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bytefield_matrix_aftergauss_fast.cpp
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bytefield_matrix_aftergauss_fast.cpp
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// bytefield.cpp : Defines the entry point for the console application.
//
#include "stdio.h"
#include "math.h"
#include "stdlib.h"
#include "time.h"
/*
基于字节有限域的秘密分享，秘密一个字节一个字节的计算影子
缺点如果秘密是有意义的话时，而不是随机值，那么如果在缺一人的情况下，可以尝试穷举缺的影子。
但如果把信息加密的话，这种尝试可能无效。
可以共享的信息为：key|msg更好
*/
typedef unsigned char word8;
typedef unsigned short word16;
typedef unsigned long word32;
word8 Logtable[256] = {
0, 0, 25, 1, 50, 2, 26, 198, 75, 199, 27, 104, 51, 238, 223, 3,
100, 4, 224, 14, 52, 141, 129, 239, 76, 113, 8, 200, 248, 105, 28, 193,
125, 194, 29, 181, 249, 185, 39, 106, 77, 228, 166, 114, 154, 201, 9, 120,
101, 47, 138, 5, 33, 15, 225, 36, 18, 240, 130, 69, 53, 147, 218, 142,
150, 143, 219, 189, 54, 208, 206, 148, 19, 92, 210, 241, 64, 70, 131, 56,
102, 221, 253, 48, 191, 6, 139, 98, 179, 37, 226, 152, 34, 136, 145, 16,
126, 110, 72, 195, 163, 182, 30, 66, 58, 107, 40, 84, 250, 133, 61, 186,
43, 121, 10, 21, 155, 159, 94, 202, 78, 212, 172, 229, 243, 115, 167, 87,
175, 88, 168, 80, 244, 234, 214, 116, 79, 174, 233, 213, 231, 230, 173, 232,
44, 215, 117, 122, 235, 22, 11, 245, 89, 203, 95, 176, 156, 169, 81, 160,
127, 12, 246, 111, 23, 196, 73, 236, 216, 67, 31, 45, 164, 118, 123, 183,
204, 187, 62, 90, 251, 96, 177, 134, 59, 82, 161, 108, 170, 85, 41, 157,
151, 178, 135, 144, 97, 190, 220, 252, 188, 149, 207, 205, 55, 63, 91, 209,
83, 57, 132, 60, 65, 162, 109, 71, 20, 42, 158, 93, 86, 242, 211, 171,
68, 17, 146, 217, 35, 32, 46, 137, 180, 124, 184, 38, 119, 153, 227, 165,
103, 74, 237, 222, 197, 49, 254, 24, 13, 99, 140, 128, 192, 247, 112, 7,
};
word8 Alogtable[256] = {
1, 3, 5, 15, 17, 51, 85, 255, 26, 46, 114, 150, 161, 248, 19, 53,
95, 225, 56, 72, 216, 115, 149, 164, 247, 2, 6, 10, 30, 34, 102, 170,
229, 52, 92, 228, 55, 89, 235, 38, 106, 190, 217, 112, 144, 171, 230, 49,
83, 245, 4, 12, 20, 60, 68, 204, 79, 209, 104, 184, 211, 110, 178, 205,
76, 212, 103, 169, 224, 59, 77, 215, 98, 166, 241, 8, 24, 40, 120, 136,
131, 158, 185, 208, 107, 189, 220, 127, 129, 152, 179, 206, 73, 219, 118, 154,
181, 196, 87, 249, 16, 48, 80, 240, 11, 29, 39, 105, 187, 214, 97, 163,
254, 25, 43, 125, 135, 146, 173, 236, 47, 113, 147, 174, 233, 32, 96, 160,
251, 22, 58, 78, 210, 109, 183, 194, 93, 231, 50, 86, 250, 21, 63, 65,
195, 94, 226, 61, 71, 201, 64, 192, 91, 237, 44, 116, 156, 191, 218, 117,
159, 186, 213, 100, 172, 239, 42, 126, 130, 157, 188, 223, 122, 142, 137, 128,
155, 182, 193, 88, 232, 35, 101, 175, 234, 37, 111, 177, 200, 67, 197, 84,
252, 31, 33, 99, 165, 244, 7, 9, 27, 45, 119, 153, 176, 203, 70, 202,
69, 207, 74, 222, 121, 139, 134, 145, 168, 227, 62, 66, 198, 81, 243, 14,
18, 54, 90, 238, 41, 123, 141, 140, 143, 138, 133, 148, 167, 242, 13, 23,
57, 75, 221, 124, 132, 151, 162, 253, 28, 36, 108, 180, 199, 82, 246, 1,
};
word8 Inv[256]= {
0, 1, 141, 246, 203, 82, 123, 209, 232, 79, 41, 192, 176, 225, 229, 199,
116, 180, 170, 75, 153, 43, 96, 95, 88, 63, 253, 204, 255, 64, 238, 178,
58, 110, 90, 241, 85, 77, 168, 201, 193, 10, 152, 21, 48, 68, 162, 194,
44, 69, 146, 108, 243, 57, 102, 66, 242, 53, 32, 111, 119, 187, 89, 25,
29, 254, 55, 103, 45, 49, 245, 105, 167, 100, 171, 19, 84, 37, 233, 9,
237, 92, 5, 202, 76, 36, 135, 191, 24, 62, 34, 240, 81, 236, 97, 23,
22, 94, 175, 211, 73, 166, 54, 67, 244, 71, 145, 223, 51, 147, 33, 59,
121, 183, 151, 133, 16, 181, 186, 60, 182, 112, 208, 6, 161, 250, 129, 130,
131, 126, 127, 128, 150, 115, 190, 86, 155, 158, 149, 217, 247, 2, 185, 164,
222, 106, 50, 109, 216, 138, 132, 114, 42, 20, 159, 136, 249, 220, 137, 154,
251, 124, 46, 195, 143, 184, 101, 72, 38, 200, 18, 74, 206, 231, 210, 98,
12, 224, 31, 239, 17, 117, 120, 113, 165, 142, 118, 61, 189, 188, 134, 87,
11, 40, 47, 163, 218, 212, 228, 15, 169, 39, 83, 4, 27, 252, 172, 230,
122, 7, 174, 99, 197, 219, 226, 234, 148, 139, 196, 213, 157, 248, 144, 107,
177, 13, 214, 235, 198, 14, 207, 173, 8, 78, 215, 227, 93, 80, 30, 179,
91, 35, 56, 52, 104, 70, 3, 140, 221, 156, 125, 160, 205, 26, 65, 28,
};
word8 mul(word8 a, word8 b) {
/* multiply two elements of GF(2^m)
* needed for MixColumn and InvMixColumn
*/
if (a && b) return Alogtable[(Logtable[a] + Logtable[b])%255];
else return 0;
};
word8 inv(word8 a) {
/* invert of GF(2^m)
*/
return Inv[a];
};
class Cbytefield
{
private:
word8 a;
public:
Cbytefield(word8 b){a=b;};
Cbytefield(){};
word8 value() {return a;};
Cbytefield operator+ (Cbytefield b){return a^b.value();};
Cbytefield operator- (Cbytefield b){return a^b.value();};
Cbytefield operator* (Cbytefield b){return mul(a,b.value());};
Cbytefield operator/ (Cbytefield b){return mul(a,inv(b.value()));};
Cbytefield operator= (Cbytefield b){return a=b.value();};
int operator== (Cbytefield b){return a==b.value();};
int operator< (Cbytefield b){return a<b.value();};
Cbytefield invert() {return inv(a);};
Cbytefield pow (Cbytefield b){ word8 c=1;
for(int i=0;i<b.value();i++) c=mul(c,a);
return c;};
};
class CbyteShare
{
private:
Cbytefield toShareBytem;
Cbytefield an[256],Ax[256],Ay[256];
Cbytefield v[256][257];
unsigned short m,n;
void setv()
{
int i,j;
for(i=0;i<n;i++)
{ Cbytefield k(i+1);
for(j=0;j<m;j++)
{
v[i][j]=k.pow(j);
}
}
/*
for(i=0;i<n;i++)
{ printf("\n");
for(j=0;j<m;j++)
printf(" %3d",v[i][j].value());
}
*/
}
void RandSetAx(){
srand( (unsigned)time( NULL ) );
for(int i=0;i<m;i++)
{ word8 r=rand()%256;
if(0==r) {i--;continue;}
Ax[i]=r;
}
};
public:
CbyteShare(unsigned short _m,unsigned short _n) {m=_m;n=_n;};
void SetShareByte(word8 bytemsg) {toShareBytem=bytemsg;RandSetAx();setv();Ax[0]=toShareBytem; };
void MakeShare();
word8 RestorShareByte(unsigned char share[]);
};
void CbyteShare::MakeShare()
{
int i,j,k;
printf("\n Ax=");
for(i=0;i<m;i++)
printf(" %d",Ax[i].value());
/*
for(i=0;i<n;i++)
{
printf("\n");
for(j=0;j<m;j++)
{
printf(" %3d",v[i][j].value());
}
}
*/ printf("\n---share--------------------\n");
for(i=0;i<n;i++)
{
Ay[i]=0;
for(j=0;j<m;j++)
{
Ay[i]=Ay[i]+v[i][j]*Ax[j];
}
v[i][j]=Ay[i]; //give v[i][m]=ay[i]
printf(" %3d ",Ay[i].value());
}
printf("\n-------share end------------");
}
word8 CbyteShare::RestorShareByte(unsigned char share[])
{
short i,j;
Cbytefield rv[256][256],tmp,numhead,tmp2; //tmp restorshare matrix
printf("\n --------------------------------------------");
for( i=0;i<m;i++)
{ printf("\n");
for( j=0;j<m+1;j++)
{
rv[i][j]=v[share[i]][j];
printf(" %3d",rv[i][j].value());
}
}
printf("\n --------------------------------------------");
for(i=0;i<m;i++)
{
tmp=rv[i][i];
for(j=i+1;j<m;j++)
{
numhead=rv[j][i];
if(numhead==0) continue;
tmp2=tmp/numhead;
for(int k=i;k<m+1;k++)
{ rv[j][k]=rv[j][k]* tmp2;
rv[j][k]=rv[j][k]-rv[i][k];
}
}
}
/*
for(i=0;i<m;i++)
{ printf("\n");
for(j=0;j<m+1;j++)
{
printf(" %3d",rv[i][j].value());
}
}
printf("\n--------------");
*/
for(i=m-1;i>0;i--)
{
//rv[i][m]=rv[i][m]/rv[i][i];
tmp=rv[i][i];
for(j=i-1;j>=0;j--)
{
numhead=rv[j][i];
if(numhead==0) continue;
tmp2=tmp/numhead;
for(int k=j;k<=m+1;k++)
{
rv[j][k]=rv[j][k]* tmp2;
rv[j][k]=rv[j][k]-rv[i][k];
}
}
}
/*
for(i=0;i<m;i++)
{ printf("\n");
for(j=0;j<m+1;j++)
{
printf(" %3d",rv[i][j].value());
}
}
*/
printf("\n");
for(i=0;i<m;i++)
{
rv[i][m]=rv[i][m]/rv[i][i];
printf(" %d,",rv[i][m].value());
}
return rv[0][m].value();
}
int main(int argc, char* argv[])
{
word16 a,b,c;
unsigned char share[256];
int m=255,n=255,msg;
scanf("%d%d%d",&m,&n,&msg);
for(a=0;a<n;a++) share[a]=a;
for(a=0;a<3*n;a++)
{ word8 r=rand()%n;
word8 tmp=share[0]; share[0]=share[r];share[r]=tmp;
}
CbyteShare mshare(m,n);
mshare.SetShareByte(msg);
mshare.MakeShare();
printf("\nm=====%d ",mshare.RestorShareByte(share));
return 0;
}