andre@0: /* This Source Code Form is subject to the terms of the Mozilla Public
andre@0:  * License, v. 2.0. If a copy of the MPL was not distributed with this
andre@0:  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
andre@0: 
andre@0: #include "mp_gf2m.h"
andre@0: #include "mp_gf2m-priv.h"
andre@0: #include "mplogic.h"
andre@0: #include "mpi-priv.h"
andre@0: 
andre@0: const mp_digit mp_gf2m_sqr_tb[16] =
andre@0: {
andre@0:       0,     1,     4,     5,    16,    17,    20,    21,
andre@0:      64,    65,    68,    69,    80,    81,    84,    85
andre@0: };
andre@0: 
andre@0: /* Multiply two binary polynomials mp_digits a, b.
andre@0:  * Result is a polynomial with degree < 2 * MP_DIGIT_BITS - 1.
andre@0:  * Output in two mp_digits rh, rl.
andre@0:  */
andre@0: #if MP_DIGIT_BITS == 32
andre@0: void 
andre@0: s_bmul_1x1(mp_digit *rh, mp_digit *rl, const mp_digit a, const mp_digit b)
andre@0: {
andre@0:     register mp_digit h, l, s;
andre@0:     mp_digit tab[8], top2b = a >> 30; 
andre@0:     register mp_digit a1, a2, a4;
andre@0: 
andre@0:     a1 = a & (0x3FFFFFFF); a2 = a1 << 1; a4 = a2 << 1;
andre@0: 
andre@0:     tab[0] =  0; tab[1] = a1;    tab[2] = a2;    tab[3] = a1^a2;
andre@0:     tab[4] = a4; tab[5] = a1^a4; tab[6] = a2^a4; tab[7] = a1^a2^a4;
andre@0: 
andre@0:     s = tab[b       & 0x7]; l  = s;
andre@0:     s = tab[b >>  3 & 0x7]; l ^= s <<  3; h  = s >> 29;
andre@0:     s = tab[b >>  6 & 0x7]; l ^= s <<  6; h ^= s >> 26;
andre@0:     s = tab[b >>  9 & 0x7]; l ^= s <<  9; h ^= s >> 23;
andre@0:     s = tab[b >> 12 & 0x7]; l ^= s << 12; h ^= s >> 20;
andre@0:     s = tab[b >> 15 & 0x7]; l ^= s << 15; h ^= s >> 17;
andre@0:     s = tab[b >> 18 & 0x7]; l ^= s << 18; h ^= s >> 14;
andre@0:     s = tab[b >> 21 & 0x7]; l ^= s << 21; h ^= s >> 11;
andre@0:     s = tab[b >> 24 & 0x7]; l ^= s << 24; h ^= s >>  8;
andre@0:     s = tab[b >> 27 & 0x7]; l ^= s << 27; h ^= s >>  5;
andre@0:     s = tab[b >> 30      ]; l ^= s << 30; h ^= s >>  2;
andre@0: 
andre@0:     /* compensate for the top two bits of a */
andre@0: 
andre@0:     if (top2b & 01) { l ^= b << 30; h ^= b >> 2; } 
andre@0:     if (top2b & 02) { l ^= b << 31; h ^= b >> 1; } 
andre@0: 
andre@0:     *rh = h; *rl = l;
andre@0: } 
andre@0: #else
andre@0: void 
andre@0: s_bmul_1x1(mp_digit *rh, mp_digit *rl, const mp_digit a, const mp_digit b)
andre@0: {
andre@0:     register mp_digit h, l, s;
andre@0:     mp_digit tab[16], top3b = a >> 61;
andre@0:     register mp_digit a1, a2, a4, a8;
andre@0: 
andre@0:     a1 = a & (0x1FFFFFFFFFFFFFFFULL); a2 = a1 << 1; 
andre@0:     a4 = a2 << 1; a8 = a4 << 1;
andre@0:     tab[ 0] = 0;     tab[ 1] = a1;       tab[ 2] = a2;       tab[ 3] = a1^a2;
andre@0:     tab[ 4] = a4;    tab[ 5] = a1^a4;    tab[ 6] = a2^a4;    tab[ 7] = a1^a2^a4;
andre@0:     tab[ 8] = a8;    tab[ 9] = a1^a8;    tab[10] = a2^a8;    tab[11] = a1^a2^a8;
andre@0:     tab[12] = a4^a8; tab[13] = a1^a4^a8; tab[14] = a2^a4^a8; tab[15] = a1^a2^a4^a8;
andre@0: 
andre@0:     s = tab[b       & 0xF]; l  = s;
andre@0:     s = tab[b >>  4 & 0xF]; l ^= s <<  4; h  = s >> 60;
andre@0:     s = tab[b >>  8 & 0xF]; l ^= s <<  8; h ^= s >> 56;
andre@0:     s = tab[b >> 12 & 0xF]; l ^= s << 12; h ^= s >> 52;
andre@0:     s = tab[b >> 16 & 0xF]; l ^= s << 16; h ^= s >> 48;
andre@0:     s = tab[b >> 20 & 0xF]; l ^= s << 20; h ^= s >> 44;
andre@0:     s = tab[b >> 24 & 0xF]; l ^= s << 24; h ^= s >> 40;
andre@0:     s = tab[b >> 28 & 0xF]; l ^= s << 28; h ^= s >> 36;
andre@0:     s = tab[b >> 32 & 0xF]; l ^= s << 32; h ^= s >> 32;
andre@0:     s = tab[b >> 36 & 0xF]; l ^= s << 36; h ^= s >> 28;
andre@0:     s = tab[b >> 40 & 0xF]; l ^= s << 40; h ^= s >> 24;
andre@0:     s = tab[b >> 44 & 0xF]; l ^= s << 44; h ^= s >> 20;
andre@0:     s = tab[b >> 48 & 0xF]; l ^= s << 48; h ^= s >> 16;
andre@0:     s = tab[b >> 52 & 0xF]; l ^= s << 52; h ^= s >> 12;
andre@0:     s = tab[b >> 56 & 0xF]; l ^= s << 56; h ^= s >>  8;
andre@0:     s = tab[b >> 60      ]; l ^= s << 60; h ^= s >>  4;
andre@0: 
andre@0:     /* compensate for the top three bits of a */
andre@0: 
andre@0:     if (top3b & 01) { l ^= b << 61; h ^= b >> 3; } 
andre@0:     if (top3b & 02) { l ^= b << 62; h ^= b >> 2; } 
andre@0:     if (top3b & 04) { l ^= b << 63; h ^= b >> 1; } 
andre@0: 
andre@0:     *rh = h; *rl = l;
andre@0: } 
andre@0: #endif
andre@0: 
andre@0: /* Compute xor-multiply of two binary polynomials  (a1, a0) x (b1, b0)  
andre@0:  * result is a binary polynomial in 4 mp_digits r[4].
andre@0:  * The caller MUST ensure that r has the right amount of space allocated.
andre@0:  */
andre@0: void 
andre@0: s_bmul_2x2(mp_digit *r, const mp_digit a1, const mp_digit a0, const mp_digit b1,
andre@0:            const mp_digit b0)
andre@0: {
andre@0:     mp_digit m1, m0;
andre@0:     /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
andre@0:     s_bmul_1x1(r+3, r+2, a1, b1);
andre@0:     s_bmul_1x1(r+1, r, a0, b0);
andre@0:     s_bmul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
andre@0:     /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
andre@0:     r[2] ^= m1 ^ r[1] ^ r[3];  /* h0 ^= m1 ^ l1 ^ h1; */
andre@0:     r[1]  = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0;  /* l1 ^= l0 ^ h0 ^ m0; */
andre@0: }
andre@0: 
andre@0: /* Compute xor-multiply of two binary polynomials  (a2, a1, a0) x (b2, b1, b0)  
andre@0:  * result is a binary polynomial in 6 mp_digits r[6].
andre@0:  * The caller MUST ensure that r has the right amount of space allocated.
andre@0:  */
andre@0: void 
andre@0: s_bmul_3x3(mp_digit *r, const mp_digit a2, const mp_digit a1, const mp_digit a0, 
andre@0: 	const mp_digit b2, const mp_digit b1, const mp_digit b0)
andre@0: {
andre@0: 	mp_digit zm[4];
andre@0: 
andre@0: 	s_bmul_1x1(r+5, r+4, a2, b2);         /* fill top 2 words */
andre@0: 	s_bmul_2x2(zm, a1, a2^a0, b1, b2^b0); /* fill middle 4 words */
andre@0: 	s_bmul_2x2(r, a1, a0, b1, b0);        /* fill bottom 4 words */
andre@0: 
andre@0: 	zm[3] ^= r[3];
andre@0: 	zm[2] ^= r[2]; 
andre@0: 	zm[1] ^= r[1] ^ r[5];
andre@0: 	zm[0] ^= r[0] ^ r[4];
andre@0: 
andre@0: 	r[5]  ^= zm[3];
andre@0: 	r[4]  ^= zm[2];
andre@0: 	r[3]  ^= zm[1];
andre@0: 	r[2]  ^= zm[0];
andre@0: }
andre@0: 
andre@0: /* Compute xor-multiply of two binary polynomials  (a3, a2, a1, a0) x (b3, b2, b1, b0)  
andre@0:  * result is a binary polynomial in 8 mp_digits r[8].
andre@0:  * The caller MUST ensure that r has the right amount of space allocated.
andre@0:  */
andre@0: void s_bmul_4x4(mp_digit *r, const mp_digit a3, const mp_digit a2, const mp_digit a1, 
andre@0: 	const mp_digit a0, const mp_digit b3, const mp_digit b2, const mp_digit b1, 
andre@0: 	const mp_digit b0)
andre@0: {
andre@0: 	mp_digit zm[4];
andre@0: 
andre@0: 	s_bmul_2x2(r+4, a3, a2, b3, b2);            /* fill top 4 words */
andre@0: 	s_bmul_2x2(zm, a3^a1, a2^a0, b3^b1, b2^b0); /* fill middle 4 words */
andre@0: 	s_bmul_2x2(r, a1, a0, b1, b0);              /* fill bottom 4 words */
andre@0: 
andre@0: 	zm[3] ^= r[3] ^ r[7]; 
andre@0: 	zm[2] ^= r[2] ^ r[6]; 
andre@0: 	zm[1] ^= r[1] ^ r[5]; 
andre@0: 	zm[0] ^= r[0] ^ r[4]; 
andre@0: 
andre@0: 	r[5]  ^= zm[3];    
andre@0: 	r[4]  ^= zm[2];
andre@0: 	r[3]  ^= zm[1];    
andre@0: 	r[2]  ^= zm[0];
andre@0: }
andre@0: 
andre@0: /* Compute addition of two binary polynomials a and b,
andre@0:  * store result in c; c could be a or b, a and b could be equal; 
andre@0:  * c is the bitwise XOR of a and b.
andre@0:  */
andre@0: mp_err
andre@0: mp_badd(const mp_int *a, const mp_int *b, mp_int *c)
andre@0: {
andre@0:     mp_digit *pa, *pb, *pc;
andre@0:     mp_size ix;
andre@0:     mp_size used_pa, used_pb;
andre@0:     mp_err res = MP_OKAY;
andre@0: 
andre@0:     /* Add all digits up to the precision of b.  If b had more
andre@0:      * precision than a initially, swap a, b first
andre@0:      */
andre@0:     if (MP_USED(a) >= MP_USED(b)) {
andre@0:         pa = MP_DIGITS(a);
andre@0:         pb = MP_DIGITS(b);
andre@0:         used_pa = MP_USED(a);
andre@0:         used_pb = MP_USED(b);
andre@0:     } else {
andre@0:         pa = MP_DIGITS(b);
andre@0:         pb = MP_DIGITS(a);
andre@0:         used_pa = MP_USED(b);
andre@0:         used_pb = MP_USED(a);
andre@0:     }
andre@0: 
andre@0:     /* Make sure c has enough precision for the output value */
andre@0:     MP_CHECKOK( s_mp_pad(c, used_pa) );
andre@0: 
andre@0:     /* Do word-by-word xor */
andre@0:     pc = MP_DIGITS(c);
andre@0:     for (ix = 0; ix < used_pb; ix++) {
andre@0:         (*pc++) = (*pa++) ^ (*pb++);
andre@0:     }
andre@0: 
andre@0:     /* Finish the rest of digits until we're actually done */
andre@0:     for (; ix < used_pa; ++ix) {
andre@0:         *pc++ = *pa++;
andre@0:     }
andre@0: 
andre@0:     MP_USED(c) = used_pa;
andre@0:     MP_SIGN(c) = ZPOS;
andre@0:     s_mp_clamp(c);
andre@0: 
andre@0: CLEANUP:
andre@0:     return res;
andre@0: } 
andre@0: 
andre@0: #define s_mp_div2(a) MP_CHECKOK( mpl_rsh((a), (a), 1) );
andre@0: 
andre@0: /* Compute binary polynomial multiply d = a * b */
andre@0: static void 
andre@0: s_bmul_d(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *d)
andre@0: {
andre@0:     mp_digit a_i, a0b0, a1b1, carry = 0;
andre@0:     while (a_len--) {
andre@0:         a_i = *a++;
andre@0:         s_bmul_1x1(&a1b1, &a0b0, a_i, b);
andre@0:         *d++ = a0b0 ^ carry;
andre@0:         carry = a1b1;
andre@0:     }
andre@0:     *d = carry;
andre@0: }
andre@0: 
andre@0: /* Compute binary polynomial xor multiply accumulate d ^= a * b */
andre@0: static void 
andre@0: s_bmul_d_add(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *d)
andre@0: {
andre@0:     mp_digit a_i, a0b0, a1b1, carry = 0;
andre@0:     while (a_len--) {
andre@0:         a_i = *a++;
andre@0:         s_bmul_1x1(&a1b1, &a0b0, a_i, b);
andre@0:         *d++ ^= a0b0 ^ carry;
andre@0:         carry = a1b1;
andre@0:     }
andre@0:     *d ^= carry;
andre@0: }
andre@0: 
andre@0: /* Compute binary polynomial xor multiply c = a * b.  
andre@0:  * All parameters may be identical.
andre@0:  */
andre@0: mp_err 
andre@0: mp_bmul(const mp_int *a, const mp_int *b, mp_int *c)
andre@0: {
andre@0:     mp_digit *pb, b_i;
andre@0:     mp_int tmp;
andre@0:     mp_size ib, a_used, b_used;
andre@0:     mp_err res = MP_OKAY;
andre@0: 
andre@0:     MP_DIGITS(&tmp) = 0;
andre@0: 
andre@0:     ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
andre@0: 
andre@0:     if (a == c) {
andre@0:         MP_CHECKOK( mp_init_copy(&tmp, a) );
andre@0:         if (a == b)
andre@0:             b = &tmp;
andre@0:         a = &tmp;
andre@0:     } else if (b == c) {
andre@0:         MP_CHECKOK( mp_init_copy(&tmp, b) );
andre@0:         b = &tmp;
andre@0:     }
andre@0: 
andre@0:     if (MP_USED(a) < MP_USED(b)) {
andre@0:         const mp_int *xch = b;      /* switch a and b if b longer */
andre@0:         b = a;
andre@0:         a = xch;
andre@0:     }
andre@0: 
andre@0:     MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
andre@0:     MP_CHECKOK( s_mp_pad(c, USED(a) + USED(b)) );
andre@0: 
andre@0:     pb = MP_DIGITS(b);
andre@0:     s_bmul_d(MP_DIGITS(a), MP_USED(a), *pb++, MP_DIGITS(c));
andre@0: 
andre@0:     /* Outer loop:  Digits of b */
andre@0:     a_used = MP_USED(a);
andre@0:     b_used = MP_USED(b);
andre@0: 	MP_USED(c) = a_used + b_used;
andre@0:     for (ib = 1; ib < b_used; ib++) {
andre@0:         b_i = *pb++;
andre@0: 
andre@0:         /* Inner product:  Digits of a */
andre@0:         if (b_i)
andre@0:             s_bmul_d_add(MP_DIGITS(a), a_used, b_i, MP_DIGITS(c) + ib);
andre@0:         else
andre@0:             MP_DIGIT(c, ib + a_used) = b_i;
andre@0:     }
andre@0: 
andre@0:     s_mp_clamp(c);
andre@0: 
andre@0:     SIGN(c) = ZPOS;
andre@0: 
andre@0: CLEANUP:
andre@0:     mp_clear(&tmp);
andre@0:     return res;
andre@0: }
andre@0: 
andre@0: 
andre@0: /* Compute modular reduction of a and store result in r.  
andre@0:  * r could be a. 
andre@0:  * For modular arithmetic, the irreducible polynomial f(t) is represented 
andre@0:  * as an array of int[], where f(t) is of the form: 
andre@0:  *     f(t) = t^p[0] + t^p[1] + ... + t^p[k]
andre@0:  * where m = p[0] > p[1] > ... > p[k] = 0.
andre@0:  */
andre@0: mp_err
andre@0: mp_bmod(const mp_int *a, const unsigned int p[], mp_int *r)
andre@0: {
andre@0:     int j, k;
andre@0:     int n, dN, d0, d1;
andre@0:     mp_digit zz, *z, tmp;
andre@0:     mp_size used;
andre@0:     mp_err res = MP_OKAY;
andre@0: 
andre@0:     /* The algorithm does the reduction in place in r, 
andre@0:      * if a != r, copy a into r first so reduction can be done in r
andre@0:      */
andre@0:     if (a != r) {
andre@0:         MP_CHECKOK( mp_copy(a, r) );
andre@0:     }
andre@0:     z = MP_DIGITS(r);
andre@0: 
andre@0:     /* start reduction */
andre@0:     /*dN = p[0] / MP_DIGIT_BITS; */
andre@0:     dN = p[0] >> MP_DIGIT_BITS_LOG_2;
andre@0:     used = MP_USED(r);
andre@0: 
andre@0:     for (j = used - 1; j > dN;) {
andre@0: 
andre@0:         zz = z[j];
andre@0:         if (zz == 0) {
andre@0:             j--; continue;
andre@0:         }
andre@0:         z[j] = 0;
andre@0: 
andre@0:         for (k = 1; p[k] > 0; k++) {
andre@0:             /* reducing component t^p[k] */
andre@0:             n = p[0] - p[k];
andre@0:             /*d0 = n % MP_DIGIT_BITS;   */
andre@0:             d0 = n & MP_DIGIT_BITS_MASK;
andre@0:             d1 = MP_DIGIT_BITS - d0;
andre@0:             /*n /= MP_DIGIT_BITS; */
andre@0:             n >>= MP_DIGIT_BITS_LOG_2;
andre@0:             z[j-n] ^= (zz>>d0);
andre@0:             if (d0) 
andre@0:                 z[j-n-1] ^= (zz<<d1);
andre@0:         }
andre@0: 
andre@0:         /* reducing component t^0 */
andre@0:         n = dN;  
andre@0:         /*d0 = p[0] % MP_DIGIT_BITS;*/
andre@0:         d0 = p[0] & MP_DIGIT_BITS_MASK;
andre@0:         d1 = MP_DIGIT_BITS - d0;
andre@0:         z[j-n] ^= (zz >> d0);
andre@0:         if (d0) 
andre@0:             z[j-n-1] ^= (zz << d1);
andre@0: 
andre@0:     }
andre@0: 
andre@0:     /* final round of reduction */
andre@0:     while (j == dN) {
andre@0: 
andre@0:         /* d0 = p[0] % MP_DIGIT_BITS; */
andre@0:         d0 = p[0] & MP_DIGIT_BITS_MASK;
andre@0:         zz = z[dN] >> d0;  
andre@0:         if (zz == 0) break;
andre@0:         d1 = MP_DIGIT_BITS - d0;
andre@0: 
andre@0:         /* clear up the top d1 bits */
andre@0:         if (d0) {
andre@0: 	    z[dN] = (z[dN] << d1) >> d1; 
andre@0: 	} else {
andre@0: 	    z[dN] = 0;
andre@0: 	}
andre@0:         *z ^= zz; /* reduction t^0 component */
andre@0: 
andre@0:         for (k = 1; p[k] > 0; k++) {
andre@0:             /* reducing component t^p[k]*/
andre@0:             /* n = p[k] / MP_DIGIT_BITS; */
andre@0:             n = p[k] >> MP_DIGIT_BITS_LOG_2;
andre@0:             /* d0 = p[k] % MP_DIGIT_BITS; */
andre@0:             d0 = p[k] & MP_DIGIT_BITS_MASK;
andre@0:             d1 = MP_DIGIT_BITS - d0;
andre@0:             z[n] ^= (zz << d0);
andre@0:             tmp = zz >> d1;
andre@0:             if (d0 && tmp)
andre@0:                 z[n+1] ^= tmp;
andre@0:         }
andre@0:     }
andre@0: 
andre@0:     s_mp_clamp(r);
andre@0: CLEANUP:
andre@0:     return res;
andre@0: }
andre@0: 
andre@0: /* Compute the product of two polynomials a and b, reduce modulo p, 
andre@0:  * Store the result in r.  r could be a or b; a could be b.
andre@0:  */
andre@0: mp_err 
andre@0: mp_bmulmod(const mp_int *a, const mp_int *b, const unsigned int p[], mp_int *r)
andre@0: {
andre@0:     mp_err res;
andre@0:     
andre@0:     if (a == b) return mp_bsqrmod(a, p, r);
andre@0:     if ((res = mp_bmul(a, b, r) ) != MP_OKAY)
andre@0: 	return res;
andre@0:     return mp_bmod(r, p, r);
andre@0: }
andre@0: 
andre@0: /* Compute binary polynomial squaring c = a*a mod p .  
andre@0:  * Parameter r and a can be identical.
andre@0:  */
andre@0: 
andre@0: mp_err 
andre@0: mp_bsqrmod(const mp_int *a, const unsigned int p[], mp_int *r)
andre@0: {
andre@0:     mp_digit *pa, *pr, a_i;
andre@0:     mp_int tmp;
andre@0:     mp_size ia, a_used;
andre@0:     mp_err res;
andre@0: 
andre@0:     ARGCHK(a != NULL && r != NULL, MP_BADARG);
andre@0:     MP_DIGITS(&tmp) = 0;
andre@0: 
andre@0:     if (a == r) {
andre@0:         MP_CHECKOK( mp_init_copy(&tmp, a) );
andre@0:         a = &tmp;
andre@0:     }
andre@0: 
andre@0:     MP_USED(r) = 1; MP_DIGIT(r, 0) = 0;
andre@0:     MP_CHECKOK( s_mp_pad(r, 2*USED(a)) );
andre@0: 
andre@0:     pa = MP_DIGITS(a);
andre@0:     pr = MP_DIGITS(r);
andre@0:     a_used = MP_USED(a);
andre@0: 	MP_USED(r) = 2 * a_used;
andre@0: 
andre@0:     for (ia = 0; ia < a_used; ia++) {
andre@0:         a_i = *pa++;
andre@0:         *pr++ = gf2m_SQR0(a_i);
andre@0:         *pr++ = gf2m_SQR1(a_i);
andre@0:     }
andre@0: 
andre@0:     MP_CHECKOK( mp_bmod(r, p, r) );
andre@0:     s_mp_clamp(r);
andre@0:     SIGN(r) = ZPOS;
andre@0: 
andre@0: CLEANUP:
andre@0:     mp_clear(&tmp);
andre@0:     return res;
andre@0: }
andre@0: 
andre@0: /* Compute binary polynomial y/x mod p, y divided by x, reduce modulo p.
andre@0:  * Store the result in r. r could be x or y, and x could equal y.
andre@0:  * Uses algorithm Modular_Division_GF(2^m) from 
andre@0:  *     Chang-Shantz, S.  "From Euclid's GCD to Montgomery Multiplication to 
andre@0:  *     the Great Divide".
andre@0:  */
andre@0: int 
andre@0: mp_bdivmod(const mp_int *y, const mp_int *x, const mp_int *pp, 
andre@0:     const unsigned int p[], mp_int *r)
andre@0: {
andre@0:     mp_int aa, bb, uu;
andre@0:     mp_int *a, *b, *u, *v;
andre@0:     mp_err res = MP_OKAY;
andre@0: 
andre@0:     MP_DIGITS(&aa) = 0;
andre@0:     MP_DIGITS(&bb) = 0;
andre@0:     MP_DIGITS(&uu) = 0;
andre@0: 
andre@0:     MP_CHECKOK( mp_init_copy(&aa, x) );
andre@0:     MP_CHECKOK( mp_init_copy(&uu, y) );
andre@0:     MP_CHECKOK( mp_init_copy(&bb, pp) );
andre@0:     MP_CHECKOK( s_mp_pad(r, USED(pp)) );
andre@0:     MP_USED(r) = 1; MP_DIGIT(r, 0) = 0;
andre@0: 
andre@0:     a = &aa; b= &bb; u=&uu; v=r;
andre@0:     /* reduce x and y mod p */
andre@0:     MP_CHECKOK( mp_bmod(a, p, a) );
andre@0:     MP_CHECKOK( mp_bmod(u, p, u) );
andre@0: 
andre@0:     while (!mp_isodd(a)) {
andre@0:         s_mp_div2(a);
andre@0:         if (mp_isodd(u)) {
andre@0:             MP_CHECKOK( mp_badd(u, pp, u) );
andre@0:         }
andre@0:         s_mp_div2(u);
andre@0:     }
andre@0: 
andre@0:     do {
andre@0:         if (mp_cmp_mag(b, a) > 0) {
andre@0:             MP_CHECKOK( mp_badd(b, a, b) );
andre@0:             MP_CHECKOK( mp_badd(v, u, v) );
andre@0:             do {
andre@0:                 s_mp_div2(b);
andre@0:                 if (mp_isodd(v)) {
andre@0:                     MP_CHECKOK( mp_badd(v, pp, v) );
andre@0:                 }
andre@0:                 s_mp_div2(v);
andre@0:             } while (!mp_isodd(b));
andre@0:         }
andre@0:         else if ((MP_DIGIT(a,0) == 1) && (MP_USED(a) == 1))
andre@0:             break;
andre@0:         else {
andre@0:             MP_CHECKOK( mp_badd(a, b, a) );
andre@0:             MP_CHECKOK( mp_badd(u, v, u) );
andre@0:             do {
andre@0:                 s_mp_div2(a);
andre@0:                 if (mp_isodd(u)) {
andre@0:                     MP_CHECKOK( mp_badd(u, pp, u) );
andre@0:                 }
andre@0:                 s_mp_div2(u);
andre@0:             } while (!mp_isodd(a));
andre@0:         }
andre@0:     } while (1);
andre@0: 
andre@0:     MP_CHECKOK( mp_copy(u, r) );
andre@0: 
andre@0: CLEANUP:
andre@0:     mp_clear(&aa);
andre@0:     mp_clear(&bb);
andre@0:     mp_clear(&uu);
andre@0:     return res;
andre@0: 
andre@0: }
andre@0: 
andre@0: /* Convert the bit-string representation of a polynomial a into an array
andre@0:  * of integers corresponding to the bits with non-zero coefficient.
andre@0:  * Up to max elements of the array will be filled.  Return value is total
andre@0:  * number of coefficients that would be extracted if array was large enough.
andre@0:  */
andre@0: int
andre@0: mp_bpoly2arr(const mp_int *a, unsigned int p[], int max)
andre@0: {
andre@0:     int i, j, k;
andre@0:     mp_digit top_bit, mask;
andre@0: 
andre@0:     top_bit = 1;
andre@0:     top_bit <<= MP_DIGIT_BIT - 1;
andre@0: 
andre@0:     for (k = 0; k < max; k++) p[k] = 0;
andre@0:     k = 0;
andre@0: 
andre@0:     for (i = MP_USED(a) - 1; i >= 0; i--) {
andre@0:         mask = top_bit;
andre@0:         for (j = MP_DIGIT_BIT - 1; j >= 0; j--) {
andre@0:             if (MP_DIGITS(a)[i] & mask) {
andre@0:                 if (k < max) p[k] = MP_DIGIT_BIT * i + j;
andre@0:                 k++;
andre@0:             }
andre@0:             mask >>= 1;
andre@0:         }
andre@0:     }
andre@0: 
andre@0:     return k;
andre@0: }
andre@0: 
andre@0: /* Convert the coefficient array representation of a polynomial to a 
andre@0:  * bit-string.  The array must be terminated by 0.
andre@0:  */
andre@0: mp_err
andre@0: mp_barr2poly(const unsigned int p[], mp_int *a)
andre@0: {
andre@0: 
andre@0:     mp_err res = MP_OKAY;
andre@0:     int i;
andre@0: 
andre@0:     mp_zero(a);
andre@0:     for (i = 0; p[i] > 0; i++) {
andre@0: 	MP_CHECKOK( mpl_set_bit(a, p[i], 1) );
andre@0:     }
andre@0:     MP_CHECKOK( mpl_set_bit(a, 0, 1) );
andre@0: 	
andre@0: CLEANUP:
andre@0:     return res;
andre@0: }