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本帖最后由 gclome 于 2021-11-8 19:46 编辑
easyecc
ECC求公钥
使用场景：
- 已知椭圆曲线加密Ep(a,b)参数为
- p = 15424654874903
- a = 16546484
- b = 4548674875
- G(6478678675,5636379357093)
- 私钥为
- k = 546768
- 求公钥K(x,y)
代码如下：
- import collections
- import random
- EllipticCurve = collections.namedtuple('EllipticCurve', 'name p a b g n h')
- curve = EllipticCurve(
- 'secp256k1',
- # Field characteristic.
- p=15424654874903, //有限域的p，就是要mod的数
- # Curve coefficients.
- a=16546484,
- b=4548674875, //a,b是椭圆曲线方程上的参数
- # Base point.
- g=(6478678675,5636379357093), //取一个基点
- # Subgroup order.
- n=546768, //私钥
- # Subgroup cofactor.
- h=1,
- )
- # Modular arithmetic ##########################################################
- def inverse_mod(k, p): //使用扩展欧几里得算法求模逆
- """Returns the inverse of k modulo p.
- This function returns the only integer x such that (x * k) % p == 1.
- k must be non-zero and p must be a prime.
- """
- if k == 0:
- raise ZeroDivisionError('division by zero') //被除数不能为0
- if k < 0:
- # k ** -1 = p - (-k) ** -1 (mod p) //负数求mod
- return p - inverse_mod(-k, p)
- # Extended Euclidean algorithm. //扩展欧几里得算法
- s, old_s = 0, 1
- t, old_t = 1, 0
- r, old_r = p, k
- while r != 0:
- quotient = old_r // r
- old_r, r = r, old_r - quotient * r
- old_s, s = s, old_s - quotient * s
- old_t, t = t, old_t - quotient * t
- gcd, x, y = old_r, old_s, old_t
- assert gcd == 1
- assert (k * x) % p == 1
- return x % p
- # Functions that work on curve points #########################################
- def is_on_curve(point):
- """Returns True if the given point lies on the elliptic curve."""
- if point is None:
- # None represents the point at infinity.
- return True
- x, y = point
- return (y * y - x * x * x - curve.a * x - curve.b) % curve.p == 0
- def point_neg(point):
- """Returns -point."""
- assert is_on_curve(point)
- if point is None:
- # -0 = 0
- return None
- x, y = point
- result = (x, -y % curve.p)
- assert is_on_curve(result)
- return result
- def point_add(point1, point2):
- """Returns the result of point1 + point2 according to the group law."""
- assert is_on_curve(point1)
- assert is_on_curve(point2)
- if point1 is None:
- # 0 + point2 = point2
- return point2
- if point2 is None:
- # point1 + 0 = point1
- return point1
- x1, y1 = point1
- x2, y2 = point2
- if x1 == x2 and y1 != y2:
- # point1 + (-point1) = 0
- return None
- if x1 == x2:
- # This is the case point1 == point2.
- m = (3 * x1 * x1 + curve.a) * inverse_mod(2 * y1, curve.p)
- else:
- # This is the case point1 != point2.
- m = (y1 - y2) * inverse_mod(x1 - x2, curve.p)
- x3 = m * m - x1 - x2
- y3 = y1 + m * (x3 - x1)
- result = (x3 % curve.p,
- -y3 % curve.p)
- assert is_on_curve(result)
- return result
- def scalar_mult(k, point):
- """Returns k * point computed using the double and point_add algorithm."""
- assert is_on_curve(point)
- if k < 0:
- # k * point = -k * (-point)
- return scalar_mult(-k, point_neg(point))
- result = None
- addend = point
- while k:
- if k & 1:
- # Add.
- result = point_add(result, addend)
- # Double.
- addend = point_add(addend, addend)
- k >>= 1
- assert is_on_curve(result)
- return result
- # Keypair generation and ECDHE ################################################
- def make_keypair():
- """Generates a random private-public key pair."""
- private_key = curve.n
- public_key = scalar_mult(private_key, curve.g)
- return private_key, public_key
- private_key, public_key = make_keypair()
- print("private key:", hex(private_key))
- #print("public key: (0x{:x}, 0x{:x})".format(*public_key))
- #print("public key".public_key)
- print(public_key)
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发表于 2021-11-7 16:25:21
楼主
