use less clone and builtin modinv

ecc_rs.pyi

@@ -1,4 +1,51 @@
 # ecc_rs.pyi
 
-def add(p1: tuple[int, int], p2: tuple[int, int]) -> tuple[int, int]: ...
+point = tuple[int, int]
-def multiply(point: tuple[int, int], n: int) -> tuple[int, int]: ...
+
+def add(p1: point, p2: point) -> point:
+    """
+    Adds two points on the SM2 elliptic curve.
+
+    Performs point addition on the SM2 curve defined by `sm2p256v1()`.
+
+    Args:
+        p1 (point): A tuple representing the x and y coordinates of the first point.
+        p2 (point): A tuple representing the x and y coordinates of the second point.
+
+    Raises:
+        Panic: If the x or y coordinates of either point are not valid on the curve.
+
+    Returns:
+        point: A tuple representing the x and y coordinates of the resulting point after addition.
+
+    Example:
+        >>> p1 = (x1, y1)
+        >>> p2 = (x2, y2)
+        >>> result = add(p1, p2)
+    """
+    ...
+
+def multiply(point: point, n: int) -> point:
+    """
+    multiply(point, n)
+
+    Performs scalar multiplication of a point on the SM2 curve.
+
+    performs the multiplication operation on the SM2 curve defined by `sm2p256v1()`.
+
+    Args:
+        point (point): representing the x and y coordinates of the point.
+        n (int): representing the scalar to multiply the point by.
+
+    Raises:
+        Panic: If the x or y coordinates of the point are not less than the curve parameter `p`.
+
+    Returns:
+        point: representing the x and y coordinates of the result point.
+
+    Example:
+        >>> point = (g, g)
+        >>> n = 10
+        >>> result = multiply(point, n)
+    """
+    ...

readme.md

@@ -0,0 +1,4 @@
+# ecc_rs
+
+a simple rust implementation of SM2 binding for python.  
+powered by pyo3.

src/lib.rs

@@ -16,10 +16,19 @@ struct CurveFp {
 }
 
 #[derive(Debug, Clone)]
-struct Point {
+struct Point<'a> {
     x: BigUint,
     y: BigUint,
-    curve: CurveFp,
+    curve: &'a CurveFp,
+}
+
+/// 椭圆曲线上的点（雅可比坐标）
+#[derive(Clone)]
+struct JacobianPoint<'a> {
+    x: BigUint,         // X 坐标
+    y: BigUint,         // Y 坐标
+    z: BigUint,         // Z 坐标
+    curve: &'a CurveFp, // 椭圆曲线的参数
 }
 
 // Initialize the SM2 Curve
@@ -59,137 +68,180 @@ fn sm2p256v1() -> CurveFp {
     }
 }
 
-/// Calculates the greatest common divisor (GCD) of two `BigUint` numbers.
+fn point_addition<'a>(p1: &'a Point<'a>, p2: &'a Point<'a>) -> Point<'a> {
-///
+    // 如果 p1 是零点，返回一个新构造的 p2 点，而不是克隆
-/// The function uses the Euclidean algorithm to compute the GCD. The algorithm is based on
-/// the principle that the greatest common divisor of two numbers does not change if the larger
-/// number is replaced by its difference with the smaller number.
-///
-/// # Arguments
-///
-/// * `a` - The first `BigUint` number.
-/// * `b` - The second `BigUint` number.
-///
-/// # Returns
-///
-/// * `BigUint` - The greatest common divisor of `a` and `b`.
-///
-/// # Example
-///
-/// ```
-/// let a = BigUint::from(60u32);
-/// let b = BigUint::from(48u32);
-/// let result = gcd(a, b);
-/// assert_eq!(result, BigUint::from(12u32));
-/// ```
-fn gcd(a: &BigUint, b: &BigUint) -> BigUint {
-    let mut c = a.clone();
-    let mut d = b.clone();
-    while !a.is_zero() {
-        let temp = c.clone();
-        c = d % c;
-        d = temp;
-    }
-    d
-}
-
-/// Computes the modular inverse of `a` under modulo `m`.
-///
-/// # Arguments
-///
-/// * `a` - A reference to a BigUint representing the number to find the modular inverse of.
-/// * `p` - A reference to a BigUint representing the modulus.
-///
-/// # Return1
-///
-/// * A BigUint representing the modular inverse of `a` modulo `p`.
-///
-/// # Panics
-///
-/// This function will panic if the modular inverse does not exist (i.e., if `a` and `p` are not coprime).
-fn mod_inverse(a: &BigUint, m: &BigUint) -> BigUint {
-    let (mut t, mut new_t) = (BigUint::zero(), BigUint::one());
-    let (mut r, mut new_r) = (m.clone(), a.clone());
-
-    while !new_r.is_zero() {
-        let quotient = &r / &new_r;
-
-        let temp_t = new_t.clone();
-        new_t = if t < (quotient.clone() * &temp_t) {
-            // BigUint can't be negative,
-            // so we use mod to handle the case where t < quotient * temp_t
-            (&t + m - &(quotient.clone() * &temp_t) % m) % m
-        } else {
-            &t - &(quotient.clone() * &temp_t)
-        };
-
-        let temp_r = new_r.clone();
-        new_r = &r - &(quotient.clone() * &temp_r);
-        r = temp_r;
-        t = temp_t;
-    }
-
-    if r > BigUint::one() {
-        panic!("Modular inverse does not exist");
-    }
-
-    if t < BigUint::zero() {
-        t += m;
-    }
-
-    t
-}
-fn point_addition(p1: &Point, p2: &Point) -> Point {
-    let curve = &p1.curve;
-    let p = &curve.p;
-
     if p1.x.is_zero() && p1.y.is_zero() {
+        return Point {
+            x: p2.x.clone(),
+            y: p2.y.clone(),
+            curve: p2.curve, // 如果 curve 是引用，保持引用即可
+        };
+    }
+
+    // 如果 p2 是零点，返回一个新构造的 p1 点，而不是克隆
+    if p2.x.is_zero() && p2.y.is_zero() {
+        return Point {
+            x: p1.x.clone(),
+            y: p1.y.clone(),
+            curve: p1.curve, // 如果 curve 是引用，保持引用即可
+        };
+    }
+
+    from_jacobian(jacobian_add(to_jacobian(p1), to_jacobian(p2)))
+}
+
+/// 将仿射坐标转换为雅可比坐标 (X, Y, Z)
+fn to_jacobian<'a>(p: &'a Point) -> JacobianPoint<'a> {
+    JacobianPoint {
+        x: p.x.clone(),
+        y: p.y.clone(),
+        z: BigUint::one(), // Z = 1 表示仿射坐标
+        curve: p.curve,
+    }
+}
+
+/// 将雅可比坐标转换为仿射坐标
+fn from_jacobian(p: JacobianPoint) -> Point {
+    if p.z.is_zero() {
+        return Point {
+            x: BigUint::zero(),
+            y: BigUint::zero(),
+            curve: p.curve,
+        };
+    }
+    let p_mod = &p.curve.p;
+
+    // 计算 Z 的模反
+    let z_inv = p.z.modinv(p_mod).expect("modinv failed");
+    let z_inv2 = (&z_inv * &z_inv) % p_mod; // Z_inv^2
+    let z_inv3 = (&z_inv2 * &z_inv) % p_mod; // Z_inv^3
+
+    // 计算 x = X * Z_inv^2, y = Y * Z_inv^3
+    let x_affine = (&p.x * &z_inv2) % p_mod;
+    let y_affine = (&p.y * &z_inv3) % p_mod;
+
+    Point {
+        x: x_affine,
+        y: y_affine,
+        curve: p.curve,
+    }
+}
+
+/// 雅可比坐标下的点加法
+fn jacobian_add<'a>(p1: JacobianPoint<'a>, p2: JacobianPoint<'a>) -> JacobianPoint<'a> {
+    if p1.z.is_zero() {
         return p2.clone();
     }
-    if p2.x.is_zero() && p2.y.is_zero() {
+    if p2.z.is_zero() {
         return p1.clone();
     }
 
-    let lambda = if p1.x == p2.x && p1.y == p2.y {
+    let p_mod = &p1.curve.p;
-        let num = (BigUint::from(3u32) * &p1.x * &p1.x + &curve.a) % p;
-        let denom = (BigUint::from(2u32) * &p1.y) % p;
-        (num * mod_inverse(&denom, p)) % p
-    } else {
-        let num = ((&p2.y + p) - &p1.y) % p;
-        let denom = ((&p2.x + p) - &p1.x) % p;
 
-        (num * mod_inverse(&denom, p)) % p
+    // U1 = X1 * Z2^2, U2 = X2 * Z1^2
-    };
+    let z1z1 = (&p1.z * &p1.z) % p_mod;
+    let z2z2 = (&p2.z * &p2.z) % p_mod;
+    let u1 = (&p1.x * &z2z2) % p_mod;
+    let u2 = (&p2.x * &z1z1) % p_mod;
 
-    let x3 = (lambda.clone() * &lambda - &p1.x - &p2.x) % p;
+    // S1 = Y1 * Z2^3, S2 = Y2 * Z1^3
-    let y3 = (lambda * (&p1.x + p - &x3) - &p1.y) % p;
+    let z1z1z1 = (&z1z1 * &p1.z) % p_mod;
+    let z2z2z2 = (&z2z2 * &p2.z) % p_mod;
+    let s1 = (&p1.y * &z2z2z2) % p_mod;
+    let s2 = (&p2.y * &z1z1z1) % p_mod;
 
-    Point {
+    if u1 == u2 && s1 == s2 {
+        // 点倍运算 (p1 == p2)
+        return jacobian_double(p1);
+    }
+
+    // H = U2 - U1, R = S2 - S1
+    let h = (u2 + p_mod - &u1) % p_mod;
+    let r = (s2 + p_mod - &s1) % p_mod;
+
+    // X3 = R^2 - H^3 - 2 * U1 * H^2
+    let h2 = (&h * &h) % p_mod;
+    let h3 = (&h2 * &h) % p_mod;
+    let x3 = (&r * &r + p_mod - &h3 - (&BigUint::from(2u32) * &u1 * &h2) % p_mod) % p_mod;
+
+    // Y3 = R * (U1 * H^2 - X3) - S1 * H^3
+    let y3 =
+        (&r * ((&u1 * &h2 + p_mod - (&x3 % p_mod)) % p_mod) + p_mod - (&s1 * &h3) % p_mod) % p_mod;
+
+    // Z3 = Z1 * Z2 * H
+    let z3 = (&p1.z * &p2.z * &h) % p_mod;
+
+    JacobianPoint {
         x: x3,
         y: y3,
-        curve: curve.clone(),
+        z: z3,
+        curve: p1.curve,
     }
 }
 
-fn point_multiplication(p: &Point, n: &BigUint) -> Point {
+/// 雅可比坐标下的点倍运算
-    let mut result = Point {
+fn jacobian_double(p: JacobianPoint) -> JacobianPoint {
+    let p_mod = &p.curve.p;
+
+    if p.y.is_zero() {
+        return JacobianPoint {
+            x: BigUint::zero(),
+            y: BigUint::zero(),
+            z: BigUint::zero(),
+            curve: p.curve,
+        };
+    }
+
+    // S = 4 * X * Y^2
+    let y2 = (&p.y * &p.y) % p_mod;
+    let s = (&p.x * &y2 * BigUint::from(4u32)) % p_mod;
+
+    // M = 3 * X^2 + a * Z^4
+    let z2 = (&p.z * &p.z) % p_mod;
+    let z4 = (&z2 * &z2) % p_mod;
+    let m = ((&p.x * &p.x * BigUint::from(3u32)) + &p.curve.a * &z4) % p_mod;
+
+    // X3 = M^2 - 2 * S
+    let x3 = (&m * &m + p_mod - &s * BigUint::from(2u32)) % p_mod;
+
+    // Y3 = M * (S - X3) - 8 * Y^4
+    let y4 = (&y2 * &y2) % p_mod;
+    let y3 = (&m * (&s + p_mod - &x3) + p_mod - BigUint::from(8u32) * &y4) % p_mod;
+
+    // Z3 = 2 * Y * Z
+    let z3 = (&p.y * &p.z * BigUint::from(2u32)) % p_mod;
+
+    JacobianPoint {
+        x: x3,
+        y: y3,
+        z: z3,
+        curve: p.curve,
+    }
+}
+
+fn point_multiplication<'a>(p: &'a Point<'a>, n: &BigUint) -> Point<'a> {
+    let mut result = JacobianPoint {
         x: BigUint::zero(),
-        y: BigUint::zero(),
+        y: BigUint::one(), // 无穷远点的雅可比坐标表示
-        curve: p.curve.clone(),
+        z: BigUint::zero(),
+        curve: p.curve,
     };
 
-    let mut addend = p.clone();
+    // 将输入点从仿射坐标转换为雅可比坐标
+    let mut addend = to_jacobian(p);
     let mut k = n.clone();
 
+    // 使用二进制展开法进行点乘运算
     while !k.is_zero() {
         if &k % 2u32 == BigUint::one() {
-            result = point_addition(&result, &addend);
+            result = jacobian_add(result, addend.clone());
         }
-        addend = point_addition(&addend, &addend);
+        addend = jacobian_double(addend); // 倍点运算
         k >>= 1;
     }
 
-    result
+    // 将结果从雅可比坐标转换为仿射坐标
+    from_jacobian(result)
 }
 
 /// SM2 addition
@@ -202,24 +254,24 @@ fn add(p1: (BigUint, BigUint), p2: (BigUint, BigUint)) -> (BigUint, BigUint) {
     let x2 = p2.0;
     let y2 = p2.1;
 
-    // 检查 x 和 y 是否小于曲线参数 p
+    // Check if x and y are less than the curve parameter p
-    if x1 >= curve.p || y1 >= curve.p {
+    match (x1 >= curve.p, y1 >= curve.p, x2 >= curve.p, y2 >= curve.p) {
-        panic!("Point p1 coordinates are out of range");
+        (true, _, _, _) | (_, true, _, _) | (_, _, true, _) | (_, _, _, true) => {
-    }
+            panic!("Point coordinates are out of range");
-    if x2 >= curve.p || y2 >= curve.p {
+        }
-        panic!("Point p2 coordinates are out of range");
+        _ => (),
     }
 
     let point1 = Point {
         x: x1,
         y: y1,
-        curve: curve.clone(),
+        curve: &curve,
     };
 
     let point2 = Point {
         x: x2,
         y: y2,
-        curve: curve.clone(),
+        curve: &curve,
     };
 
     let result = point_addition(&point1, &point2);
@@ -228,13 +280,23 @@ fn add(p1: (BigUint, BigUint), p2: (BigUint, BigUint)) -> (BigUint, BigUint) {
 
 /// SM2 multiply
 #[pyfunction]
-fn multiply(point: (BigUint, BigUint), n: BigUint) -> (BigUint, BigUint) {
+fn multiply(point: (BigUint, BigUint), mut n: BigUint) -> (BigUint, BigUint) {
     let curve = sm2p256v1();
+
+    if n >= curve.n {
+        n %= &curve.n;
+    }
+
+    match (point.0 < curve.p, point.1 < curve.p) {
+        (false, _) | (_, false) => panic!("Point coordinates are out of range"),
+        _ => {}
+    }
+
     // Construct the point with BigUint values
     let point = Point {
-        x: point.0.clone(),
+        x: point.0,
-        y: point.1.clone(),
+        y: point.1,
-        curve: curve.clone(),
+        curve: &curve,
     };
     // Perform point multiplication
     let result = point_multiplication(&point, &n);

test.py

@@ -1,5 +1,7 @@
 import ecc_rs
+import time
 
+point = tuple[int, int]
 # Example point coordinates for P1 and P2 as tuples (x1, y1) and (x2, y2)
 p1 = (
     1234567890123456789012345678901234567890123456789012345678901234,
@@ -17,3 +19,55 @@ print(f"Resulting Point: x = {result_x}, y = {result_y}")
 
 result = ecc_rs.multiply(p1, 2)
 print(f"Resulting Point: x = {result[0]}, y = {result[1]}")
+
+
+# 生成密钥对模块
+class CurveFp:
+    def __init__(self, A, B, P, N, Gx, Gy, name):
+        self.A = A
+        self.B = B
+        self.P = P
+        self.N = N
+        self.Gx = Gx
+        self.Gy = Gy
+        self.name = name
+
+
+sm2p256v1 = CurveFp(
+    name="sm2p256v1",
+    A=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC,
+    B=0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93,
+    P=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF,
+    N=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123,
+    Gx=0x32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7,
+    Gy=0xBC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0,
+)
+
+# 生成元
+g = (sm2p256v1.Gx, sm2p256v1.Gy)
+
+
+def multiply(a: point, n: int) -> point:
+
+    result = ecc_rs.multiply(a, n)
+    return result
+
+
+def add(a: point, b: point) -> point:
+    result = ecc_rs.add(a, b)
+    return result
+
+
+start_time = time.time()  # 获取开始时间
+for i in range(10):
+    result = multiply(g, 10000)  # 执行函数
+end_time = time.time()  # 获取结束时间
+elapsed_time = end_time - start_time  # 计算执行时间
+print(f"rust multiply 执行时间: {elapsed_time:.6f} 秒")
+
+start_time = time.time()  # 获取开始时间
+for i in range(10):
+    result = add(g, g)  # 执行函数
+end_time = time.time()  # 获取结束时间
+elapsed_time = end_time - start_time  # 计算执行时间
+print(f"rust add 执行时间: {elapsed_time:.6f} 秒")