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share.c
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share.c
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#include "secshare.h"
/*Solve a random system of linear equations using the Gauss-Jordan-Function
*
*This version computes inside the field (M,+,*) for M being the set 0<=k<p for p being a prime number and modulus of the field.
*
*Other than gje_intmod.c it uses interdependent coefficients: each row is formed as k ~~ (m x x^2 x^3 ... x^(n-1)), so that
*k=m*1 + a*x + b*x^2 ... z*x^(n-1)
*This can be used to split a secret m among n persons by creating random a,b,c,... and x and giving each person his/her k and x,
*the algorithm below can then compute m,a,b,c... from n sets of k and x.
*
*Other than gje_intmod2.c it uses large integers and can thus handle much larger numbers.
*
*written by Konrad Rosenbaum, 2004
*This code is protected by the GNU GPL v2
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <gmp.h>
/*the matrix and result field*/
mpz_t **kmatrix,**hmatrix,*kvec,*hvec;
/*n=size of the matrix*/
static int n,np;
/*p is the prime and modulo*/
static mpz_t p;
static void setbin(mpz_t n,byte*b,int l)
{
char buf[1024];
static const char hex[]="0123456789ABCDEF";
int i;
for(i=0;i<l;i++){
buf[i*2]=hex[b[i]>>4];
buf[i*2+1]=hex[b[i]&0xf];
}
buf[l*2]=0;
mpz_set_str(n,buf,16);
}
void sharevector(int n_)
{
int i,j;
byte hdl[17];
n=n_;
/*intialize vector and p*/
kvec=malloc(n*sizeof(mpz_t));
hvec=malloc(n*sizeof(mpz_t));
for(i=0;i<n;i++){
mpz_init(kvec[i]);
mpz_init(hvec[i]);
if(i==0){
setbin(kvec[0],key,16);
setbin(hvec[0],hashv,16);
printf("Setting key: %s\n",key_prints(0,key));
printf("Setting hash: %s\n",key_prints(0,hashv));
}else{
for(j=0;j<16;j++)
hdl[j]=randbyte();
setbin(kvec[i],hdl,16);
for(j=0;j<16;j++)
hdl[j]=randbyte();
setbin(hvec[i],hdl,16);
}
}
mpz_init(p);
/*generate random prime*/
hdl[0]=1;
for(i=0;i<500;i++){
for(j=1;j<17;j++)
hdl[j]=randbyte();
hdl[16]|=1;
setbin(p,hdl,17);
j=mpz_probab_prime_p(p,100);
if(j)break;
}
if(!j){
fprintf(stderr,"Unable to generate a good prime. Giving up.\n");
exit(1);
}
}
void sharematrix(int n_)
{
int i,j;
n=n_;np=0;
kmatrix=malloc(n*sizeof(mpz_t*));
hmatrix=malloc(n*sizeof(mpz_t*));
for(i=0;i<n;i++){
kmatrix[i]=malloc((n+1)*sizeof(mpz_t));
hmatrix[i]=malloc((n+1)*sizeof(mpz_t));
for(j=0;j<=n;j++)mpz_init(kmatrix[i][j]);
for(j=0;j<=n;j++)mpz_init(hmatrix[i][j]);
}
mpz_init(p);
}
void share(char*fn)
{
int i;
mpz_t x,k,t,e;
byte rnd[16];
char buf[1024];
FILE *f;
f=fopen(fn,"w+");
if(f==NULL){
fprintf(stderr,"Unable to open file %s.\n",fn);
return;
}
/*generate random x*/
mpz_init(x);
for(i=0;i<16;i++)rnd[i]=randbyte();
setbin(x,rnd,16);
/*calculate k*/
mpz_init(k);
mpz_init(t);
mpz_init(e);
for(i=0;i<n;i++){
/*k=k + kvec[i]*x^i*/
mpz_powm(t,x,e,p);
mpz_mul(t,t,kvec[i]);
mpz_add(k,k,t);
mpz_mod(k,k,p);
/*incr e so that it matches the next i*/
mpz_add_ui(e,e,1);
}
fprintf(f,"%s\n",mpz_get_str(buf,16,p));
fprintf(f,"%s\n",mpz_get_str(buf,16,x));
fprintf(f,"%s\n",mpz_get_str(buf,16,k));
mpz_set_ui(e,0);
mpz_set_ui(k,0);
for(i=0;i<n;i++){
/*k=k + hvec[i]*x^i*/
mpz_powm(t,x,e,p);
mpz_mul(t,t,hvec[i]);
mpz_add(k,k,t);
mpz_mod(k,k,p);
/*incr e so that it matches the next i*/
mpz_add_ui(e,e,1);
}
fprintf(f,"%s\n",mpz_get_str(buf,16,k));
fclose(f);
mpz_clear(x);
mpz_clear(k);
mpz_clear(t);
mpz_clear(e);
}
void unshare(char*fn)
{
FILE *f;
char buf[1024];
mpz_t x,kk,kh,e;
int i;
if(np>=n)return;
/*read file, fill values*/
f=fopen(fn,"r");
if(f==NULL){
fprintf(stderr,"Unable to read file %s. Continuing.\n",fn);
return;
}
mpz_init(x);
mpz_init(kk);
mpz_init(kh);
mpz_init(e);
fscanf(f,"%s",buf);
mpz_set_str(p,buf,16);
fscanf(f,"%s",buf);
mpz_set_str(x,buf,16);
fscanf(f,"%s",buf);
mpz_set_str(kk,buf,16);
fscanf(f,"%s",buf);
mpz_set_str(kh,buf,16);
fclose(f);
/*generate matrixes*/
for(i=0;i<n;i++){
mpz_powm(kmatrix[np][i],x,e,p);
mpz_powm(hmatrix[np][i],x,e,p);
mpz_add_ui(e,e,1);
}
mpz_set(kmatrix[np][n],kk);
mpz_set(hmatrix[np][n],kh);
/*next line...*/
np++;
mpz_clear(x);
mpz_clear(kk);
mpz_clear(kh);
mpz_clear(e);
}
/*print the matrix*/
void printm(mpz_t**matrix)
{
int i,j;
char buf[1024];
for(i=0;i<n;i++){
for(j=0;j<=n;j++)
printf(" %s",mpz_get_str(buf,16,matrix[i][j]));
printf("\n");
}
printf("\n");
}
static void solve(mpz_t**matrix)
{
int i,j,k;
mpz_t f,*t,t1;
mpz_init(f);
mpz_init(t1);
/*bring matrix into Row Echelon Form*/
/*printf("Calculating.\n");*/
for(i=0;i<n;i++){/*iterate main diagonal*/
j=1;
while(!mpz_cmp_ui(matrix[i][i],0)){
/*exchange rows if working position is zero*/
if(i+j>=n){
fprintf(stderr,"System is unsolvable!\n");
exit(1);
}
t=matrix[i];
matrix[i]=matrix[i+j];
matrix[i+j]=t;
j++;
}
/*divide row by working position*/
mpz_invert(f,matrix[i][i],p);/*f=1/m[i,i]*/
for(j=0;j<=n;j++){
/*m[i,j]=m[i,j]/m[i,i] mod p*/
mpz_mul(matrix[i][j],matrix[i][j],f);
mpz_mod(matrix[i][j],matrix[i][j],p);
}
/*go through rows beneath*/
for(j=i+1;j<n;j++){
/*store value of current column next row*/
mpz_set(f,matrix[j][i]);
/*multiply with current row*/
/*subtract from processed row, so that current column in that row is forced to zero*/
for(k=0;k<=n;k++){
mpz_mul(t1,matrix[i][k],f);
mpz_sub(matrix[j][k],matrix[j][k],t1);
mpz_mod(matrix[j][k],matrix[j][k],p);
}
}
}
/*printf("Row Echelon form.\n");*/
/*bring matrix into Reduced Row Echelon Form*/
for(i=n-1;i>=0;i--){/*iterate main diagonal*/
j=1;
while(!mpz_cmp_ui(matrix[i][i],0)){
/*exchange rows if working position is zero*/
if(i-j<0){
fprintf(stderr,"System is unsolvable!\n");
exit(1);
}
t=matrix[i];
matrix[i]=matrix[i+j];
matrix[i+j]=t;
j++;
}
/*divide row by working position*/
mpz_invert(f,matrix[i][i],p);/*f=1/m[i,i]*/
for(j=0;j<=n;j++){
/*m[i,j]=m[i,j]/m[i,i] mod p*/
mpz_mul(matrix[i][j],matrix[i][j],f);
mpz_mod(matrix[i][j],matrix[i][j],p);
}
/*go through rows above*/
for(j=i-1;j>=0;j--){
/*store value of current column next row*/
mpz_set(f,matrix[j][i]);
/*multiply with current row*/
/*subtract from processed row, so that current column in that row is forced to zero*/
for(k=0;k<=n;k++){
mpz_mul(t1,matrix[i][k],f);
mpz_sub(matrix[j][k],matrix[j][k],t1);
mpz_mod(matrix[j][k],matrix[j][k],p);
}
}
}
/*printf("Reduced Row Echelon form.\n");*/
}
static int unhex(char c)
{
if(c>='0'&&c<='9')return c-'0';
if(c>='a'&&c<='f')return c-'a'+10;
if(c>='A'&&c<='F')return c-'A'+10;
return 0;
}
static void str2bin(byte*tgt,const char*str,int len)
{
int i;
char s[1024];
if(strlen(str)<(len*2)){
for(i=0;i<len*2;i++)s[i]='0';
strcpy(s+(len*2-strlen(str)),str);
}else strcpy(s,str);
for(i=0;i<len;i++){
tgt[i]=(unhex(s[i*2])<<4) | unhex(s[i*2+1]);
}
}
void sharecalc()
{
char buf[1024];
if(np<n){
fprintf(stderr,"Could not read enough shares, unable to compute.\n");
exit(1);
}
/*calculate*/
/*printf("Key-Matrix:\n");printm(kmatrix);
printf("Hash-Matrix:\n");printm(hmatrix);*/
solve(kmatrix);
solve(hmatrix);
/*output result*/
str2bin(key,mpz_get_str(buf,16,kmatrix[0][n]),16);
str2bin(hashv,mpz_get_str(buf,16,hmatrix[0][n]),16);
/*printf("Using key: %s\n",key_prints(0,key));
printf("Expected Hash: %s\n",key_prints(0,hashv));*/
/*printf("Key-Matrix:\n");printm(kmatrix);
printf("Hash-Matrix:\n");printm(hmatrix);*/
}