diffi-hellma(密钥交换算法）

#include < iostream >
#include <cmath>
#include <cstdlib>
#include <ctime>
using namespace std ;
typedef unsigned __int64 ull;
typedef unsigned int uint ;
const uint upperBound = 1000000 ; //上界的设置真纠结！！！
const  unsigned short SHORTMAX = 0Xffff ;
bool flag [ 10000000000 ] ;//10^9

#include "variable.h"
#include "millerRabin.h"
#include "get_a_p.h"
#define getxA() ( rand ( ) % ( upperBound + 1 ) )
#define getxB() ( rand ( ) % ( upperBound + 1 ) )
#define getyA powerMod
#define getyB powerMod
#define getKeyA powerMod
#define getKeyB powerMod

int main ( ) {
srand ( ( unsigned ) time ( NULL ) ) ;
uint a , p , xA , yA , xB , yB , keyA , keyB ;

consult_a_p ( a , p ) ;//a,p 属于[ushort ,upperBound ]
//xA,xB[0,upperBound]
xA = getxA ( ) ;
xB = getxB ( ) ;
//yA,yB[1,p-1]
yA = getyA ( a , xA , p ) ;
yB = getyB ( a , xB , p ) ;
//kyeA,keyB[1,p-1]
keyA = getKeyA ( yB , xA , p ) ;
keyB = getKeyB ( yA , xB , p ) ;
cout << "the diffiHellma algorithm is " ;//认证diffiHellma算法的正确性
if ( keyA == keyB ) cout  << "right !" ;
else cout << "wrong!" ;
cout << endl ;
return 0 ;
}

bool isOk ( uint a , uint p ) {
uint i ;
for ( i = 1 ; i < p ; i ++ )//[1,p-1]
flag [ i ] = false ;
uint p0 ;
for ( i = 1 ; i < p ; i ++ ) {
p0 = powerMod ( a , i , p ) ;
if ( flag [ p0 ]  ) return false ;
else flag [ p0 ] = true ;
}
return true ;
}
uint power ( uint a , uint p ) {
if ( p == 0 ) return 1 ;
uint k = 1 ;
while ( p != 1 ) {
if ( p & 1 ) k *= a ;
a *= a ;
p >>= 1 ;
}
return a * k ;
}
uint get_A_Possible_Value ( ) {
uint p , a , mi ;
do {
//get a
do {
a = rand ( ) % ( upperBound -2 ) + 3 ;//[3,upperBound]
} while ( ! millerRabin ( a ) ) ;
//get mi
const uint MAXOFMI = log ( upperBound ) / log ( a ) ;//p^mi<=upperBound
mi = rand ( ) % MAXOFMI + 1 ;//[1,upperBound]
//get p
p = power ( a , mi )  ;
} while ( p < SHORTMAX ) ;
return p ;
}
ull gcd( ull a, ull b ){
ull t;
while ( b ) {
t = b ;
b = a % b ;
a = t ;
}
return a ;
}
void consult_a_p ( uint & a , uint & p ) {
//2 , 4 , p^mi , 2*p^mi p为奇素数  ,p,a尽量取大一点;possible_Value ，使得它的每一个值都位于[ushort ,uint]
uint possible_Value [ 2 ] ;
possible_Value [ 0 ] = get_A_Possible_Value ( )  ;
do {
possible_Value [ 1 ] = get_A_Possible_Value ()  ;
} while ( possible_Value [ 1 ] > upperBound / 2 ) ;
possible_Value [ 1 ] *= 2 ;

p = possible_Value [ rand ( ) % 2 ] ; //get p

//  get a
//求出一个数的本原根求得我想死！有什么好的算法没啊？？
a = p - 1 ;
while ( gcd ( a , p ) != 1 || ! isOk ( a , p ) ) {
cout << a << endl ;
a -- ;
}
}

ull multiMod(ull a,ull b,ull m){//s=(a*b)(mod m) (n<2^62)
//  return ( (a%m) * (b%m) ) % m; // this wiull overflow!
a %= m;
b %= m;
ull s = 0;
while( b ) {
if(b & 1) {
s += a;
if(s >= m) s -= m;
}
a <<= 1; b >>= 1;//a*b=(a*2)*(b/2)
if(a >= m) a -= m;
}
return  s;
}
ull powerMod ( ull a , ull p , ull n ) {
ull k = 1 ;
while ( p != 1 ) {
if ( p & 1 ) {
k = multiMod ( k , a , n ) ;
}
p >>= 1 ;//a^p=(a^2)^(p/2)
a = multiMod ( a , a , n ) ;
}
return multiMod ( a , k , n ) ;
}
bool witness(ull a, ull n)
{
//test wether a^(n-1)%n=1 or not
//n-1=2^k*q
ull q = n - 1;
int k = 0;
while( ( q &1 ) == 0 ) {
k ++ ;
q >>= 1 ;
}
//a^(2^i*q)%n=1 or n-1  (-1<i<=k)
ull y , x = powerMod(a, q, n);
if (x == 1 || x == n-1) return false;
/*  while(k --)
{
x = x * x % n;
if (x == n-1) return false;//素数的个数少数合数，先判断素数效率低一些!
}
return true;
*/
while( k -- ){
y = multiMod ( x , x , n ) ;
if(y == 1 && x != 1 && x != n-1 ) return true;//素数的个数少数合数，先判断合数效率高一些!
x = y;
}
if ( y != 1 ) return true; // composite
return false; //may be prime

}
bool millerRabin(ull n, int T = 10) {
//	if (n == 2) return true;   取奇素数，因此n==2不要
if ((n&1) == 0 || n < 2) return false;
while(T --) {
ull a = rand() % (n-1) + 1;//  a>=1 && a<=n-1
if (witness(a, n)) return false;
}
return true;
}