📄 bigint.cpp
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#include"iostream.h"
#include"stdlib.h"
#include"time.h"
#include"math.h"
#include"string.h"
#define MAXLEN 40
class BigInt
{
public:
int Sign;
int Length;
unsigned long value[MAXLEN];
BigInt();
BigInt(int S,int L);
~BigInt();
BigInt& Mov(BigInt& A);
void Mov(unsigned __int64 A);
int Cmp(BigInt& A);
BigInt Add(BigInt& A);
BigInt Add(unsigned long A);
BigInt Sub(BigInt& A);
BigInt Sub(unsigned long A);
BigInt Mul(BigInt& A);
BigInt Mul(unsigned long A);
BigInt Div(BigInt& A);
BigInt Div(unsigned long A);
BigInt Mod(BigInt& A);
unsigned long Mod(unsigned long A);
BigInt RsaMon(BigInt& A, BigInt& B);
BigInt Euc(BigInt& A);
void Get(char* Str);
//void produce(BigInt& A);
// int Neql(BigInt& A);
// void Put(BigInt& A);
};
BigInt::BigInt()
{
Sign=1;
Length=1;
for(int i=0;i<MAXLEN;i++) value[i]=0;
}
BigInt::BigInt(int S,int L)
{
Sign=S;
Length=L;
for(int i=0;i<Length;i++) value[i]=0;
}
BigInt::~BigInt()
{
}
int BigInt::Cmp(BigInt& A)
{
if(Length>A.Length)return 1;
if(Length<A.Length)return -1;
for(int i=Length-1;i>=0;i--)
{
if(value[i]>A.value[i])return 1;
if(value[i]<A.value[i])return -1;
}
return 0;
}
BigInt& BigInt::Mov(BigInt& A)
{
Length=A.Length;
for(int i=0;i<MAXLEN;i++) value[i]=A.value[i];
return *this;
}
void BigInt::Mov(unsigned __int64 A)
{
if(A>0xffffffff)
{
Length=2;
value[1]=(unsigned long)(A>>32);
value[0]=(unsigned long)A;
}
else
{
Length=1;
value[0]=(unsigned long)A;
}
for(int i=Length;i<MAXLEN;i++)
value[i]=0;
}
BigInt BigInt::Add(BigInt& A)
{
BigInt X;
if(X.Sign==A.Sign)
{
X.Mov(*this);
int carry=0;
unsigned __int64 sum=0;
if(X.Length<A.Length)X.Length=A.Length;
for(int i=0;i<X.Length;i++)
{
sum=A.value[i];
sum=sum+X.value[i]+carry;
X.value[i]=(unsigned long)sum;
if(sum>0xffffffff)carry=1;
else carry=0;
}
if(X.Length<MAXLEN)
{
X.value[X.Length]=carry;
X.Length+=carry;
}
return X;
}
else{X.Mov(A);X.Sign=1-X.Sign;return Sub(X);}
}
BigInt BigInt::Add(unsigned long A)
{
BigInt X;
X.Mov(*this);
unsigned __int64 sum;
sum=X.value[0];
sum+=A;
X.value[0]=(unsigned long)sum;
if(sum>0xffffffff)
{
int i=1;
while(X.value[i]==0xffffffff){X.value[i]=0;i++;}
X.value[i]++;
if(Length==i)Length++;
}
return X;
}
BigInt BigInt::Sub(BigInt& A)
{
BigInt X;
if(Sign==A.Sign)
{
X.Mov(*this);
int cmp=X.Cmp(A);
if(cmp==0){X.Mov(0);return X;}
int len,carry=0;
unsigned __int64 num;
unsigned long *s,*d;
if(cmp>0)
{
s=X.value;
d=A.value;
len=X.Length;
}
if(cmp<0)
{
s=A.value;
d=X.value;
len=A.Length;
X.Sign=1-X.Sign;
}
for(int i=0;i<len;i++)
{
if((s[i]-carry)>=d[i])
{
X.value[i]=s[i]-carry-d[i];
carry=0;
}
else
{
num=0x100000000+s[i];
X.value[i]=(unsigned long)(num-carry-d[i]);
carry=1;
}
}
while(X.value[len-1]==0)len--;
X.Length=len;
return X;
}
else{X.Mov(A);X.Sign=1-X.Sign;return Add(X);}
}
BigInt BigInt::Sub(unsigned long A)
{
BigInt X;
X.Mov(*this);
if(X.value[0]>=A){X.value[0]-=A;return X;}
if(X.Length==1){X.Mov(0);return X;}
unsigned __int64 num=0x100000000+X.value[0];
X.value[0]=(unsigned long)(num-A);
int i=1;
while(X.value[i]==0){X.value[i]=0xffffffff;i++;}
X.value[i]--;
if(X.value[i]==0)X.Length--;
return X;
}
BigInt BigInt::Mul(BigInt& A)
{
BigInt X,Y;
unsigned __int64 mul;
unsigned long carry;
for(int i=0;i<A.Length;i++)
{
Y.Length=Length;
carry=0;
for(int j=0;j<Length;j++)
{
mul=value[j];
mul=mul*A.value[i]+carry;
Y.value[j]=(unsigned long)mul;
carry=(unsigned long)(mul>>32);
}
if(carry&&(Y.Length<MAXLEN))
{
Y.Length++;
Y.value[Y.Length-1]=carry;
}
if(Y.Length<MAXLEN-i)
{
Y.Length+=i;
for(int k=Y.Length-1;k>=i;k--)Y.value[k]=Y.value[k-i];
for(k=0;k<i;k++)Y.value[k]=0;
}
X.Mov(X.Add(Y));
}
if(Sign+A.Sign==1)X.Sign=0;
else X.Sign=1;
return X;
}
BigInt BigInt::Mul(unsigned long A)
{
BigInt X;
unsigned __int64 mul;
unsigned long carry=0;
X.Mov(*this);
for(int i=0;i<Length;i++)
{
mul=value[i];
mul=mul*A+carry;
X.value[i]=(unsigned long)mul;
carry=(unsigned long)(mul>>32);
}
if(carry){X.Length++;X.value[X.Length-1]=carry;}
return X;
}
BigInt BigInt::Div(BigInt& A)
{
if(A.Length==1)return Div(A.value[0]);
BigInt X,Y,Z;
unsigned i,len;
unsigned __int64 num,div;
Y.Mov(*this);
while(Y.Cmp(A)>=0)
{
div=Y.value[Y.Length-1];
num=A.value[A.Length-1];
len=Y.Length-A.Length;
if((div==num)&&(len==0)){X.Mov(X.Add(1));break;}
if((div<=num)&&len){len--;div=(div<<32)+Y.value[Y.Length-2];}
div=div/(num+1);
Z.Mov(div);
if(len)
{
Z.Length+=len;
for(i=Z.Length-1;i>=len;i--)Z.value[i]=Z.value[i-len];
for(i=0;i<len;i++)Z.value[i]=0;
}
X.Mov(X.Add(Z));
Y.Mov(Y.Sub(A.Mul(Z)));
}
return X;
}
BigInt BigInt::Div(unsigned long A)
{
BigInt X;
X.Mov(*this);
if(X.Length==1){X.value[0]=X.value[0]/A;return X;}
unsigned __int64 div,mul;
unsigned long carry=0;
for(int i=X.Length-1;i>=0;i--)
{
div=carry;
div=(div<<32)+X.value[i];
X.value[i]=(unsigned long)(div/A);
mul=(div/A)*A;
carry=(unsigned long)(div-mul);
}
if(X.value[X.Length-1]==0)X.Length--;
return X;
}
BigInt BigInt::Mod(BigInt& A)
{
BigInt X,Y;
unsigned __int64 div,num;
unsigned long carry=0;
unsigned i,len;
X.Mov(*this);
while(X.Cmp(A)>=0)
{
div=X.value[X.Length-1];
num=A.value[A.Length-1];
len=X.Length-A.Length;
if((div==num)&&(len==0)){X.Mov(X.Sub(A));break;}
if((div<=num)&&len){len--;div=(div<<32)+X.value[X.Length-2];}
div=div/(num+1);
Y.Mov(div);
Y.Mov(A.Mul(Y));
if(len)
{
Y.Length+=len;
for(i=Y.Length-1;i>=len;i--)Y.value[i]=Y.value[i-len];
for(i=0;i<len;i++)Y.value[i]=0;
}
X.Mov(X.Sub(Y));
}
return X;
}
unsigned long BigInt::Mod(unsigned long A)
{
if(Length==1)return(value[0]%A);
unsigned __int64 div;
unsigned long carry=0;
for(int i=Length-1;i>=0;i--)
{
div=value[i];
div+=carry*0x100000000;
carry=(unsigned long)(div%A);
}
return carry;
}
BigInt BigInt::RsaMon(BigInt& A, BigInt& B)
{
BigInt X,Y,Z;
X.Mov(1);
Y.Mov(*this);
Z.Mov(A);
while((Z.Length!=1)||Z.value[0])
{
if(Z.value[0]&1)
{
Z.Mov(Z.Sub(1));
X.Mov(X.Mul(Y));
X.Mov(X.Mod(B));
}
else
{
Z.Mov(Z.Div(2));
Y.Mov(Y.Mul(Y));
Y.Mov(Y.Mod(B));
}
}
return X;
}
BigInt BigInt::Euc(BigInt& A)
{
BigInt M,E,X,Y,I,J;
int x,y;
M.Mov(A);
E.Mov(*this);
X.Mov(0);
Y.Mov(1);
x=y=1;
while((E.Length!=1)||(E.value[0]!=0))
{
I.Mov(M.Div(E));
J.Mov(M.Mod(E));
M.Mov(E);
E.Mov(J);
J.Mov(Y);
Y.Mov(Y.Mul(I));
if(x==y)
{
if(X.Cmp(Y)>=0)Y.Mov(X.Sub(Y));
else{Y.Mov(Y.Sub(X));y=0;}
}
else{Y.Mov(X.Add(Y));x=1-x;y=1-y;}
X.Mov(J);
}
if(x==0)X.Mov(A.Sub(X));
return X;
}
void Put(BigInt& A)
{
for(int i=A.Length-1;i>=0;i--)
{
cout<<A.value[i];
if(i==0)
cout<<endl<<"*********************************信息安全2班***********************************"<<endl;
}
}
void produce(BigInt& A)
{
srand(unsigned long(time(NULL)));
A.value[0]=rand();
}
int set(BigInt X,BigInt Y,BigInt N)
{
X.Mul(Y);
X.Mod(N);
if(X.value[0]==1&&X.value[1]==0) return 1;
else return 0;
}
/*unsigned long gcd(unsigned long m,BigInt& n)
{
BigInt r,x;
x.value[0]=m;
while(Neql(x)!=0)
{
r.Mov(n.Mod(x));
n.Mov(x);
x.Mov(r);
}
m=n.value[0];
return m;
}
*/
int Neql(BigInt& A)
{
if(A.value[0]==0&&A.value[1]==0)
return 0;
else
return 1;
}
unsigned long Gcd(BigInt m,BigInt n)
{
BigInt r;
unsigned long j=0;
if(m.Cmp(n)==1)
{
r.Mov(n);
n.Mov(m);
m.Mov(r);
}
while(Neql(m)!=0)
{
r.Mov(n.Mod(m)); //r=n%m;
n.Mov(m); //n=m;
m.Mov(r); //m=r;
}
j=n.value[0];
return j;
}
/* temp.Mov(n);
for(int i=temp.Length-1;i>=0;i--)
if(temp.value[i]==0)
{
n.Length--;
break;
}
return (unsigned long)n;
}
unsigned long inveser(BigInt& A)
{
unsigned long *x;
*x=A.value[0];
return *x;
}
*/
void BigInt::Get(char* Str)
{
int len=strlen(Str),k;
Mov(0);
for(int i=0;i<len;i++)
{
Mov(Mul(10));
if((Str[i]>='0')&&(Str[i]<='9'))
k=Str[i]-48;
else k=0;
Mov(Add(k));
}
}
/*void BigInt::Solve(BigInt& A)
{
unsigned long k;
BigInt X,Y;
X.Mov(A);
while(A.value[A.Length-1]==0) A.Length--;
if(A.Length==1) break;
for(int i=0;i<=A.Length-1;i++)
{
A.Mov(A.Sub(0x100000000));
X.value[i]=A.value[0];
}
}
*/
int main()
{
BigInt p(1,5),q(1,5),n(1,10),N(1,10),e,m,c,D,d(1,6);
char *S;
char *Z;
char *W;
char *T;
S=new char[1280];
Z=new char[1280];
W=new char[1280];
T=new char[1280];
cout<<"please input the BigInt p:";
cin>>S;
p.Get(S);
cout<<"the BigInt p is:"<<endl;
Put(p);
cout<<"please input the BigInt q:";
cin>>Z;
q.Get(Z);
cout<<"the BigInt q is:"<<endl;
Put(q);
n.Mov(p.Mul(q));
N.Mov((p.Sub(1)).Mul(q.Sub(1)));
cout<<"N is "<<endl;
Put(N);
cout<<"the BigInt n is:"<<endl;
Put(n);
for(int i=101;i<=1001;i++)
{
d.Mov(i);
if(Gcd(d,N)==1)
{
cout<<"the BigInt d is:";
break;
}
}
cout<<"与N互素的随机整数:"<<endl;
Put(d);
for(unsigned long y=3;y<101;y++)
{
e.Mov(d.Euc(N));
if(set(e,d,N)==1) break;
}
cout<<"the BigInt e is:"<<endl;
Put(e);
cout<<"请输入您要加密的信息:"<<endl;
cin>>T;
m.Get(T);
cout<<"您输入的明文数字串为:"<<endl;
Put(m);
c.Mov(m.RsaMon(e,n));
cout<<"经加密后的信息为:"<<endl;
Put(c);
D.Mov(c.RsaMon(d,n));
cout<<"经解密后的数字串为:"<<endl;
Put(D);
cout<<endl<<"*********************************信息安全2班***********************************"<<endl;
cout<<"@退出请按 q 键@";
cin>>W;
if(W=="q") exit(1);
delete S;
delete Z;
delete W;
delete T;
return 0;
}
/*
//小素数表
const static int PrimeTable[550]=
{ 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
293, 307, 311, 313, 317, 331, 337, 347, 349, 353,
359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
613, 617, 619, 631, 641, 643, 647, 653, 659, 661,
673, 677, 683, 691, 701, 709, 719, 727, 733, 739,
743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,
1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297,
1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453,
1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597,
1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901,
1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,
1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063,
2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131,
2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221,
2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293,
2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437,
2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539,
2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,
2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689,
2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749,
2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833,
2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909,
2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001,
3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083,
3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187,
3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259,
3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343,
3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433,
3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517,
3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659,
3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,
3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823,
3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911,
3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001
};
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