(Miller-Rabin)我如何处理大指数的数字?
(Miller-Rabin)How do I deal with number with large exponents?
我有 Miller-Rabin 实现
def MillerRabin(n,a):
e = 0
q = n-1
while q % 2 == 0:
e += 1
q = q/2
if a**q % n == 1:
return 1
for i in range(e):
if a ** (q * 2 ** i) % n == n-1:
return 1
return 0
(n, minA, maxA) = map(int, sys.argv[1:4])
print [MillerRabin(n, a) for a in range(minA,maxA)]
共有三个输入:数字、最小基数、最大基数。数字低时功能正常。但是当数字太大时,我得到一个错误(测试用例是 number = 12530759607784496010584573923,min-base = 16,max-base = 32)
exponent must be at most 9223372036854775807
使用内置的 pow
函数。它可以带一个可选的 mod 参数
>>> help(pow)
Help on built-in function pow in module __builtin__:
pow(...)
pow(x, y[, z]) -> number
With two arguments, equivalent to x**y. With three arguments,
equivalent to (x**y) % z, but may be more efficient (e.g. for longs).
def MillerRabin(n, a):
e = 0
q = n-1
while q % 2 == 0:
e += 1
q = q // 2
if pow(a, q, n) == 1:
return 1
for i in range(e):
if pow(a , (q * 2 ** i) , n) == n - 1:
return 1
return 0
我有 Miller-Rabin 实现
def MillerRabin(n,a):
e = 0
q = n-1
while q % 2 == 0:
e += 1
q = q/2
if a**q % n == 1:
return 1
for i in range(e):
if a ** (q * 2 ** i) % n == n-1:
return 1
return 0
(n, minA, maxA) = map(int, sys.argv[1:4])
print [MillerRabin(n, a) for a in range(minA,maxA)]
共有三个输入:数字、最小基数、最大基数。数字低时功能正常。但是当数字太大时,我得到一个错误(测试用例是 number = 12530759607784496010584573923,min-base = 16,max-base = 32)
exponent must be at most 9223372036854775807
使用内置的 pow
函数。它可以带一个可选的 mod 参数
>>> help(pow)
Help on built-in function pow in module __builtin__:
pow(...)
pow(x, y[, z]) -> number
With two arguments, equivalent to x**y. With three arguments,
equivalent to (x**y) % z, but may be more efficient (e.g. for longs).
def MillerRabin(n, a):
e = 0
q = n-1
while q % 2 == 0:
e += 1
q = q // 2
if pow(a, q, n) == 1:
return 1
for i in range(e):
if pow(a , (q * 2 ** i) , n) == n - 1:
return 1
return 0