From c6bf1dac99102e8c47cc5ad99c69db63199f94b6 Mon Sep 17 00:00:00 2001
From: mii8080 <39086319+morioka22@users.noreply.github.com>
Date: Tue, 14 Jun 2022 01:27:12 +0000
Subject: [PATCH] =?UTF-8?q?Miller=E6=BA=96=E5=82=99?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 src/common/math.rs                   | 22 ++++++++++-
 src/elliptic_curve/elliptic_curve.rs | 56 +++++++++++++++++++++-------
 src/main.rs                          |  3 +-
 3 files changed, 65 insertions(+), 16 deletions(-)

diff --git a/src/common/math.rs b/src/common/math.rs
index a1c7054..5a36acc 100644
--- a/src/common/math.rs
+++ b/src/common/math.rs
@@ -44,7 +44,6 @@ pub fn random_n_q(p: BigInt) -> BigInt {
     let mut i = BigInt::one();
     let k = (p.clone() - BigInt::one()) >> 1i32;
     while i < p {
-        println!("pm {:?}", FiniteFieldElement::new(bigint_to_u512(i.clone()), bigint_to_u512(p.clone())).pow(bigint_to_u512(k.clone())).value);
         if bigint_to_u512(pow_mod(i.clone(),k.clone(),p.clone())) != U512::one() {
             break;
         }
@@ -53,6 +52,27 @@ pub fn random_n_q(p: BigInt) -> BigInt {
     i
 }
 
+pub fn mod_sqrt(a: BigInt, p: BigInt) -> BigInt {
+    if pow_mod(a.clone(), (p.clone() - BigInt::one()) >> 1u8, p.clone()) != BigInt::one() {
+        return -BigInt::one();
+    }
+
+    let r = (p.clone() - BigInt::one()) >> 1u8;
+    let b = random_n_q(p.clone());
+    let mut x = r.clone();
+    let mut y = BigInt::zero();
+
+    while (x.clone() & BigInt::one()) != BigInt::one() {
+        x = x >> 1u8;
+        y = y >> 1u8;
+        if abs(pow_mod(a.clone(), x.clone(), p.clone()) * pow_mod(b.clone(), y.clone(), p.clone()), p.clone()) != BigInt::one() {
+            y += r.clone();
+        }
+    }
+
+    abs(pow_mod(a.clone(), (x.clone() + BigInt::one()) >> 1u8, p.clone()) * pow_mod(b.clone(), y.clone() >> 1u8, p.clone()), p.clone())
+}
+
 pub fn mod_inv(a: BigInt, m: BigInt) -> BigInt {
     let mut a = a;
     if a < BigInt::zero() {
diff --git a/src/elliptic_curve/elliptic_curve.rs b/src/elliptic_curve/elliptic_curve.rs
index c60d4f6..9da1ff0 100644
--- a/src/elliptic_curve/elliptic_curve.rs
+++ b/src/elliptic_curve/elliptic_curve.rs
@@ -1,4 +1,4 @@
-use std::{ops::{Add, Mul, Neg}, fmt::Display, sync::mpsc};
+use std::{ops::{Add, Mul, Neg}, fmt::Display};
 
 use primitive_types::U512;
 
@@ -27,9 +27,47 @@ pub enum EllipticCurvePoint {
     Infinity
 }
 
+impl EllipticCurvePoint {
+    pub fn lambda(p: EllipticCurvePoint, q: EllipticCurvePoint) -> FiniteFieldElement {
+        let (x1, y1) = match p {
+            EllipticCurvePoint::Point { x, y, .. } => (x,y),
+            _ => panic!("P is inifinity.")
+        };
+
+        let (x2, y2) = match q {
+            EllipticCurvePoint::Point { x, y, .. } => (x,y),
+            _ => panic!("Q is inifinity.")
+        };
+
+        (y2 - y1) / (x2 - x1)
+    }
+
+    pub fn l(p: EllipticCurvePoint, q: EllipticCurvePoint, x: FiniteFieldElement, y: FiniteFieldElement) -> FiniteFieldElement {
+        let (x1, y1) = match p {
+            EllipticCurvePoint::Point { x, y, .. } => (x,y),
+            _ => panic!("P is inifinity.")
+        };
+
+        y - (Self::lambda(p, q) * (x - x1) + y1)
+    }
+
+    pub fn v(r: EllipticCurvePoint, x: FiniteFieldElement) -> FiniteFieldElement {
+        let xr = match r {
+            EllipticCurvePoint::Point { x, .. } => x,
+            _ => panic!("R is inifinity.")
+        };
+
+        x - xr
+    }
+
+    pub fn g(p: EllipticCurvePoint, q: EllipticCurvePoint, x: FiniteFieldElement, y: FiniteFieldElement) -> FiniteFieldElement {
+        Self::l(p, q, x, y) / Self::v(p + q, x)
+    }
+}
+
 impl Display for EllipticCurvePoint {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        if let EllipticCurvePoint::Point { x, y, a, b } = self {
+        if let EllipticCurvePoint::Point { x, y, .. } = self {
             write!(f, "({:x}, {:x})", x.value, y.value)
         } else {
             write!(f, "Infinity")
@@ -79,18 +117,8 @@ impl Add for EllipticCurvePoint {
                         }
 
                         let l = if x1 == x2 && y1 == y2 {
-                            let (t_tx, t_rx) = mpsc::channel();
-                            let (u_tx, u_rx) = mpsc::channel();
-                            std::thread::spawn(move || {
-                                let val = x1 * x1 * FiniteFieldElement::new(U512::from(3u8), p) + a;
-                                t_tx.send(val).unwrap();
-                            });
-                            std::thread::spawn(move || {
-                                let val = y1 * FiniteFieldElement::new(U512::from(2), p);
-                                u_tx.send(val).unwrap();
-                            });
-                            let t = t_rx.recv().unwrap();
-                            let u = u_rx.recv().unwrap();
+                            let t = x1 * x1 * FiniteFieldElement::new(U512::from(3u8), p) + a;
+                            let u = y1 * FiniteFieldElement::new(U512::from(2), p);
                             let a = t / u;
                             a
                         } else {
diff --git a/src/main.rs b/src/main.rs
index fddf71e..9560be1 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,11 +1,12 @@
 use bigdecimal::num_bigint::BigInt;
-use encrypt::{elliptic_curve::{elliptic_curve::EllipticCurve, encryption::Encryption}, common::{finite_field::FiniteFieldElement, math::random_n_q}};
+use encrypt::{elliptic_curve::{elliptic_curve::EllipticCurve, encryption::Encryption}, common::{finite_field::FiniteFieldElement, math::{random_n_q, mod_sqrt}}};
 use primitive_types::U512;
 
 fn main() {
     println!("Encryption Library");
 
     println!("{}", random_n_q(BigInt::from(23)));
+    println!("{}", mod_sqrt(BigInt::from(4), BigInt::from(23)));
 
     let p = U512::from_str_radix("115792089237316195423570985008687907853269984665640564039457584007908834671663", 10).unwrap();