RSA加密算法

RSA 算法：
其中加密encode和解密decode中的效率可以提高的log（n）

但是这个算法只是原型，只能对数字加密，对字符串加密时要将转换成AScII码的东东进行拆分才可以。要按位加密。当q，p过大时，将有溢出。改进的可以自己写一个大数类。但没有时间了，暂时就做成这个样子吧。

#include < iostream >
#include < string >
#include < ctime >
#include " math.h "
using namespace std;

bool isPrime( long ); // thenumberisprimeandreturntrue,elsereturnfalse;
long gcd( long a, long b); // findanumberwhichthetwonumberaandbdivideexactly.
long publicKey( long p, long q); // usingp,qtocalculatethepublickeye.
long privateKey( long e, long Qn); // usinge,Qntocalculatetheprivatekeyd.
long generKey( const long p, const long q, long * pubKey, long * priKey); // getthepublickeyandprivatekey.Andreturnn=p*q.
// char*encode(char*,longn,longpubKey); // encodetheText
// char*decode(char*,longn,longpriKey); // decodetheTextwhichhasbeenencoded.
long encode( long , long n, long pubKey); // encodetheText
long decode( long , long n, long priKey); // decodetheTextwhichhasbeenencoded.
int main()
... {

longp,q;
longpubKey;
longpriKey;
boolpass=true;
while(pass)
...{
cout<<"inputtwoprimenumbers!andthetwonumbersarebiggerthantwo!!"<<endl;
cin>>p>>q;
//srand(time(0));
//q=rand();
//p=rand();
if(isPrime(p)&&isPrime(q))
pass=false;
}
cout<<"p="<<p<<"q="<<q<<endl;
longn=generKey(p,q,&pubKey,&priKey);
cout<<"n:"<<n<<endl;
cout<<"inputthenumberforencoding!"<<endl;
longnum;
cin>>num;
//cout<<decode(encode(txt,n,pubKey),n,priKey);
longenText=encode(num,n,pubKey);
cout<<"encodetheText:"<<enText<<endl;
cout<<"decodetheText:"<<decode(enText,n,priKey)<<endl;
return0;
}

bool isPrime( long a)
... {
if(a>2)
...{
intb=2,c=sqrt(a);
for(;b<c;b++)
...{
if(a%b==0)
returnfalse;
}
returntrue;
}
returnfalse;
}

long gcd( long a, long b)
... {
intx=a%b;
if(x==0)
returnb;
else
returngcd(b,x);
}

long publicKey( const long p, const long q, const long Qn)
... {

srand(time(0));
longe=rand();
if(e>=Qn)
e=3;
while(gcd(e,Qn)!=1)
...{

e++;
if(e>=Qn)
...{
e=3;
}
}
cout<<"e:"<<e<<endl;
returne;
}

long privateKey( const long e, const long Qn)
... {
srand(time(0));
longd=rand();
if(d>=Qn)
d=3;
while(e*d%Qn!=1||e==d)
...{
d++;
if(d>=Qn)
...{
d=3;
}
}
cout<<"d:"<<d<<endl;
returnd;
}

long generKey( const long p, const long q, long * pubKey, long * priKey)
... {
longn=p*q;
longQn=(p-1)*(q-1);
*pubKey=publicKey(p,q,Qn);
*priKey=privateKey(*pubKey,Qn);
returnn;
}



/**/ /*

char*encode(char*txt,longn,longpubKey)
{
intlength=strlen(txt);
char*text=newchar[length];
strcpy(text,txt);
for(inti=0;i<length;i++)
{

text[i]=(int)pow(text[i],pubKey)%n;
}
returntext;
}

char*decode(char*txt,longn,longpriKey)
{
intlength=strlen(txt);
char*text=newchar[length];
strcpy(text,txt);
for(inti=0;i<length;i++)
{
text[i]=(int)pow(text[i],priKey)%n;
}
returntext;
}
*/
long encode( long num, long n, long pubKey)
... {
longtmp=1;
for(inti=0;i<pubKey;i++)
...{
tmp*=num;
tmp%=n;
}
returntmp;
}
long decode( long num, long n, long priKey)
... {
longtmp=1;
for(inti=0;i<priKey;i++)
...{
tmp*=num;
tmp%=n;
}
returntmp;
}