RSA算法优化

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()