3 This file is part of the ARM-Crypto-Lib.
4 Copyright (C) 2008 Daniel Otte (daniel.otte@rub.de)
6 This program is free software: you can redistribute it and/or modify
7 it under the terms of the GNU General Public License as published by
8 the Free Software Foundation, either version 3 of the License, or
9 (at your option) any later version.
11 This program is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 GNU General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 along with this program. If not, see <http://www.gnu.org/licenses/>.
24 * \license GPLv3 or later
30 #define STRING(x) STRING2(x)
31 #define STR_LINE STRING(__LINE__)
40 #include "uart_lowlevel.h"
41 #include "bigint_io.h"
45 #define MAX(a,b) (((a)>(b))?(a):(b))
49 #define MIN(a,b) (((a)<(b))?(a):(b))
52 #define SET_FBS(a, v) do{(a)->info &=~BIGINT_FBS_MASK; (a)->info |= (v);}while(0)
53 #define GET_FBS(a) ((a)->info&BIGINT_FBS_MASK)
54 #define SET_NEG(a) (a)->info |= BIGINT_NEG_MASK
55 #define SET_POS(a) (a)->info &= ~BIGINT_NEG_MASK
56 #define XCHG(a,b) do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0)
57 #define XCHG_PTR(a,b) do{ a = (void*)(((uint32_t)(a)) ^ ((uint32_t)(b))); \
58 b = (void*)(((uint32_t)(a)) ^ ((uint32_t)(b))); \
59 a = (void*)(((uint32_t)(a)) ^ ((uint32_t)(b)));}while(0)
61 #define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK)
63 /******************************************************************************/
64 void bigint_adjust(bigint_t* a){
65 while(a->length_B!=0 && a->wordv[a->length_B-1]==0){
73 uint8_t i = BIGINT_WORD_SIZE-1;
74 t = a->wordv[a->length_B-1];
75 while((t&(1<<(BIGINT_WORD_SIZE-1)))==0 && i){
82 /******************************************************************************/
84 uint16_t bigint_length_b(bigint_t* a){
85 if(!a->length_B || a->length_B==0){
88 return (a->length_B-1) * BIGINT_WORD_SIZE + GET_FBS(a);
91 /******************************************************************************/
93 uint16_t bigint_length_B(bigint_t* a){
94 return (bigint_length_b(a)+7)/8;
97 /******************************************************************************/
99 uint32_t bigint_get_first_set_bit(bigint_t* a){
101 return (uint32_t)(-1);
103 return (a->length_B-1)*sizeof(bigint_word_t)*8+GET_FBS(a);
107 /******************************************************************************/
109 uint32_t bigint_get_last_set_bit(bigint_t* a){
114 return (uint32_t)(-1);
116 while(a->wordv[r]==0 && r<a->length_B){
119 if(a->wordv[r] == 0){
120 return (uint32_t)(-1);
122 while((x&a->wordv[r])==0){
126 return r*BIGINT_WORD_SIZE+b;
129 /******************************************************************************/
131 void bigint_copy(bigint_t* dest, const bigint_t* src){
132 memcpy(dest->wordv, src->wordv, src->length_B*sizeof(bigint_word_t));
133 dest->length_B = src->length_B;
134 dest->info = src->info;
137 /******************************************************************************/
139 /* this should be implemented in assembly */
140 void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
142 bigint_wordplus_t t=0LL;
143 if(a->length_B < b->length_B){
146 for(i=0; i<b->length_B; ++i){
147 // t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t;
150 dest->wordv[i] = (bigint_word_t)t;
151 t>>=BIGINT_WORD_SIZE;
153 for(; i<a->length_B; ++i){
155 dest->wordv[i] = (bigint_word_t)t;
156 t>>=BIGINT_WORD_SIZE;
158 dest->wordv[i++] = (bigint_word_t)t;
163 /******************************************************************************/
165 /* this should be implemented in assembly */
166 void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){
170 bigint_wordplus_t t=0;
171 scale_w = (scale+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
172 if(scale>dest->length_B*sizeof(bigint_word_t)){
173 memset(((uint8_t*)dest->wordv)+dest->length_B*sizeof(bigint_word_t), 0, scale-dest->length_B*sizeof(bigint_word_t));
175 // a->wordv = (const uint32_t*)(((uint8_t*)a->wordv)+(scale&3));
176 dst = dest->wordv + (scale&(sizeof(bigint_word_t)-1));
177 for(i=scale/sizeof(bigint_word_t); i<a->length_B+scale_w; ++i,++j){
179 if(dest->length_B>i){
182 dst[i] = (bigint_word_t)t;
183 t>>=BIGINT_WORD_SIZE;
186 if(dest->length_B>i){
189 dst[i] = (bigint_word_t)t;
190 t>>=BIGINT_WORD_SIZE;
193 if(dest->length_B < i){
199 /******************************************************************************/
201 /* this should be implemented in assembly */
202 void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
205 bigint_wordplus_signed_t t=0LL;
206 uint16_t i, min, max;
207 min = MIN(a->length_B, b->length_B);
208 max = MAX(a->length_B, b->length_B);
209 r = bigint_cmp_u(a,b);
211 bigint_set_zero(dest);
215 bigint_copy(dest, a);
220 bigint_copy(dest, b);
225 bigint_sub_u(dest, b, a);
228 for(i=0; i<min; ++i){
234 dest->wordv[i]=(bigint_word_t)t;
237 dest->wordv[i]=(bigint_word_t)t;
241 t = a->wordv[i] - borrow;
244 dest->wordv[i]=(bigint_word_t)t;
247 dest->wordv[i]=(bigint_word_t)t;
257 /******************************************************************************/
259 int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){
260 if(a->length_B > b->length_B){
263 if(a->length_B < b->length_B){
272 if(a->wordv[i]!=b->wordv[i]){
273 if(a->wordv[i]>b->wordv[i]){
283 /******************************************************************************/
285 void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
288 s |= GET_SIGN(b)?1:0;
290 case 0: /* both positive */
291 bigint_add_u(dest, a,b);
294 case 1: /* a positive, b negative */
295 bigint_sub_u(dest, a, b);
297 case 2: /* a negative, b positive */
298 bigint_sub_u(dest, b, a);
300 case 3: /* both negative */
301 bigint_add_u(dest, a, b);
304 default: /* how can this happen?*/
309 /******************************************************************************/
311 void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
314 s |= GET_SIGN(b)?1:0;
316 case 0: /* both positive */
317 bigint_sub_u(dest, a,b);
319 case 1: /* a positive, b negative */
320 bigint_add_u(dest, a, b);
323 case 2: /* a negative, b positive */
324 bigint_add_u(dest, a, b);
327 case 3: /* both negative */
328 bigint_sub_u(dest, b, a);
330 default: /* how can this happen?*/
336 /******************************************************************************/
338 int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){
340 if(a->length_B==0 && b->length_B==0){
344 s |= GET_SIGN(b)?1:0;
346 case 0: /* both positive */
347 return bigint_cmp_u(a, b);
349 case 1: /* a positive, b negative */
352 case 2: /* a negative, b positive */
355 case 3: /* both negative */
356 return bigint_cmp_u(b, a);
358 default: /* how can this happen?*/
361 return 0; /* just to satisfy the compiler */
364 /******************************************************************************/
366 void bigint_shiftleft(bigint_t* a, uint16_t shift){
367 uint16_t byteshift, word_alloc;
371 bigint_wordplus_t t=0;
377 for(i=0;i<=byteshift/sizeof(bigint_word_t); ++i){
378 a->wordv[a->length_B+i] = 0;
381 memmove(((uint8_t*)a->wordv)+byteshift, a->wordv, a->length_B*sizeof(bigint_word_t));
382 memset(a->wordv, 0, byteshift);
384 p = (bigint_word_t*)(((uint8_t*)a->wordv)+byteshift);
385 word_alloc = a->length_B+(byteshift+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t)+1;
386 a->wordv[word_alloc-1]=0;
388 for(i=0; i<a->length_B; ++i){
389 t |= ((bigint_wordplus_t)p[i])<<bitshift;
390 p[i] = (bigint_word_t)t;
391 t >>= BIGINT_WORD_SIZE;
393 p[i] = (bigint_word_t)t;
395 a->length_B = word_alloc;
399 /******************************************************************************/
401 void bigint_shiftright(bigint_t* a, uint16_t shift){
405 bigint_wordplus_t t=0;
408 if(byteshift >= a->length_B*sizeof(bigint_word_t)){ /* we would shift out more than we have */
412 if(byteshift == a->length_B*sizeof(bigint_word_t)-1 && bitshift>GET_FBS(a)){
417 memmove(a->wordv, (uint8_t*)a->wordv+byteshift, a->length_B-byteshift);
418 memset((uint8_t*)a->wordv+a->length_B-byteshift, 0, byteshift);
420 byteshift /= sizeof(bigint_word_t);
422 /* shift to the right */
423 for(i=a->length_B-byteshift-1; i>0; --i){
424 t |= ((bigint_wordplus_t)(a->wordv[i]))<<(BIGINT_WORD_SIZE-bitshift);
425 a->wordv[i] = (bigint_word_t)(t>>BIGINT_WORD_SIZE);
426 t <<= BIGINT_WORD_SIZE;
428 t |= ((bigint_wordplus_t)(a->wordv[0]))<<(BIGINT_WORD_SIZE-bitshift);
429 a->wordv[0] = (bigint_word_t)(t>>BIGINT_WORD_SIZE);
431 a->length_B -= ((shift/8)+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t);
435 /******************************************************************************/
437 void bigint_xor(bigint_t* dest, const bigint_t* a){
439 for(i=0; i<a->length_B; ++i){
440 dest->wordv[i] ^= a->wordv[i];
445 /******************************************************************************/
447 void bigint_set_zero(bigint_t* a){
451 /******************************************************************************/
453 /* using the Karatsuba-Algorithm */
454 /* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */
455 void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){
456 if(a->length_B==0 || b->length_B==0){
457 bigint_set_zero(dest);
460 if(dest==a || dest==b){
462 bigint_word_t d_b[a->length_B+b->length_B];
464 bigint_mul_u(&d, a, b);
465 bigint_copy(dest, &d);
468 if(a->length_B==1 || b->length_B==1){
472 bigint_wordplus_t i, t=0;
473 bigint_word_t x = a->wordv[0];
474 for(i=0; i<b->length_B; ++i){
475 t += ((bigint_wordplus_t)b->wordv[i])*((bigint_wordplus_t)x);
476 dest->wordv[i] = (bigint_word_t)t;
477 t>>=BIGINT_WORD_SIZE;
479 dest->wordv[i] = (bigint_word_t)t;
484 if(a->length_B<=4/sizeof(bigint_word_t) && b->length_B<=4/sizeof(bigint_word_t)){
487 memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t));
488 memcpy(&q, b->wordv, b->length_B*sizeof(bigint_word_t));
489 r = (uint64_t)p*(uint64_t)q;
490 memcpy(dest->wordv, &r, (a->length_B+b->length_B)*sizeof(bigint_word_t));
491 dest->length_B = a->length_B+b->length_B;
495 bigint_set_zero(dest);
496 /* split a in xh & xl; split b in yh & yl */
498 n=(MAX(a->length_B, b->length_B)+1)/2;
499 bigint_t xl, xh, yl, yh;
505 xl.length_B = a->length_B;
511 xh.wordv = a->wordv+n;
512 xh.length_B = a->length_B-n;
518 yl.length_B = b->length_B;
524 yh.wordv = b->wordv+n;
525 yh.length_B = b->length_B-n;
528 /* now we have split up a and b */
529 bigint_word_t tmp_b[2*n+2], m_b[2*(n+1)];
530 bigint_t tmp, tmp2, m;
532 tmp2.wordv = tmp_b+n+1;
535 bigint_mul_u(dest, &xl, &yl); /* dest <= xl*yl */
536 bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl */
537 bigint_add_u(&tmp, &yh, &yl); /* tmp <= yh+yl */
538 bigint_mul_u(&m, &tmp2, &tmp); /* m <= tmp2*tmp */
539 bigint_mul_u(&tmp, &xh, &yh); /* h <= xh*yh */
540 bigint_sub_u(&m, &m, dest); /* m <= m-dest */
541 bigint_sub_u(&m, &m, &tmp); /* m <= m-h */
542 bigint_add_scale_u(dest, &m, n*sizeof(bigint_word_t));
543 bigint_add_scale_u(dest, &tmp, 2*n*sizeof(bigint_word_t));
546 /******************************************************************************/
548 void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){
551 s |= GET_SIGN(b)?1:0;
553 case 0: /* both positive */
554 bigint_mul_u(dest, a,b);
557 case 1: /* a positive, b negative */
558 bigint_mul_u(dest, a,b);
561 case 2: /* a negative, b positive */
562 bigint_mul_u(dest, a,b);
565 case 3: /* both negative */
566 bigint_mul_u(dest, a,b);
569 default: /* how can this happen?*/
574 /******************************************************************************/
577 /* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */
578 void bigint_square(bigint_t* dest, const bigint_t* a){
579 if(a->length_B*sizeof(bigint_word_t)<=4){
581 memcpy(&r, a->wordv, a->length_B*sizeof(bigint_word_t));
583 memcpy(dest->wordv, &r, 2*a->length_B*sizeof(bigint_word_t));
585 dest->length_B=2*a->length_B;
591 bigint_word_t d_b[a->length_B*2];
593 bigint_square(&d, a);
594 bigint_copy(dest, &d);
599 bigint_t xh, xl, tmp; /* x-high, x-low, temp */
600 bigint_word_t buffer[2*n+1];
603 xh.wordv = &(a->wordv[n]);
604 xh.length_B = a->length_B-n;
606 // cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl);
607 // cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh);
608 bigint_square(dest, &xl);
609 // cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest);
610 bigint_square(&tmp, &xh);
611 // cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp);
612 bigint_add_scale_u(dest, &tmp, 2*n*sizeof(bigint_word_t));
613 // cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest);
614 bigint_mul_u(&tmp, &xl, &xh);
615 // cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp);
616 bigint_shiftleft(&tmp, 1);
617 // cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp);
618 bigint_add_scale_u(dest, &tmp, n*sizeof(bigint_word_t));
619 // cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest);
620 // cli_putstr("\r\n");
623 /******************************************************************************/
624 void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){
626 bigint_word_t tmp_b[b->length_B+4];
627 uint16_t i,j,word_shift=bitscale/(8*sizeof(bigint_word_t));
629 bigint_wordplus_signed_t t;
631 if(a->length_B < b->length_B+word_shift){
632 cli_putstr("\r\nDBG: *bang*\r\n");
637 bigint_copy(&tmp, b);
638 bigint_shiftleft(&tmp, bitscale&(BIGINT_WORD_SIZE-1));
639 // cli_putstr("\r\nDBG(sub_ub.0) tmp_shift = "); bigint_print_hex(&tmp);
640 for(j=0,i=word_shift; i<tmp.length_B+word_shift; ++i, ++j){
644 a->wordv[i] = (bigint_word_t)t;
652 if(i+1 > a->length_B){
653 cli_putstr("\r\nDBG: *boom*\r\n");
657 a->wordv[i] -= borrow;
658 if(a->wordv[i]!=0xff){
666 /******************************************************************************/
668 void bigint_reduce(bigint_t* a, const bigint_t* r){
669 // bigint_adjust((bigint_t*)r);
670 uint8_t rfbs = GET_FBS(r);
672 // cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
673 if(r->length_B==0 || a->length_B==0){
676 if((r->length_B*sizeof(bigint_word_t)<=4) && (a->length_B*sizeof(bigint_word_t)<=4)){
678 memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t));
679 memcpy(&q, r->wordv, r->length_B*sizeof(bigint_word_t));
681 memcpy(a->wordv, &p, a->length_B*sizeof(bigint_word_t));
683 // cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a);
687 while(a->length_B > r->length_B){
688 shift = (a->length_B - r->length_B) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1;
689 if(a->wordv[a->length_B-1] > r->wordv[r->length_B-1]){
692 // cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2);
693 // cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_B, 2);
694 // cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_B, 2);
696 bigint_sub_u_bitscale(a, r, shift);
697 // cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a);
699 while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){
700 shift = GET_FBS(a)-rfbs-1;
701 // cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2);
702 bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1);
703 // cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a);
705 while(bigint_cmp_u(a,r)>=0){
707 // cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a);
710 // cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a);
711 // cli_putstr("\r\n");
714 /******************************************************************************/
716 /* calculate dest = a**exp % r */
717 /* using square&multiply */
718 void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){
719 if(a->length_B==0 || r->length_B==0){
724 bigint_word_t t, base_b[MAX(a->length_B,r->length_B*2)], res_b[r->length_B*2];
727 // uint16_t *xaddr = &i;
728 // cli_putstr("\r\npre-alloc (");
729 // cli_hexdump_rev(&xaddr, 4);
730 // cli_putstr(") ...");
733 bigint_copy(&base, a);
734 // cli_putstr("\r\npost-copy");
735 bigint_reduce(&base, r);
739 // cli_putstr("\r\nadjust ");
741 // cli_putstr("\r\nexpmod ");
742 for(i=0; i+1<exp->length_B; ++i){
744 for(j=0; j<BIGINT_WORD_SIZE; ++j){
746 bigint_mul_u(&res, &res, &base);
747 bigint_reduce(&res, r);
749 bigint_square(&base, &base);
750 bigint_reduce(&base, r);
759 bigint_mul_u(&res, &res, &base);
760 bigint_reduce(&res, r);
762 bigint_square(&base, &base);
763 bigint_reduce(&base, r);
767 bigint_copy(dest, &res);
770 /******************************************************************************/
772 #define cli_putstr(a)
773 #define bigint_print_hex(a)
774 #define cli_hexdump_rev(a,b)
775 #define uart_flush(a)
777 /* gcd <-- gcd(x,y) a*x+b*y=gcd */
778 void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, const bigint_t* y){
779 bigint_t g, x_, y_, u, v, a_, b_, c_, d_;
781 if(x->length_B==0 || y->length_B==0){
784 if(x->length_B==1 && x->wordv[0]==1){
798 if(y->length_B==1 && y->wordv[0]==1){
813 while(x->wordv[i]==0 && y->wordv[i]==0){
816 bigint_word_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i];
817 bigint_word_t u_b[x->length_B-i], v_b[y->length_B-i];
818 bigint_word_t a_b[y->length_B+2], c_b[y->length_B+2];
819 bigint_word_t b_b[x->length_B+2], d_b[x->length_B+2];
824 memset(g_b, 0, i*sizeof(bigint_word_t));
828 x_.info = y_.info = 0;
829 x_.length_B = x->length_B-i;
830 y_.length_B = y->length_B-i;
831 memcpy(x_.wordv, x->wordv+i, x_.length_B*sizeof(bigint_word_t));
832 memcpy(y_.wordv, y->wordv+i, y_.length_B*sizeof(bigint_word_t));
833 for(i=0; (x_.wordv[0]&(1<<i))==0 && (y_.wordv[0]&(1<<i))==0; ++i){
840 bigint_shiftleft(&g, i);
841 bigint_shiftright(&x_, i);
842 bigint_shiftright(&y_, i);
852 bigint_copy(&u, &x_);
853 bigint_copy(&v, &y_);
860 bigint_set_zero(&b_);
861 bigint_set_zero(&c_);
863 cli_putstr("\r\nDBG (gcdext) 0");
864 while((u.wordv[0]&1)==0){
865 cli_putstr("\r\nDBG (gcdext) 0.1");
866 bigint_shiftright(&u, 1);
867 if((a_.wordv[0]&1) || (b_.wordv[0]&1)){
868 bigint_add_s(&a_, &a_, &y_);
869 bigint_sub_s(&b_, &b_, &x_);
871 bigint_shiftright(&a_, 1);
872 bigint_shiftright(&b_, 1);
874 while((v.wordv[0]&1)==0){
875 cli_putstr("\r\nDBG (gcdext) 0.2");
876 bigint_shiftright(&v, 1);
877 if((c_.wordv[0]&1) || (d_.wordv[0]&1)){
878 bigint_add_s(&c_, &c_, &y_);
879 bigint_sub_s(&d_, &d_, &x_);
881 bigint_shiftright(&c_, 1);
882 bigint_shiftright(&d_, 1);
885 if(bigint_cmp_u(&u, &v)>=0){
886 bigint_sub_u(&u, &u, &v);
887 bigint_sub_s(&a_, &a_, &c_);
888 bigint_sub_s(&b_, &b_, &d_);
890 bigint_sub_u(&v, &v, &u);
891 bigint_sub_s(&c_, &c_, &a_);
892 bigint_sub_s(&d_, &d_, &b_);
896 bigint_mul_s(gcd, &v, &g);
906 /******************************************************************************/
908 void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* m){
909 bigint_gcdext(NULL, dest, NULL, a, m);
910 while(dest->info&BIGINT_NEG_MASK){
911 bigint_add_s(dest, dest, m);
915 /******************************************************************************/
917 void bigint_changeendianess(bigint_t* a){
919 p = (uint8_t*)(a->wordv);
920 q = ((uint8_t*)p)+a->length_B*sizeof(bigint_word_t)-1;
929 /******************************************************************************/