一.题目
二.解题过程
1.打开附件，考察ECC加密
2.参考脚本：
import collections
import random
EllipticCurve = collections.namedtuple('EllipticCurve', 'name p a b g n h')
curve = EllipticCurve(
'secp256k1',
# Field characteristic.
p=int(input('p=')),
# Curve coefficients.
a=int(input('a=')),
b=int(input('b=')),
# Base point.
g=(int(input('Gx=')),
int(input('Gy='))),
# Subgroup order.
n=int(input('k=')),
# Subgroup cofactor.
h=1,
)
# Modular arithmetic ##########################################################
def inverse_mod(k, p):
"""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')
if k < 0:
# k ** -1 = p - (-k) ** -1 (mod p)
return p - inverse_mod(-k, p)
# Extended Euclidean algorithm.
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))
3.运行，得到公钥：(0xcb19fe553fa, 0x50545408eb4)
4.将公钥x,y转为10进制相加，得到flag：cyberpeace{19477226185390}
三.总结
