整数判断是否互质并求逆元的 python 实现

算法来自《密码学原理与实践》page129

其余两个待补充

#!/usr/dev/python
#-*- coding:utf-8 -*-

'''
Extended Euclidean algorithm(a,b)
code by ShaNgZ
algorithm from <cryptography theory and pratice,third editon>
2019_01_09
'''

a = input("a=")
b = input("b=")

s0 = 0
s  = 1
t0 = 0
t  = 1
q  = a/b
r  = a%b
# Ri = Si*R0 + Ti*R1

def euclidean_algorithen():
	pass

def extended_euclidean():
	global a,b,s0,s,t0,t,q,r
	ex_a = a
	ex_b = b
	ex_s0 = s0
	ex_s = 1
	ex_t0 = 0
	ex_t = 1
	ex_q = q
	ex_r = r
	while(ex_r>0):
		temp = ex_t0-ex_q*ex_t
		ex_t0 = ex_t
		ex_t = temp

		temp = ex_s0-ex_q*ex_s
		ex_s0 = ex_s
		ex_s = temp

		ex_a = ex_b
		ex_b = ex_r
		ex_q = ex_a/ex_b
		ex_r = ex_a%ex_b
	ex_r = ex_b
	
	print "exr_gcd(%d,%d) = "  % (a,b) + str(ex_r)
	if ex_r == 1:
		print "inverse(%d) mod %d = %d" % (a,b,ex_s)

	#comment: r=gcd(a,b) and sa+tb=r

def multiplicative_inverse():
	pass

if __name__ == '__main__':
	extended_euclidean()