Montgomery_Params::Montgomery_Params(const BigInt& p)
{
if(p.is_negative() || p.is_even())
throw Invalid_Argument("Montgomery_Params invalid modulus");
m_p = p;
m_p_words = m_p.sig_words();
m_p_dash = monty_inverse(m_p.word_at(0));
const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS);
Modular_Reducer mod_p(p);
m_r1 = mod_p.reduce(r);
m_r2 = mod_p.square(m_r1);
m_r3 = mod_p.multiply(m_r1, m_r2);
}
static void create_systematic_generator_matrices(MINDIST *MD)
//create systematic generator matrices
//$(S[1]=(I,*),...,S[z]=(*,I,*),...,S[M]=(*,I))$
//with identity-matrix $I$ beginning at $P+1 = k*(z-1)+1$
//(k = \# lines, m = \# systematic generator matrices),
//by elementary row-transformations and permutations in
//generator matrix G
//allocates S[u] for $1 \le u \le M$,
//allocates S[u][i] for $1 \le u \le M, 1 \le i \le k$,
//allocates Size
{
int n = MD->n;
int k = MD->k;
int q = MD->q;
int i,I = 0,j,J,l;
int P, h, h1, h2, h3, pivot, pivot_inv;
int K;
int M;
/* allocate memory for systematic generator matrix S[1] */
MD->S[1] = (int **)calloc(k+2,sizeof(int *));
for (i=1;i<=k;i++)
MD->S[1][i] = (int *)calloc(n+2,sizeof(int));
/* S[1] := G */
for (i=1;i<=k;i++)
for (j=1;j<=n;j++)
MD->S[1][i][j] = MD->G[i][j];
/* allocate memory for size of information subsets of S[1] */
MD->Size = (int *)calloc(n+1,sizeof(int ));
M = 1;
P = 0;
K = k;
while (1) {
if (MD->f_vvv) {
printf("loop with M = %d, P = %d K = %d\n",M, P, K);
}
/* create identity matrix, columns P+1,...,P+k */
for (i=1;i<=K;i++) {
if (MD->f_vvv) {
printf("i = %d ", i);
printf(" (M = %d, P = %d K = %d)\n",M, P, K);
fflush(stdout);
}
/* search for pivot:
if the entry is 0 at (i,P+i),
first check the entries below
(-> row-permutation necessary)
then check the columns behind
(-> column-permutation necessary) */
/* printf("i=%d, P=%d, S[M][i][P+i]=%d\n",i,P,S[M][i][P+i]); */
for (J=P+i;J<=n;J++) {
for (I = i; I <= K; I++) {
if (MD->S[M][I][J] != MD->idx_zero)
break;
}
if (I <= K) /* pivot found ? */
break;
} // next J
if (MD->f_vvv) {
printf("I=%d, J=%d\n",I,J); fflush(stdout);
}
/* if pivot found but end of columns reached: */
if ((I <= K) && (J == n)) {
if (MD->f_vvv) {printf("end reached, I = %d\n",I);}
if (P+K >= n)
K = n - P;
}
if (MD->f_vvv) {
printf("pivot in I=%d J=%d\n", I, J);
fflush(stdout);
}
/* if there doesn't exist a pivot: */
/* P(s,t)=0 for s>=i and t>=P+i */
if (I > K && J > n) {
K = i-1; /* */
if (MD->f_vvv) {
printf("no pivot\n");
fflush(stdout);
}
break;
}
/* if necessary: row-permutation i<->I */
if (I != i) {
if (MD->f_vvv) {
printf("\nswapping rows: %d<->%d\n",i,I);
fflush(stdout);
}
for (j=1;j<=n;j++) {
h = MD->S[M][i][j];
MD->S[M][i][j] = MD->S[M][I][j];
MD->S[M][I][j] = h;
}
}
/* if necessary: column-permutation P+i<->J */
if (J != P+i) {
if (MD->f_vvv) {
printf("\nswapping columns: %d<->%d\n",P+i,J);
fflush(stdout);
}
for (j=1;j<=k;j++) {
h = MD->S[M][j][i+P];
MD->S[M][j][i+P] = MD->S[M][j][J];
MD->S[M][j][J] = h;
}
}
pivot = MD->S[M][i][P + i];
if (pivot == MD->idx_zero) {
printf("pivot is 0, exiting!\n");
exit(1);
}
pivot_inv = MD->ff_inv[pivot];
if (MD->f_vvv) {
printf("pivot = %d, pivot_inv = %d\n", pivot, pivot_inv);
fflush(stdout);
}
/* replace pivot by 1 [multiply pivot-row by inv(pivot)] */
if (MD->S[M][i][P+i] != MD->idx_one) {
for (j=1;j<=n;j++) {
MD->S[M][i][j] = MD->ff_mult[MD->S[M][i][j] * q + pivot_inv];
}
}
if (MD->f_vvv) {
printf("pivot row normalized\n");
fflush(stdout);
}
/* replace all elements of pivot-column, except pivot
element, by 0 by elementary row-trans. */
for (l=1;l<=k;l++) {
if (l != i) {
if ((h = MD->S[M][l][i+P]) != MD->idx_zero)
for (j=1;j<=n;j++) {
h1 = MD->ff_mult[MD->S[M][i][j] * q + h];
h2 = MD->ff_mult[h1 * q + MD->idx_mone];
h3 = MD->ff_add[MD->S[M][l][j] * q + h2];
MD->S[M][l][j] = h3;
#if 0
MD->S[M][l][j] =
mod_p(MD->S[M][l][j] - MD->S[M][i][j] * h);
#endif
} // next j
} /* if */
} /* l */
if (MD->f_vvv) {
printf("pivot col normalized\n");
fflush(stdout);
}
} /* i */
if (MD->f_v) {
printf("\nsystematic generator matrix s[%d]:\n",M);
print_matrix(MD, MD->S[M]);
//printf("K = %d\n",K);
}
MD->Size[M] = K;
if (K == 0) {
if (MD->f_v) {
printf("K = 0, the generator matrix has %d zero columns\n", n - P);
}
}
if (P+K >= n || K == 0) {
if (K == 0)
MD->ZC = n - P; /* number of zero columns in G */
break;
}
else {
P = P + K;
}
M++;
/* find first column P+1 */
MD->S[M] = (int **)calloc(k+2,sizeof(int *));
for (i=1;i<=k;i++)
MD->S[M][i] = (int *)calloc(n+2,sizeof(int));
/* S[M] := S[M-1] */
for (i=1;i<=k;i++)
for (j=1;j<=n;j++)
MD->S[M][i][j] = MD->S[M-1][i][j];
} /* infinite loop */
if (MD->f_v) {
//printf("M = %d\n", M);
//printf("ZC = %d\n", MD->ZC);
printf("size of information subsets:\n");
for (i = 1; i <= M; i++) {
printf("%d ", MD->Size[i]);
}
printf("\n");
}
MD->M = M;
}