RSA算法优化
- 大数乘法
- 模乗优化
- 剩余定理（孙子定理）
- RSA加解密
- python的RSA计算优化
#-*- coding: utf-8 -*-
'''
/*********************************************************************************
*Copyright(C),2000-2013,KK Studio
*FileName: rsa
*Author: KingKong
*Version: 1.0
*Date: 20130709
*Description: //用于主要说明此程序文件完成的主要功能
//与其他模块或函数的接口、输出值、取值范围、
//含义及参数间的控制、顺序、独立及依赖关系
*Others: //其他内容说明
*Function List: //主要函数列表，每条记录应包含函数名及功能简要说明
1.RSA
2.RSA CRT
3.RSA MulMod
*History: //修改历史记录列表，每条修改记录应包含修改日期、修改者及修改内容简介
1.20130702:
**********************************************************************************/
'''
# sudo apt-get install python-setuptools
# sudo easy_install rsa-3.1.1-py2.7.egg
# import binascii
#print repr(binascii.unhexlify('0123456789abcdef'))
EASYKEY = True
def CRT_SRC(c, n, p, q, d=None, exp1=None, exp2=None):
'''
剩余定理的基础实现
c是密文
exp1 = d % (p-1)
exp2 = d % (q-1)
(1)计算d1←d(mod(p-1))与d2←d(mod(q-1));
(2)计算C1←c(modp)与C2←c(modq);
(3)计算M1←C1^d1 (modp)与M2←C2^d2(modq);
(4)计算B1←q-1(modp)与B2←p-1(modq);
(5)计算m←(M1*B1*q+M2*B2*p)(modN)
'''
c1 = c % p
c2 = c % q
if d != None:
d1 = d % (p-1)
d2 = d % (q-1)
elif exp1 != None:
d1 = exp1
d2 = exp2
else:
return 0
import rsa
y1 = rsa.common.inverse(q, p)
y2 = rsa.common.inverse(p, q)
m1 = pow(c1, d1, p)
m2 = pow(c2, d2, q)
m = (m1*q*y1 + m2*p*y2)%n
return m
def CRT_MMRC(c, n, p, q, coef, d=None, exp1=None, exp2=None):
'''
剩余定理的快速实现
c是密文
exp1 = d % (p-1)
exp2 = d % (q-1)
self.coef = rsa.common.inverse(q, p)
(1)计算d1←d(mod(p-1))与d2←d(mod(q-1));
(2)计算C1←c(mod p)与C2←c(mod q);
(3)计算M1←C1^d1 (modp)与M2←C2^d2(modq);
(4)计算B←p^-1(modp);
(5)计算m←M1+[(M2-M1)*B(modq)]*p
'''
c1 = c % p
c2 = c % q
if d != None:
d1 = d % (p-1)
d2 = d % (q-1)
elif exp1 != None:
d1 = exp1
d2 = exp2
else:
return 0
y1 = coef
m1 = pow(c1, d1, p)
m2 = pow(c2, d2, q)
m = m2 + (((m1-m2)*y1)%p)*q
return m
def dec2bin(number):
'''
转换数字为二进制字符串
:param number:
'''
m = {'0':'0000', '1':'0001', '2':'0010', '3':'0011',
'4':'0100', '5':'0101', '6':'0110', '7':'0111',
'8':'1000', '9':'1001', 'a':'1010', 'b':'1011',
'c':'1100', 'd':'1101', 'e':'1110', 'f':'1111'}
s = hex(number)[2:].rstrip('L')
return ''.join(m[x] for x in s).lstrip('0')
#print dec2bin(10), len(dec2bin(10))
def MulMod(m, r, e):
'''
a^m%r
343^474%2003=1819
'''
c = 1L
b = dec2bin(e)
length = 0;
while(length < (len(b))):
c = (c*c)%r;
# print c, b[length]
if (b[length] == "1"):
c = (c * m) % r;
length = length + 1;
return c
def RSA_ENC(m, n, e):
'''
RSA加密，处理小数据
:param m:
:param n:
:param e:
'''
return m**e%n
def RSA_DEC(c, n, d):
'''
RSA解密，处理小数据
:param c:
:param n:
:param d:
'''
return c**d%n
def RSA_ENC_Fast(m, n, e):
'''
RSA加密，处理大数，加速处理
:param m:
:param n:
:param e:
'''
return pow(m, e, n)
def RSA_DEC_Fast(c, n, d):
'''
RSA解密，处理大数，加速处理
:param c:
:param n:
:param d:
'''
return pow(c, d, n)
def main():
if EASYKEY == True:
n = 3727264081
d = 3349121513
e = 65537
p = 65063
q = 57287
exp1 = 55063
exp2 = 10095
coef = 50797
else:
n = 133258714669197804455201327242498072620373933399830946281753432589524373262313529490829857553863402092345114025453326547226675345976454214588491707723768296657213731743431331618394950680996499630699923360897031860272219245284778878593279460078556127568327691304405295451439978360703575209901885763486177804307
d = 88839143112798536303467551494998715080249288933220630854502288393016248841542352993886571702575601394896742683635551031484450230650969476392327805149178849037945720743702166302175205762735121467799910708222531056914667451445033725048565810909623712841116051352011118012226070375134490825522121220289982706011
e = 3
p = 11933806723950669295207846073987787705734940703054957716278358174994444687961839258803748173125990183157845108140695431551588508864566689717312651807708143
q = 11166488426677208786957286068049106111694059354243605518996542043073672540329181171939965947432316470456431280477737669321209492974404928986620399396037149
exp1 = 7955871149300446196805230715991858470489960468703305144185572116662963125307892839202498782083993455438563405427130287701059005909711126478208434538472095
exp2 = 7444325617784805857971524045366070741129372902829070345997694695382448360219454114626643964954877646970954186985158446214139661982936619324413599597358099
coef = 9906165481638181059785426924280606820580988396251355030296387570862138753002899617836092623649635665775562393844489153345463178213574659230193241203692517
m = 9999
print '********RSA BEGIN********************************************'
print 'message:', m
c = RSA_ENC(m, n, e)
print 'encrypt:', c
r = RSA_DEC_Fast(c, n, d)
print 'decrypt:', r
print '********RSA END**********************************************'
print '********RSA FAST BEGIN***************************************'
print 'message:', m
c = RSA_ENC_Fast(m, n, e)
print 'encrypt:', c
r = RSA_DEC_Fast(c, n, d)
print 'decrypt:', r
print '********RSA FAST END*****************************************'
print '********RSA MulMod BEGIN*************************************'
print 'message:', m
c = MulMod(m, n, e)
print 'encrypt:', c
r = MulMod(c, n, d)
print 'decrypt:', r
print '********RSA MulMod END***************************************'
print '********RSA CRT BEGIN****************************************'
print 'message:', m
c = RSA_ENC_Fast(m, n, e)
print 'encrypt:', c
r = CRT_SRC(c, n, p, q, d)
print 'decrypt:', r
print '********RSA CRT END******************************************'
print '********RSA CRT FAST BEGIN***********************************'
print 'message:', m
c = RSA_ENC_Fast(m, n, e)
print 'encrypt:', c
r = CRT_MMRC(c, n, p, q, coef, d, exp1, exp2)
print 'decrypt:', r
print '********RSA CRT FAST END*************************************'
if __name__ == '__main__':
main()