import base64, libnum,gmpy2
def continuedFra(x, y):
"""计算连分数
:param x: 分子
:param y: 分母
:return: 连分数列表
"""
cf = []
while y:
cf.append(x // y)
x, y = y, x % y
return cf
def gradualFra(cf):
"""计算传入列表最后的渐进分数
:param cf: 连分数列表
:return: 该列表最后的渐近分数
"""
numerator = 0
denominator = 1
for x in cf[::-1]:
numerator, denominator = denominator, x * denominator + numerator
return numerator, denominator
def solve_pq(a, b, c):
"""使用韦达定理解出pq，x^2−(p+q)∗x+pq=0
:param a:x^2的系数
:param b:x的系数
:param c:pq
:return:p，q
"""
par = gmpy2.isqrt(b * b - 4 * a * c)
return (-b + par) // (2 * a), (-b - par) // (2 * a)
def getGradualFra(cf):
"""计算列表所有的渐近分数
:param cf: 连分数列表
:return: 该列表所有的渐近分数
"""
gf = []
for i in range(1, len(cf) + 1):
gf.append(gradualFra(cf[:i]))
return gf
def wienerAttack(e, n):
"""
:param e:
:param n:
:return: 私钥d
"""
cf = continuedFra(e, n)
gf = getGradualFra(cf)
for d, k in gf:
if k == 0: continue
if (e * d - 1) % k != 0:
continue
phi = (e * d - 1) // k
p, q = solve_pq(1, n - phi + 1, n)
if p * q == n:
return d
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