s, self.neg(p2).s,
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// p1.r == p2.r && p1.s == self.neg(p2).s,
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// );
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//}
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// case 1: both infty
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// case 1: both infty
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if p1.is_infinity_point && p2.is_infinity_point {
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if p1.is_infinity_point && p2.is_infinity_point {
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if self.verbose {
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if self.verbose {
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@ -315,10 +307,6 @@ impl ElipticCurve {
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panic!("No rules for adding these two points, mathmatically impossible.")
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panic!("No rules for adding these two points, mathmatically impossible.")
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}
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}
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}
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}
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else {
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return Err(String::from("Only prime fields are supported currently"));
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}
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}
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/// get negative of a point
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/// get negative of a point
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pub fn neg(&self, p: ElipticCurvePoint) -> ElipticCurvePoint {
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pub fn neg(&self, p: ElipticCurvePoint) -> ElipticCurvePoint {
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@ -18,7 +18,7 @@
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use crate::{math::modexp, cplex::printing::seperator, math::modred::modred};
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use crate::{math::modexp, cplex::printing::seperator, math::modred::modred};
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use core::fmt;
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use core::fmt;
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use std::{fmt::Debug, ops::BitXor};
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use std::fmt::Debug;
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use num::{Integer, NumCast};
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use num::{Integer, NumCast};
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@ -205,7 +205,41 @@ impl GalloisField {
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}
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}
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else {
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else {
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r = a ^ b;
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r = a ^ b;
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println!("r = a ^ b = {a:b} ^ {b:b} = {r:b}");
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println!("r = a ^ b = {a:b} ^ {b:b} = {r:b}\n\
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r = a + b = ({}) + ({}) = {}",
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self.display(a),
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self.display(b),
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self.display(r),
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);
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}
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num::cast(self.reduce::<_, T>(r)).unwrap()
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}
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/// subtraction in the field
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///
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/// in case of a prime base, addition works as normal,
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/// if the base is a prime power, all elements are treated as polynomials, so the
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/// operations are changed too.
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pub fn sub<T>(&self, a: T, b: T) -> T
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where
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T: Integer,
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T: Debug,
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T: NumCast
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{
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let a: i128 = self.reduce(num::cast::<_, u128>(a).unwrap());
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let b: i128 = self.reduce(num::cast::<_, u128>(b).unwrap());
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let r: i128;
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if self.prime_base {
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r = a - b;
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}
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else {
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r = a ^ b;
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println!("r = a ^ b = {a:b} ^ {b:b} = {r:b}\n\
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r = a + b = ({}) + ({}) = {}",
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self.display(a),
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self.display(b),
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self.display(r),
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);
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}
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}
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num::cast(self.reduce::<_, T>(r)).unwrap()
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num::cast(self.reduce::<_, T>(r)).unwrap()
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}
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}
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@ -405,9 +439,10 @@ impl GalloisField {
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seperator();
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seperator();
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println!("calculating characteristic of F_{}", self.base);
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println!("calculating characteristic of F_{}", self.base);
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}
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}
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if self.prime_base {
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let mut i = 1u128;
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let mut i = 1u128;
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while self.reduce::<_, u128>(i) != 0 {
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while self.reduce::<_, u128>(i) != 0 {
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i = self.add(i, 1);
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i += 1;
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}
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}
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if self.verbose {
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if self.verbose {
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println!("{i} = {} (mod {})", self.reduce::<_, u128>(i), self.base);
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println!("{i} = {} (mod {})", self.reduce::<_, u128>(i), self.base);
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@ -418,6 +453,17 @@ impl GalloisField {
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self.cha = i;
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self.cha = i;
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return i;
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return i;
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}
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}
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else {
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if self.base.is_power_of_two() {
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// if you need the k part of 2**k = self.base
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//let l: u32 = self.base.ilog2();
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return 2;
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}
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else {
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panic!("GalloisField for bases other then primes or powers of two not implemented.")
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}
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}
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}
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/// display an element in the field
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/// display an element in the field
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///
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///
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@ -428,7 +474,7 @@ impl GalloisField {
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T: NumCast,
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T: NumCast,
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T: Debug
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T: Debug
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{
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{
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let mut n: u128 = self.reduce(num::cast::<_, u128>(n).unwrap());
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let n: u128 = self.reduce(num::cast::<_, u128>(n).unwrap());
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let mut buf: String = String::new();
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let mut buf: String = String::new();
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let n_len = n.count_ones() + n.count_zeros();
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let n_len = n.count_ones() + n.count_zeros();
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let mut first: bool = true;
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let mut first: bool = true;
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@ -597,6 +643,31 @@ pub mod test {
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assert_eq!(field.add(0b1010101, 0b10101010), field.reduce(0b11111111));
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assert_eq!(field.add(0b1010101, 0b10101010), field.reduce(0b11111111));
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}
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}
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#[test]
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fn test_gallois_sub() {
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let field = GalloisField::new(977, true, None);
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let ns = [132,1232,121,424];
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for i in 0..976 {
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for n in ns {
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assert_eq!(field.sub(i, n), field.reduce(i-n));
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}
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}
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let field = GalloisField::new(8, true, None);
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assert_eq!(field.sub(0b1, 0b10), field.reduce(0b11));
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assert_eq!(field.sub(0b11, 0b10), field.reduce(0b01));
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assert_eq!(field.sub(0b101, 0b1010), field.reduce(0b1111));
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assert_eq!(field.sub(0b1010101, 0b10101010), field.reduce(0b11111111));
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let field = GalloisField::new(16, true, None);
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assert_eq!(field.sub(0b1, 0b10), field.reduce(0b11));
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assert_eq!(field.sub(0b11, 0b10), field.reduce(0b01));
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assert_eq!(field.sub(0b1111, 0b1011), field.reduce(0b0100));
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assert_eq!(field.sub(0b101, 0b1010), field.reduce(0b1111));
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assert_eq!(field.sub(0b1000, 0b111), field.reduce(0b1111));
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assert_eq!(field.sub(0b1010101, 0b10101010), field.reduce(0b11111111));
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}
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#[test]
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#[test]
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fn test_gallois_reduce_c2() {
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fn test_gallois_reduce_c2() {
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let field = GalloisField::new(16, true, None);
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let field = GalloisField::new(16, true, None);
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