Matrix
m_inverse(Matrix A, Matrix out)
{
int *indexarray = NewAtom_N(int, A->dim);
Matrix A1 = new_matrix(A->dim);
m_copy(A, A1);
LUfactor(A1, indexarray);
return LUinverse(A1, indexarray, out);
}
MAT *m_inverse(const MAT *A, MAT *out)
{
unsigned int i;
char MatrixTempBuffer[ 4000 ];
VEC *tmp = VNULL, *tmp2 = VNULL;
MAT *A_cp = MNULL;
PERM *pivot = PNULL;
if ( ! A )
error(E_NULL,"m_inverse");
if ( A->m != A->n )
error(E_SQUARE,"m_inverse");
if ( ! out || out->m < A->m || out->n < A->n )
out = m_resize(out,A->m,A->n);
if( SET_MAT_SIZE( A->m, A->n ) < 1000 )
mat_get( &A_cp, (void *)( MatrixTempBuffer + 2000 ), A->m, A->n );
else
A_cp = matrix_get( A->m, A->n );
A_cp = m_copy( A, A_cp );
if( SET_VEC_SIZE( A->m ) < 1000 ) {
vec_get( &tmp, (void *)MatrixTempBuffer, A->m );
vec_get( &tmp2, (void *)(MatrixTempBuffer + 1000), A->m );
} else {
tmp = v_get( A->m );
tmp2 = v_get( A->m );
}
if( SET_PERM_SIZE( A->m ) < 1000 ) {
perm_get( &pivot, (void *)( MatrixTempBuffer + 3000 ), A->m );
} else {
pivot = px_get( A->m );
}
LUfactor(A_cp,pivot);
//tracecatch_matrix(LUfactor(A_cp,pivot),"m_inverse");
for ( i = 0; i < A->n; i++ ){
v_zero(tmp);
tmp->ve[i] = 1.0;
LUsolve(A_cp,pivot,tmp,tmp2);
//tracecatch_matrix(LUsolve(A_cp,pivot,tmp,tmp2),"m_inverse");
set_col(out,i,tmp2);
}
if( tmp != (VEC *)(MatrixTempBuffer ) ) // память выделялась, надо освободить
V_FREE(tmp);
if( tmp2 != (VEC *)(MatrixTempBuffer + 1000) ) // память выделялась, надо освободить
V_FREE(tmp2);
if( A_cp != (MAT *)(MatrixTempBuffer + 2000) ) // память выделялась, надо освободить
M_FREE(A_cp);
if( pivot != (PERM *)(MatrixTempBuffer + 3000) ) // память выделялась, надо освободить
PX_FREE( pivot );
return out;
}
MAT *m_inverse(const MAT *A, MAT *out)
#endif
{
int i;
STATIC VEC *tmp = VNULL, *tmp2 = VNULL;
STATIC MAT *A_cp = MNULL;
STATIC PERM *pivot = PNULL;
if ( ! A )
error(E_NULL,"m_inverse");
if ( A->m != A->n )
error(E_SQUARE,"m_inverse");
if ( ! out || out->m < A->m || out->n < A->n )
out = m_resize(out,A->m,A->n);
A_cp = m_resize(A_cp,A->m,A->n);
A_cp = m_copy(A,A_cp);
tmp = v_resize(tmp,A->m);
tmp2 = v_resize(tmp2,A->m);
pivot = px_resize(pivot,A->m);
MEM_STAT_REG(A_cp,TYPE_MAT);
MEM_STAT_REG(tmp, TYPE_VEC);
MEM_STAT_REG(tmp2,TYPE_VEC);
MEM_STAT_REG(pivot,TYPE_PERM);
tracecatch(LUfactor(A_cp,pivot),"m_inverse");
for ( i = 0; i < A->n; i++ )
{
v_zero(tmp);
tmp->ve[i] = 1.0;
tracecatch(LUsolve(A_cp,pivot,tmp,tmp2),"m_inverse");
set_col(out,i,tmp2);
}
#ifdef THREADSAFE
V_FREE(tmp); V_FREE(tmp2);
M_FREE(A_cp); PX_FREE(pivot);
#endif
return out;
}
//FIXME: add LOCALFUNC? (OR GLOBAL?)
BYTE* RECURSIVE_SUBROUTINE(BYTE t, list *cur_guess, list *guesses, list_node *first_guess)
{
if ( t == key_length)
{
unsigned char* key=NULL;
// generate key from the cur_guess (push guesses into a matrix and use some matrix solving library?)
MAT* A;
VEC *x,*b;
PERM* pivot;
A=m_get(key_length,key_length);
b=v_get(key_length);
x=v_get(key_length);
int c=0,r=0;
for(list_node* iter=list_head(cur_guess); iter != NULL && r<key_length; iter=list_node_next(iter)){
for(c=list_node_data_ptr(iter,byte_sum_guess_t)->i1;
c <= list_node_data_ptr(iter,byte_sum_guess_t)->i2;
++c){
A->me[r][c]=1;
}
b->ve[r]=list_node_data_ptr(iter,byte_sum_guess_t)->value;
++r;
}
//Calculate matrix determinant
SQRMATRIX A_det;
SQRMATRIX_CreateMatrix(&A_det,key_length);
for(r=0;r<key_length;++r){
for(c=0;c<key_length;++c){
A_det.array[r][c]=A->me[r][c];
}
}
int det;
det=SQRMATRIX_CalcDeterminant(&A_det);
//TODO: return this later
SQRMATRIX_DestroyMatrix(&A_det);
if(det==0){//If determinant is 0 continue to next guess
++count_bad_matrix;
#ifdef __DEBUG
//SQRMATRIX_DisplayMatrix(&A_det);
v_output(b);
#endif
DEBUG_PRINT("Matrix determinant is 0\n");
}else{
++count_guesses;
pivot = px_get(A->m);
LUfactor(A,pivot);
x=LUsolve(A,pivot,b,VNULL);
PX_FREE(pivot);
//test key (use our RC4 impl)
key=(unsigned char*)malloc(sizeof(unsigned char)*key_length);
for(int i=0;i<key_length;++i){
key[i]=x->ve[i];
}
int res=rc4_test_key(key);
if(res){
printf("MAZAL TOV! we got the right key.\n");
print_key(key);
printf("\n");
}else{
printf("Tried key: ");
print_key(key);
printf("\n");
free(key);key=NULL;
}
}
//release matrix vars
M_FREE(A);
V_FREE(x);
V_FREE(b);
return key;
}
byte_sum_guess_t cur;
//list *new_list_head=guesses;
//TODO: (later) add a for loop running along the "lambeda_t" values here, for the initial impl we'll try the best guess
//for ()
//{
for(int i=0; i<LAMBDA_T; ++i){
cur = *(list_node_data_ptr(first_guess, byte_sum_guess_t));
list_node *biatch = list_add_head(cur_guess, &cur);
BYTE* res=RECURSIVE_SUBROUTINE(t+1, cur_guess, guesses, list_node_next(first_guess));
if(res!=NULL){
return res;
}
list_del(cur_guess,biatch);
first_guess = list_node_next(first_guess);
}
return NULL;
//TODO: do something to find the next guess and link it to the current guess
//when I say something I mean find best guess (i.e best weight) of all the guesses that give us new information
//(i.e not linearily dependent in our byte values and sums matrix that can be deduced from the cur_guess)
//see also the note above (intuition)
//IMPORTANT!
//explaination how cur_guess is a matrix: each entry in cur_guess contains a list of bytes that are part of the sum and a
//guess as to the value of the sum. if this matrix is solvable then solving it should give us a value for each byte of the
//key thus the entire key
//note: we probably should change cur_guess to a smarter database (for example a (L)x(L+1) matrix as an array?) but we
//need to consider that we need to keep the ability to backtrack without making it too expensive
//TODO: if weight of the guess is too small -> return FAIL (section 4.6)
//These are based on section 4.4
//correct suggestions (this can be done later, basic alg should work without it)
//adjust weights (this can be done later, basic alg should work without it)
//merge counters (section 4.2), also skip for initial impl? need to check
//go to next iteration in the recurtion
//RECURSIVE_SUBROUTINE(t+1, cur_guess, );
//} end of for
}
void
test(const int n, const int lb, const int ub, bool dumpfull) {
// Generate a special-band-matrix mfull With lb lower diagonals, ub upper
// diagonals and the elements of the highest upper diagonal extended across
// each row
MAT *mfull = m_get(n, n);
//m_rand(mfull);
randlist(mfull->base, (mfull->n)*(mfull->n));
double **me = mfull->me;
for(int i = 0; i < n; i++) {
for(int j = 0; j < i - lb; j++)
me[i][j] = 0.0;
for(int j = i+ub+1; j < n; j++)
me[i][j] = me[i][i+ub];
}
// Copy matrix mfull to a compactly stored version
// mcmpct
// First lb columns padding for later use
// Next lb columns for lower diagonals
// Next column for diagonal
// Next ub columns for upper diagonals
// as the highest upper diagonal of the same row
const int mm = 2*lb+ub+1;
double mcmpct[n][mm];
zero(&mcmpct[0][0], n*mm);
for(int i = 0; i < n; i++)
for(int j = MAX(i-lb, 0); j < MIN(i+ub+1, n); j++)
mcmpct[i][j-i+lb+lb] = me[i][j];
// Replace unused values with NAN to be sure they aren't used
for(int k = 0; k < n; k++)
for(int i = 0; i < lb; i++)
mcmpct[k][i] = NAN;
for(int k = 0; k < lb; k++)
for(int i = 0; i < lb-k; i++)
mcmpct[k][i+lb] = NAN;
for(int k=n-1; k >= n-ub; k--)
for(int i = n-1-k+1+lb; i < mm; i++)
mcmpct[k][i+lb] = NAN;
// Generate start vector x1 for test
VEC *x1 = v_get(n);
randlist(x1->ve, n);
// Calculate mfull*x1 = dfull
VEC *dfull = v_get(n);
mv_mlt(mfull, x1, dfull);
// Calculate mcmpct*x1 = dcmpct
double dcmpct[n];
bdspecLUmlt(&mcmpct[0][0], n, lb, ub, x1->ve, dcmpct);
if(dumpfull) {
printf("Vector x (random values)\n");
printf("========================\n");
v_out(x1->ve, n);
printf("Matrix A (random values)\n");
printf("========================\n");
printf("Full NxN Meschach Matrix\n");
m_out(mfull->base, n, n);
printf("Compact bdspec Array\n");
m_out(&mcmpct[0][0], n, mm);
printf("Vector d = A*x\n");
printf("==============\n");
printf("Calculated from Full Meschach Matrix:\n");
v_out(dfull->ve, n);
printf("Calculated from Compact bdspec Array:\n");
v_out(dcmpct, n);
printf("L2 norm of difference between Meschach and bdspec calculations of d\n");
}
double ddiff = v_diff(dfull->ve, dcmpct, n);
printf("d diff=%6.0E ", ddiff);
if(ddiff*ddiff > DBL_EPSILON*v_normsq(dfull->ve, n))
printf("FAIL,");
else
printf("PASS,");
PERM *p = px_get(n);
LUfactor(mfull, p);
int indx[n];
bdspecLUfactormeschscale(&mcmpct[0][0], n, lb, ub, indx);
VEC *yfull = v_get(n);
catchall(LUsolve(mfull, p, dfull, yfull), printf("--matrix singular--:\n"));
double ycmpct[n];
for(int i = 0; i < n; i++)
ycmpct[i] = dcmpct[i];
bdspecLUsolve(&mcmpct[0][0], n, lb, ub, indx, ycmpct);
if(dumpfull) {
printf("\n\n");
printf("LU Factorization\n");
printf("================\n");
printf("Meschach LU Array\n");
m_out(mfull->base, n, n);
printf("Compact bdspec LU Array\n");
m_out(&mcmpct[0][0], n, mm);
printf("Permutation\n");
printf("===========\n");
printf("Meschach permutation vector\n");
p_out((int *) p->pe, n);
printf("bdspec indx vector\n");
p_out(indx, n);
printf("A*y = d Solved for y\n");
printf("====================\n");
printf("Meschach result\n");
v_out(yfull->ve, n);
printf("bdspec result\n");
v_out(ycmpct, n);
printf("L2 norm of difference between Meschach and bdspec calculations of y:\n");
}
double ydiff = v_diff(yfull->ve, ycmpct, n);
printf("y diff=%6.0E ", ydiff);
if(ydiff*ydiff > DBL_EPSILON*v_normsq(yfull->ve, n))
printf("FAIL,");
else
printf("PASS,");
if(dumpfull) {
printf("\n\n");
printf("L2 norm of error = y-x\n");
printf("======================\n");
}
double x1normsq = v_normsq(x1->ve, n);
double mescherr = v_diff(yfull->ve, x1->ve, n);
printf("mesch err=%6.0E ", mescherr);
if(mescherr*mescherr > DBL_EPSILON*x1normsq)
printf("FAIL,");
else
printf("PASS,");
double bdspecerr = v_diff(ycmpct, x1->ve, n);
printf("bdspec err=%6.0E ", bdspecerr);
if(bdspecerr*bdspecerr > DBL_EPSILON*x1normsq)
printf("FAIL ");
else
printf("PASS ");
if(dumpfull) {
printf("\n\n");
}
fflush(stdout);
}
