ecc cli interface and half working add

Cargo.toml

@@ -20,6 +20,7 @@ name = "plexcryptool"
 path = "src/main.rs"
 
 [dependencies]
+bitvec = "1.0.1"
 clap = { version = "4.2.7", features = ["derive"]}
 clap-num = "1.0.2"
 num = "0.4.0"

src/cplex/cli.rs

@@ -71,11 +71,12 @@ pub enum MathActions {
     /// p minus 1 prime test
     Pm1(PM1Args),
     /// calculate in a gallois field
+    /// includes Eliptic curves
     Gallois(GalloisAction),
     /// Euklidian Algorithm
     Gcd(GcdArgs),
     /// factorize a natural number
-    Factorize(FactorizeArgs)
+    Factorize(FactorizeArgs),
 }
 
 #[derive(Args, Clone, Debug, PartialEq, Eq)]
@@ -137,7 +138,9 @@ pub enum GalloisActions {
     /// reduce n to the range of the field
     Reduce(GalloisReduceArgs),
     /// calculate the (multiplicative) inverse of n
-    Invert(GalloisInvertArgs),
+    Inverse(GalloisInverseArgs),
+    /// eliptic curves
+    ECC(ECCAction)
 }
 
 #[derive(Args, Clone, Debug, PartialEq, Eq)]
@@ -152,11 +155,62 @@ pub struct GalloisReduceArgs {
 }
 
 #[derive(Args, Clone, Debug, PartialEq, Eq)]
-pub struct GalloisInvertArgs {
+pub struct GalloisInverseArgs {
     #[clap(value_parser=maybe_hex::<u128>)]
     pub n: u128,
 }
 
+#[derive(Args, Clone, Debug, PartialEq, Eq)]
+pub struct ECCAction {
+    #[clap(allow_hyphen_values=true)]   // allow negative inputs like -19
+    pub a: i128,
+    #[clap(allow_hyphen_values=true)]   // allow negative inputs like -19
+    pub b: i128,
+    #[command(subcommand)]
+    pub action: ECCActions
+}
+
+#[derive(Subcommand, Clone, Debug, PartialEq, Eq)]
+pub enum ECCActions {
+    /// negate a point
+    Neg(ECCNegArgs),
+    /// add a twp poimts
+    Add(ECCAddArgs),
+    /// multiply a point with an integer
+    /// uses double and add
+    Mul(ECCMulArgs),
+}
+
+#[derive(Args, Clone, Debug, PartialEq, Eq)]
+pub struct ECCNegArgs {
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub r: u128,
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub s: u128,
+}
+
+#[derive(Args, Clone, Debug, PartialEq, Eq)]
+pub struct ECCMulArgs {
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub r: u128,
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub s: u128,
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub n: u128,
+}
+
+#[derive(Args, Clone, Debug, PartialEq, Eq)]
+pub struct ECCAddArgs {
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub r1: u128,
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub s1: u128,
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub r2: u128,
+    #[clap(value_parser=maybe_hex::<u128>)]
+    pub s2: u128,
+}
+
 #[derive(Subcommand, Clone, Debug, PartialEq, Eq)]
 pub enum BinaryActions {
     /// bit rotation/circular shifting (only 32bit)
@@ -166,7 +220,6 @@ pub enum BinaryActions {
     Xor(XorArgs),
     /// use a pbox
     Pbox(PboxArgs),
-
 }
 
 #[derive(Args, Clone, Debug, PartialEq, Eq)]

src/cplex/printing.rs

@@ -88,6 +88,18 @@ pub fn proc_num<T>(num: T, args: Cli)
     }
 }
 
+pub fn proc_display<T>(item: T, args: Cli)
+    where
+    T: Display,
+{
+    if args.machine {
+        println!("{}", item);
+    }
+    else {
+        println!("result is {}", item);
+    }
+}
+
 /// process some int tuple
 pub fn proc_result_tup_num<T, K>(result: Result<(T, T), K>, args: Cli)
     where

src/main.rs

@@ -68,13 +68,62 @@ pub fn main() {
                             cplex::printing::proc_result_tup_num(result, args);
                         }
                         GalloisActions::Reduce(gal_red_args) => {
-                            let result = field.reduce(gal_red_args.n);
+                            let result = field.reduce::<_, u128>(gal_red_args.n);
                             cplex::printing::proc_num(result, args);
                         }
-                        GalloisActions::Invert(gal_inv_args) => {
+                        GalloisActions::Inverse(gal_inv_args) => {
                             let result = field.inverse(gal_inv_args.n);
                             cplex::printing::proc_result_num(result, args);
                         }
+                        GalloisActions::ECC(ecc_args) => {
+                            let ec = math::ecc::ElipticCurve::new(field, ecc_args.a, ecc_args.b, args.verbose).expect("Could not create eliptic curve");
+                            match ecc_args.action {
+                                ECCActions::Neg(ecc_neg_args) => {
+                                    let p = ec.new_point(ecc_neg_args.r, ecc_neg_args.s);
+                                    match p {
+                                        Ok(p) => {
+                                            let item = ec.neg(p);
+                                            cplex::printing::proc_display(item, args)
+                                        }
+                                        Err(e) => {
+                                            cplex::printing::proc_err(e, args);
+                                        }
+                                    }
+                                }
+                                ECCActions::Mul(ecc_mul_args) => {
+                                    let p = ec.new_point(ecc_mul_args.r, ecc_mul_args.s);
+                                    if p.is_err() {
+                                        cplex::printing::proc_err(p, args);
+                                    }
+                                    else {
+                                        let item = ec.mul(p.unwrap(), ecc_mul_args.n);
+                                        if item.is_err() {
+                                            cplex::printing::proc_err(item.unwrap_err(), args)
+                                        }
+                                        else {
+                                            cplex::printing::proc_display(item.unwrap(), args);
+                                        }
+                                    }
+                                }
+                                ECCActions::Add(ecc_add_args) => {
+                                    let p1 = ec.new_point(ecc_add_args.r1, ecc_add_args.s1);
+                                    let p2 = ec.new_point(ecc_add_args.r2, ecc_add_args.s2);
+                                    if p1.is_err() || p2.is_err() {
+                                        cplex::printing::proc_err(p1, args.clone());
+                                        cplex::printing::proc_err(p2, args);
+                                    }
+                                    else {
+                                        let item = ec.add(p1.unwrap(), p2.unwrap());
+                                        if item.is_err() {
+                                            cplex::printing::proc_err(item.unwrap_err(), args)
+                                        }
+                                        else {
+                                            cplex::printing::proc_display(item.unwrap(), args);
+                                        }
+                                    }
+                                }
+                            }
+                        }
                     }
                 }
                 MathActions::Factorize(fac_args) => {

src/math/ecc.rs

@@ -1,5 +1,5 @@
 #![allow(dead_code)]
-use std::{ops::{Mul, Neg}, fmt::Debug, f32::consts::PI};
+use crate::cplex::printing::seperator;
 
 /// eliptic curve cryptograp.s
 ///
@@ -12,7 +12,12 @@ use std::{ops::{Mul, Neg}, fmt::Debug, f32::consts::PI};
 
 use super::gallois::GalloisField;
 
-use num::Integer;
+use std::{ops::{Mul, Neg}, fmt::{Debug, Display}, f32::consts::PI};
+
+use num::{Integer, Unsigned, NumCast};
+
+use bitvec::prelude::*;
+
 use pyo3::prelude::*;
 
 #[derive(Debug, Clone, Eq, PartialEq)]
@@ -31,30 +36,43 @@ pub struct ElipticCurve {
 }
 
 impl ElipticCurve {
-    pub fn new(field: GalloisField, a: i128, b: i128, verbose: bool) -> Result<Self, String> {
+    pub fn new<T>(field: GalloisField, a: T, b: T, verbose: bool) -> Result<Self, String>
+    where
+        T: Integer,
+        T: Debug,
+        T: num::cast::AsPrimitive<i128>,
+    {
+        // convert from generics to i128
+        let a: i128 = num::cast::AsPrimitive::as_(a);
+        let b: i128 = num::cast::AsPrimitive::as_(b);
 
-        // convert numbers to u128 in the fields
+        // reduce a and b if possible
-        let a = field.reduce(a);
+        let a = field.reduce::<_, u128>(a);
-        let b = field.reduce(b);
+        let b = field.reduce::<_, u128>(b);
+
+        if verbose {
+            println!("On eliptic curve:\n\
+            F(X, Y) = Y² - X³ - {a}X - {b}")
+        }
 
         // check diskriminante
         let d = 4*a.pow(3) + 27*b.pow(2);
-        if field.reduce(d) == 0 {
+        if field.reduce::<_, u128>(d) == 0 {
             if verbose {
                 println!("4*{a}³ + 27*{b}² = {d} = {} != 0\n\
-                Check for Diskriminante not passed", field.reduce(d));
+                Check for Diskriminante not passed", field.reduce::<_, u128>(d));
             }
             return Err(String::from("Diskriminante not 0"));
         }
         else if verbose {
             println!("4*{a}³ + 27*{b}² = {d} = {} != 0\n\
-                Check for Diskriminante passed", field.reduce(d));
+                Check for Diskriminante passed", field.reduce::<_, u128>(d));
         }
 
         let mut infty = ElipticCurvePoint::new(0, 0, field, false);
         infty.is_infinity_point = true;
         let infty = infty;
-        let mut e = ElipticCurve {
+        let e = ElipticCurve {
             field,
             a,
             b,
@@ -65,6 +83,22 @@ impl ElipticCurve {
         return Ok(e);
     }
 
+    /// build a new point in the EC
+    pub fn new_point(&self, r: u128, s: u128) -> Result<ElipticCurvePoint, String> {
+        let p = ElipticCurvePoint::new(r, s, self.field, self.verbose);
+        if self.verbose {
+            println!("{p}")
+        }
+        match self.check_point(p, self.verbose) {
+            true => {
+                return Ok(p);
+            }
+            false => {
+                return Err(String::from("the point you want to create is not on the EC"));
+            }
+        }
+    }
+
     /// calculate a value for coordinates
     pub fn poly<T>(&self, r: T, s: T) -> i128 
         where
@@ -79,7 +113,7 @@ impl ElipticCurve {
             let r: u128 = num::cast::AsPrimitive::as_(r);
             let s: u128 = num::cast::AsPrimitive::as_(s);
             let res =  (s.pow(2) as u128) - (r.pow(3) as u128) - (self.a * r) - self.b;
-            let res1 = self.field.reduce(res);
+            let res1 = self.field.reduce::<_, u128>(res);
             if self.verbose {
                 println!("F({}, {}) = {}² - {}³ - {} * {} - {} = {res} = {res1}",
                 r, s, s, r, self.a, r, self.b
@@ -88,13 +122,13 @@ impl ElipticCurve {
             return res1 as i128;
         }
 
-    pub fn check_point(self, p: ElipticCurvePoint) -> bool {
+    pub fn check_point(&self, p: ElipticCurvePoint, verbose: bool) -> bool {
         let mut valid = true;
 
         // insert into poly
-        let left =  self.field.reduce(p.s.pow(2));
+        let left =  self.field.reduce::<_, u128>(p.s.pow(2));
-        let right =  self.field.reduce((p.r.pow(3) as u128) + self.a*p.r + self.b);
+        let right =  self.field.reduce::<_, u128>((p.r.pow(3) as u128) + self.a*p.r + self.b);
-        if self.verbose {
+        if self.verbose && verbose {
             let unred_left = p.s.pow(2);
             let unred_right = p.r.pow(3) + self.a*p.r + self.b;
             println!("All Points need to fullfill this equation:\n\
@@ -117,68 +151,148 @@ impl ElipticCurve {
 
 
     /// add two points
-    pub fn add(&self, p1: ElipticCurvePoint, p2: ElipticCurvePoint) -> Result<ElipticCurvePoint, String> {
+    pub fn add(&self, p1: ElipticCurvePoint, p2: ElipticCurvePoint) -> 
+        Result<ElipticCurvePoint, String> {
+        if self.verbose {
+            seperator();
+            println!("adding {p1} + {p2}");
+            seperator();
+        }
         if p1.field != p2.field {
             return Err(String::from("Points are not on the same field"));
         }
+        if !self.check_point(p1, self.verbose) {
+            return Err(String::from("{p1} is not a valid point"));
+        }
+        if !self.check_point(p2, self.verbose) {
+            return Err(String::from("{p2} is not a valid point"));
+        }
         if p1.field.prime_base {
+            // verbisity stuff
+            if self.verbose {
+                println!("{} = {}; {} = -{} = {} <=> {}",
+                         p1.r, p2.r, p1.s, p2.s, self.neg(p2).s, 
+                         p1.r == p2.r && p1.s == self.neg(p2).s,
+                         );
+            }
             // case 1: both infty
             if p1.is_infinity_point && p2.is_infinity_point {
+                if self.verbose {
+                    println!("case 1");
+                }
                 return Ok(self.INFINITY_POINT);
             }
             // case 2: one is infty
-            else if p1.is_infinity_point && !p2.is_infinity_point {
+            else if p1.is_infinity_point && !p2.is_infinity_point || 
+                    !p1.is_infinity_point && p2.is_infinity_point
+                {
+                if self.verbose {
+                    println!("case 2");
+                }
                 return Ok(self.INFINITY_POINT);
             }
-            else if !p1.is_infinity_point && p2.is_infinity_point {
+            // case 4: r_1 = r_2 && s_1 = -s_2
-                return Ok(p1);
+            else if p1.r == p2.r && p1.s == self.neg(p2).s {
+                if self.verbose {
+                    println!("case 4");
+                }
+                return Ok(self.INFINITY_POINT);
             }
             // case 3: r_1 != r_2
             else if p1.r != p2.r {
-                if self.field.prime_base {
-                    let m = self.field.reduce(p2.s - p1.s) * 
-                        self.field.inverse(
-                            self.field.reduce(p2.r - p1.r)
-                            ).expect("could not find inverse");
-                    if self.verbose || p2.verbose {
-                        println!("m = [s_2 - s_1]/[r_2 - r_1] = [{} - {}]/[{} - {}] = {} = {}",
-                                 p2.s, p1.s, p2.r, p1.r, m, p1.field.reduce(m))
-                    }
-                    let m = self.field.reduce(m);
-
-                    let r3 = self.field.reduce(m.pow(3)) - p1.r - p2.r;
                 if self.verbose {
-                        println!("r_3 = m³ - r_1 - r_2 = {} - {} - {} = {} = {}",
+                    println!("case 3");
-                                 m.pow(3), p1.r, p2.r, r3, p1.field.reduce(r3));
                 }
-                    let r3 = self.field.reduce(r3);
+                if self.field.prime_base {
-
+                    let m: u128 = self.field.reduce::<i128, u128>(p2.s as i128 - p1.s as i128) * 
-                    let s3 = m.pow(3) - 2*m*p1.r - m*p2.r + p1.s;
+                        self.field.inverse(
-                    if self.verbose || p2.verbose {
+                            self.field.reduce::<i128, u128>(p2.r as i128 - p1.r as i128)
-                        println!("s_3 = m³ − 2*m*r_1 − m*r_2 + s1 = {} - 2*{m}*{} - {m}*{} + {} = {} = {}",
+                            ).expect("could not find inverse");
-                                 m.pow(3), p1.r, p2.r, p1.s, s3, self.field.reduce(s3));
+                    let m: i128 = m as i128;
+                    if self.verbose {
+                        println!("m = [s_2 - s_1]/[r_2 - r_1] = [{} - {}]/[{} - {}] = {} = {}",
+                                 p2.s, p1.s, p2.r, p1.r, m, p1.field.reduce::<_, u128>(m))
                     }
-                    let s3 = self.field.reduce(s3) as i128;
+                    let m: i128 = self.field.reduce(m);
-                    let p = ElipticCurvePoint::new(r3, self.field.reduce(-s3), self.field, self.verbose);
 
-                    panic!("TODO");
+                    let r3 = m.pow(2) - p1.r as i128 - p2.r as i128;
+                    if self.verbose {
+                        println!("r_3 = m² - r_1 - r_2 = {} - {} - {} = {} = {}",
+                                 m.pow(2), p1.r, p2.r, r3, p1.field.reduce::<_, u128>(r3));
+                    }
+                    let r3 = self.field.reduce::<_, u128>(r3);
+
+                    let s3 = m.pow(3) - 2*m*p1.r as i128 - m*p2.r as i128 + p1.s as i128;
+                    if self.verbose {
+                        println!("s_3 = m³ − 2*m*r_1 − m*r_2 + s1 =\
+                        {} - 2*{m}*{} - {m}*{} + {} = {} = {}",
+                                 m.pow(3), p1.r, p2.r, p1.s, s3, 
+                                 self.field.reduce::<_, u128>(s3));
+                    }
+                    let s3 = self.field.reduce::<_, u128>(s3) as i128;
+                    if self.verbose {
+                        println!("-s_3 = - {s3} = {}", self.field.reduce::<_, u128>(-s3));
+                    }
+                    let p3 = ElipticCurvePoint::new(r3, self.field.reduce::<_, u128>(-s3), 
+                                                    self.field, self.verbose);
+
+                    if self.verbose {
+                        seperator();
+                        println!("result: ({}, {})", p3.r, p3.s);
+                        seperator();
+                    }
+                    return Ok(p3);
                 }
                 else {
                     panic!("TODO");
                 }
             }
-            // case 4: r_1 = r_2 && s_1 = -s_2
-            else if p1.r == p2.r && p1.s == self.neg(p2).s {
-                return Ok(self.INFINITY_POINT);
-            }
             // case 5: P + P where P = (r, 0)
             else if p1 == p2 && p1.s == 0 {
+                if self.verbose {
+                    println!("case 5");
+                }
                 return Ok(self.INFINITY_POINT);
             }
             // case 6: P + P where s != 0
             else if p1 == p2 && p1.s != 0 {
+                if self.verbose {
+                    println!("case 6");
+                }
                 if self.field.prime_base {
-                    panic!("TODO");
+                    let m: i128 = (self.field.reduce::<_, u128>(3 * p1.r.pow(2) + self.a) * 
+                        self.field.inverse(
+                            self.field.reduce::<u128, u128>(2 * p1.r)
+                            ).expect("could not find inverse")) as i128;
+                    if self.verbose {
+                        println!("m = [3*r²]/[2s] = [3*{}²]/[2*{}] = {} = {}",
+                                 p1.r, p1.s, m, self.field.reduce::<_, u128>(m));
+                    }
+                    let m: i128 = self.field.reduce(m);
+
+                    let r3: i128 = self.field.reduce::<_, i128>(m.pow(2)) - p1.r as i128 - p2.r as i128;
+                    if self.verbose {
+                        println!("r_3 = m² - r_1 - r_2 = {} - {} - {} = {} = {}",
+                                 m.pow(2), p1.r, p2.r, r3, p1.field.reduce::<_, u128>(r3));
+                    }
+                    let r3: i128 = self.field.reduce(r3);
+
+                    let s3: i128 = m.pow(3) - 2*m*p1.r as i128 - m*p2.r as i128 + p1.s as i128;
+                    if self.verbose || p2.verbose {
+                        println!("s_3 = m³ − 2*m*r_1 − m*r_2 + s1 = {} - 2*{m}*{} - {m}*{} + {} = \
+                        {} = {}",
+                                 m.pow(3), p1.r, p2.r, p1.s, s3, self.field.reduce::<_, u128>(s3));
+                    }
+                    let s3: i128 = self.field.reduce(s3);
+                    let p3 = ElipticCurvePoint::new(r3 as u128, self.field.reduce::<_, u128>(-s3), 
+                                                    self.field, self.verbose);
+
+                    if self.verbose {
+                        seperator();
+                        println!("result: ({}, {})", p3.r, p3.s);
+                        seperator();
+                    }
+                    return Ok(p3);
                 }
                 else {
                     panic!("TODO");
@@ -188,7 +302,7 @@ impl ElipticCurve {
             // how do we get here?
             // this should never occur
             else {
-                panic!("No rules for adding these two points, should not be possible mathmatically.")
+                panic!("No rules for adding these two points, mathmatically impossible.")
             }
         }
         else {
@@ -198,18 +312,70 @@ impl ElipticCurve {
 
     /// get negative of a point
     pub fn neg(&self, p: ElipticCurvePoint) -> ElipticCurvePoint {
-        return ElipticCurvePoint::new(
+        self.new_point(p.r, self.field.reduce::<_, u128>(-(p.s as i128))).expect("negation of \
-            p.r, 
+        point is not on field, math error")
-            p.field.reduce(-(p.s as i128)), 
-            p.field,
-            p.verbose
-            );
     }
 
     /// multip.s a point by an integer
-    pub fn mul(self, p: ElipticCurvePoint, n: u128) -> ElipticCurvePoint {
+    pub fn mul<T>(&self, g: ElipticCurvePoint, t: T) -> Result<ElipticCurvePoint, String>
-        // TODO
+        where
-        panic!("TODO");
+        T: Integer,
+        T: NumCast,
+        T: Debug,
+        T: Unsigned,
+    {
+        if !self.check_point(g, self.verbose) {
+            return Err(String::from("invalid point"));
+        }
+        let t: usize = num::cast(t).unwrap();
+        if t < 1 {
+            return Err(String::from("point multiplication works only if t > 0"));
+        }
+        if self.verbose {
+            println!("h = t * g = {t} * {g}\n\
+            t = [{:b}]2", t)
+        }
+        let mut t_bits = BitVec::<_, Msb0>::from_element(t);
+        t_bits.reverse();
+        while t_bits[t_bits.len() - 1] == false {
+            t_bits.pop();
+        }
+        t_bits.reverse();
+        let l = t_bits.len() - 1;
+        let mut lh: ElipticCurvePoint = g;
+        let mut h: ElipticCurvePoint = g;
+        let mut index: usize = l;
+        if l == 0 {
+            return Ok(h);
+        }
+        for bit in t_bits {
+            if index == l {
+                if self.verbose {
+                    println!("h_{index} = {h}")
+                }
+                index -= 1;
+            }
+            h = self.add(lh, lh).expect("error while performing point multiplication");
+            if bit == false {
+                h = self.add(h, g).expect("error while performing point multiplication");
+            }
+            // else h = h
+            assert!(self.check_point(h, false));
+            lh = h;
+            if self.verbose {
+                println!("h_{index} = {h}")
+            }
+            index -= 1;
+        }
+        // now we should have reached h_0
+
+        return Ok(h);
+    }
+}
+
+impl std::fmt::Display for ElipticCurve{
+    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
+        write!(f, "F(X, Y) = Y² - X³ -{}X - {}", self.a, self.b)
     }
 }
 
@@ -238,6 +404,17 @@ impl ElipticCurvePoint {
     }
 }
 
+impl std::fmt::Display for ElipticCurvePoint {
+    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
+        if self.is_infinity_point {
+            write!(f, "(∞ INFINITY)")
+        }
+        else {
+            write!(f, "({}, {})", self.r, self.s)
+        }
+    }
+}
+
 #[cfg(test)]
 pub mod test {
 
@@ -278,10 +455,71 @@ pub mod test {
             ElipticCurvePoint::new(1, 4, f, false),
         ];
         for i in p {
-            assert!(ec.clone().check_point(i));
+            assert!(ec.clone().check_point(i, true));
         }
         for i in np {
-            assert!(!ec.clone().check_point(i));
+            assert!(!ec.clone().check_point(i, true));
         }
     }
+
+    #[test]
+    fn test_add_points() {
+        let f = GalloisField::new(11, true, None);
+        let ec = ElipticCurve::new(f, 1, 1, true).expect("ec cant be created");
+        let p1 = ec.new_point(3, 3).expect("point is on ec but an error occurs");
+        let p2 = ec.new_point(6, 5).expect("point is on ec but an error occurs");
+        let p3 = ec.new_point(0, 10).expect("point is on ec but an error occurs");
+        assert_eq!(ec.add(p1, p2).expect("error for possible addition"), p3);
+
+        let f = GalloisField::new(13, true, None);
+        let ec = ElipticCurve::new(f, -3, 3, true).expect("ec cant be created");
+        let p1 = ec.new_point(1, 1).expect("point is on ec but an error occurs");
+        let p2 = ec.new_point(5, 3).expect("point is on ec but an error occurs");
+        let p3 = ec.new_point(4, 4).expect("point is on ec but an error occurs");
+        let p4 = ec.new_point(8, 6).expect("point is on ec but an error occurs");
+        let p5 = ec.new_point(11, 12).expect("point is on ec but an error occurs");
+        assert_eq!(ec.add(p1, p2).expect("error for possible addition"), p3);
+        assert_eq!(ec.add(p2, p4).expect("error for possible addition"), p1);
+        assert_eq!(ec.add(p1, p1).expect("error for possible addition"), p5);
+
+        let f = GalloisField::new(19, true, None);
+        let ec = ElipticCurve::new(f, 7, 13, true).expect("ec cant be created");
+        let p1 = ec.new_point(2, 15).expect("point is on ec but an error occurs");
+        let p2 = ec.new_point(6, 10).expect("point is on ec but an error occurs");
+        let p3 = ec.new_point(9, 8).expect("point is on ec but an error occurs");
+        assert_eq!(ec.add(p1, p2).expect("error for possible addition"), p3);
+
+        let f = GalloisField::new(13, true, None);
+        let ec = ElipticCurve::new(f, 7, 11, true).expect("ec cant be created");
+        let p1 = ec.new_point(4, 5).expect("point is on ec but an error occurs");
+        let p2 = ec.new_point(6, 10).expect("point is on ec but an error occurs");
+        assert_eq!(ec.add(p1, p1).expect("error for possible addition"), p2);
+    }
+
+    #[test]
+    fn test_mul_points() {
+        // from ecc lectures
+        let f = GalloisField::new(13, true, None);
+        let ec = ElipticCurve::new(f, 7, 11, true).expect("ec cant be created");
+        let p1 = ec.new_point(4, 5).expect("point is on ec but an error occurs");
+        let p2 = ec.new_point(6, 10).expect("point is on ec but an error occurs");
+        let p3 = ec.new_point(4, 8).expect("point is on ec but an error occurs");
+        let p4 = ec.new_point(6, 3).expect("point is on ec but an error occurs");
+        assert_eq!(ec.mul(p1, 2u32).expect("error for possible addition"), p2);
+        assert_eq!(ec.mul(p1, 4u32).expect("error for possible addition"), p3);
+        assert_eq!(ec.mul(p3, 2u32).expect("error for possible addition"), p4);
+        assert_eq!(ec.mul(p2, 4u32).expect("error for possible addition"), p4);
+
+        //let f = GalloisField::new(13, true, None);
+        //let ec = ElipticCurve::new(f, -3, 3, true).expect("ec cant be created");
+        //let p1 = ec.new_point(1, 1).expect("point is on ec but an error occurs");
+        //let p2 = ec.new_point(11, 12).expect("point is on ec but an error occurs");
+        //assert_eq!(ec.mul(p1, 2u64).expect("error for possible addition"), p2);
+
+        //let f = GalloisField::new(17, true, None);
+        //let ec = ElipticCurve::new(f, 11, 3, true).expect("ec cant be created");
+        //let p1 = ec.new_point(5, 8).expect("point is on ec but an error occurs");
+        //let p2 = ec.new_point(6, 8).expect("point is on ec but an error occurs");
+        //assert_eq!(ec.mul(p1, 10u128).expect("error for possible addition"), p2);
+    }
 }

src/math/gallois.rs

@@ -35,11 +35,13 @@ pub const F_256_DEFAULT_RELATION: u128 = 0x11b;
 ///////////////////////////////////////////////////////////////////////////////////////////////////
 #[derive(Debug)]
 /// used when trying to find a root for a number which does not have a root.
-pub struct NoInverseError;
+pub struct NoInverseError {
+    pub n: u128
+}
 
 impl fmt::Display for NoInverseError {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "inverse for 0 does not exist")
+        write!(f, "inverse for {} does not exist", self.n)
     }
 }
 ///////////////////////////////////////////////////////////////////////////////////////////////////
@@ -136,12 +138,10 @@ impl GalloisField {
         T: Integer,
         T: NumCast,
         T: Debug,
-        K: Unsigned,
         K: Integer,
         K: NumCast,
         K: Debug,
         {
-        dbg!(&n);
             let mut n: i128 = num::cast(n).unwrap();
             if self.prime_base {
                 if n < 0 {
@@ -175,9 +175,8 @@ impl GalloisField {
 
     /// find the multiplicative inverse of a number
     pub fn inverse(self, n: u128) -> Result<u128, NoInverseError> {
-        dbg!(&n);
         if n == 0 {
-            return Err(NoInverseError);
+            return Err(NoInverseError{n});
         }
         let egcd = (n as i128).extended_gcd(&(self.base as i128));
         let egcd = self.reduce(egcd.x);
@@ -462,6 +461,12 @@ impl GalloisField {
 }
 
 ///////////////////////////////////////////////////////////////////////////////////////////////////
+
+#[cfg(test)]
+pub mod test {
+
+    use super::*;
+
 	#[test]
     fn test_gallois_sqrt() {
         let field = GalloisField::new(977, true, None);
@@ -514,3 +519,4 @@ fn test_calc_char() {
         //assert_eq!(GalloisField::new(64, true, None).calc_char(), 2);
         ////assert_eq!(GalloisField::new(2u128.pow(64u32), true, None).calc_char(), 2);
     }
+}