RSA算法优化

 

RSA算法优化

分类： 加解密算法 2013-07-10 20:05  81人阅读  评论(0)  收藏  举报

RSA 剩余定理孙子定理 速度优化 python

RSA算法优化

1. 大数乘法
2. 模乗优化
3. 剩余定理（孙子定理）
4. RSA加解密
5. 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()