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 "ecp.h"
andre@0: #include "mpi.h"
andre@0: #include "mplogic.h"
andre@0: #include "mpi-priv.h"
andre@0: 
andre@0: /* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1.  a can be r. 
andre@0:  * Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to 
andre@0:  * Elliptic Curve Cryptography. */
andre@0: static mp_err
andre@0: ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_size a_used = MP_USED(a);
andre@0: 	int a_bits = mpl_significant_bits(a);
andre@0: 	mp_digit carry;
andre@0: 
andre@0: #ifdef ECL_THIRTY_TWO_BIT
andre@0: 	mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0;
andre@0: 	mp_digit r0, r1, r2, r3, r4, r5, r6, r7;
andre@0: 	int r8; /* must be a signed value ! */
andre@0: #else
andre@0: 	mp_digit a4=0, a5=0, a6=0, a7=0;
andre@0: 	mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l;
andre@0: 	mp_digit r0, r1, r2, r3;
andre@0: 	int r4; /* must be a signed value ! */
andre@0: #endif
andre@0: 	/* for polynomials larger than twice the field size 
andre@0: 	 * use regular reduction */
andre@0: 	if (a_bits < 256) {
andre@0: 		if (a == r) return MP_OKAY;
andre@0: 		return mp_copy(a,r);
andre@0: 	}
andre@0: 	if (a_bits > 512)  {
andre@0: 		MP_CHECKOK(mp_mod(a, &meth->irr, r));
andre@0: 	} else {
andre@0: 
andre@0: #ifdef ECL_THIRTY_TWO_BIT
andre@0: 		switch (a_used) {
andre@0: 		case 16:
andre@0: 			a15 = MP_DIGIT(a,15);
andre@0: 		case 15:
andre@0: 			a14 = MP_DIGIT(a,14);
andre@0: 		case 14:
andre@0: 			a13 = MP_DIGIT(a,13);
andre@0: 		case 13:
andre@0: 			a12 = MP_DIGIT(a,12);
andre@0: 		case 12:
andre@0: 			a11 = MP_DIGIT(a,11);
andre@0: 		case 11:
andre@0: 			a10 = MP_DIGIT(a,10);
andre@0: 		case 10:
andre@0: 			a9 = MP_DIGIT(a,9);
andre@0: 		case 9:
andre@0: 			a8 = MP_DIGIT(a,8);
andre@0: 		}
andre@0: 
andre@0: 		r0 = MP_DIGIT(a,0);
andre@0: 		r1 = MP_DIGIT(a,1);
andre@0: 		r2 = MP_DIGIT(a,2);
andre@0: 		r3 = MP_DIGIT(a,3);
andre@0: 		r4 = MP_DIGIT(a,4);
andre@0: 		r5 = MP_DIGIT(a,5);
andre@0: 		r6 = MP_DIGIT(a,6);
andre@0: 		r7 = MP_DIGIT(a,7);
andre@0: 
andre@0: 		/* sum 1 */
andre@0: 		MP_ADD_CARRY(r3, a11, r3, 0,     carry);
andre@0: 		MP_ADD_CARRY(r4, a12, r4, carry, carry);
andre@0: 		MP_ADD_CARRY(r5, a13, r5, carry, carry);
andre@0: 		MP_ADD_CARRY(r6, a14, r6, carry, carry);
andre@0: 		MP_ADD_CARRY(r7, a15, r7, carry, carry);
andre@0: 		r8 = carry;
andre@0: 		MP_ADD_CARRY(r3, a11, r3, 0,     carry);
andre@0: 		MP_ADD_CARRY(r4, a12, r4, carry, carry);
andre@0: 		MP_ADD_CARRY(r5, a13, r5, carry, carry);
andre@0: 		MP_ADD_CARRY(r6, a14, r6, carry, carry);
andre@0: 		MP_ADD_CARRY(r7, a15, r7, carry, carry);
andre@0: 		r8 += carry;
andre@0: 		/* sum 2 */
andre@0: 		MP_ADD_CARRY(r3, a12, r3, 0,     carry);
andre@0: 		MP_ADD_CARRY(r4, a13, r4, carry, carry);
andre@0: 		MP_ADD_CARRY(r5, a14, r5, carry, carry);
andre@0: 		MP_ADD_CARRY(r6, a15, r6, carry, carry);
andre@0: 		MP_ADD_CARRY(r7,   0, r7, carry, carry);
andre@0: 		r8 += carry;
andre@0: 		/* combine last bottom of sum 3 with second sum 2 */
andre@0: 		MP_ADD_CARRY(r0, a8,  r0, 0,     carry);
andre@0: 		MP_ADD_CARRY(r1, a9,  r1, carry, carry);
andre@0: 		MP_ADD_CARRY(r2, a10, r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a12, r3, carry, carry);
andre@0: 		MP_ADD_CARRY(r4, a13, r4, carry, carry);
andre@0: 		MP_ADD_CARRY(r5, a14, r5, carry, carry);
andre@0: 		MP_ADD_CARRY(r6, a15, r6, carry, carry);
andre@0: 		MP_ADD_CARRY(r7, a15, r7, carry, carry); /* from sum 3 */
andre@0: 		r8 += carry;
andre@0: 		/* sum 3 (rest of it)*/
andre@0: 		MP_ADD_CARRY(r6, a14, r6, 0,     carry);
andre@0: 		MP_ADD_CARRY(r7,   0, r7, carry, carry);
andre@0: 		r8 += carry;
andre@0: 		/* sum 4 (rest of it)*/
andre@0: 		MP_ADD_CARRY(r0, a9,  r0, 0,     carry);
andre@0: 		MP_ADD_CARRY(r1, a10, r1, carry, carry);
andre@0: 		MP_ADD_CARRY(r2, a11, r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a13, r3, carry, carry);
andre@0: 		MP_ADD_CARRY(r4, a14, r4, carry, carry);
andre@0: 		MP_ADD_CARRY(r5, a15, r5, carry, carry);
andre@0: 		MP_ADD_CARRY(r6, a13, r6, carry, carry);
andre@0: 		MP_ADD_CARRY(r7, a8,  r7, carry, carry);
andre@0: 		r8 += carry;
andre@0: 		/* diff 5 */
andre@0: 		MP_SUB_BORROW(r0, a11, r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a12, r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, a13, r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3,   0, r3, carry, carry);
andre@0: 		MP_SUB_BORROW(r4,   0, r4, carry, carry);
andre@0: 		MP_SUB_BORROW(r5,   0, r5, carry, carry);
andre@0: 		MP_SUB_BORROW(r6, a8,  r6, carry, carry);
andre@0: 		MP_SUB_BORROW(r7, a10, r7, carry, carry);
andre@0: 		r8 -= carry;
andre@0: 		/* diff 6 */
andre@0: 		MP_SUB_BORROW(r0, a12, r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a13, r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, a14, r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3, a15, r3, carry, carry);
andre@0: 		MP_SUB_BORROW(r4,   0, r4, carry, carry);
andre@0: 		MP_SUB_BORROW(r5,   0, r5, carry, carry);
andre@0: 		MP_SUB_BORROW(r6, a9,  r6, carry, carry);
andre@0: 		MP_SUB_BORROW(r7, a11, r7, carry, carry);
andre@0: 		r8 -= carry;
andre@0: 		/* diff 7 */
andre@0: 		MP_SUB_BORROW(r0, a13, r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a14, r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, a15, r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3, a8,  r3, carry, carry);
andre@0: 		MP_SUB_BORROW(r4, a9,  r4, carry, carry);
andre@0: 		MP_SUB_BORROW(r5, a10, r5, carry, carry);
andre@0: 		MP_SUB_BORROW(r6, 0,   r6, carry, carry);
andre@0: 		MP_SUB_BORROW(r7, a12, r7, carry, carry);
andre@0: 		r8 -= carry;
andre@0: 		/* diff 8 */
andre@0: 		MP_SUB_BORROW(r0, a14, r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a15, r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, 0,   r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3, a9,  r3, carry, carry);
andre@0: 		MP_SUB_BORROW(r4, a10, r4, carry, carry);
andre@0: 		MP_SUB_BORROW(r5, a11, r5, carry, carry);
andre@0: 		MP_SUB_BORROW(r6, 0,   r6, carry, carry);
andre@0: 		MP_SUB_BORROW(r7, a13, r7, carry, carry);
andre@0: 		r8 -= carry;
andre@0: 
andre@0: 		/* reduce the overflows */
andre@0: 		while (r8 > 0) {
andre@0: 			mp_digit r8_d = r8;
andre@0: 			MP_ADD_CARRY(r0, r8_d,         r0, 0,     carry);
andre@0: 			MP_ADD_CARRY(r1, 0,            r1, carry, carry);
andre@0: 			MP_ADD_CARRY(r2, 0,            r2, carry, carry);
andre@0: 			MP_ADD_CARRY(r3, 0-r8_d,       r3, carry, carry);
andre@0: 			MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry, carry);
andre@0: 			MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry, carry);
andre@0: 			MP_ADD_CARRY(r6, 0-(r8_d+1),   r6, carry, carry);
andre@0: 			MP_ADD_CARRY(r7, (r8_d-1),     r7, carry, carry);
andre@0: 			r8 = carry;
andre@0: 		}
andre@0: 
andre@0: 		/* reduce the underflows */
andre@0: 		while (r8 < 0) {
andre@0: 			mp_digit r8_d = -r8;
andre@0: 			MP_SUB_BORROW(r0, r8_d,         r0, 0,     carry);
andre@0: 			MP_SUB_BORROW(r1, 0,            r1, carry, carry);
andre@0: 			MP_SUB_BORROW(r2, 0,            r2, carry, carry);
andre@0: 			MP_SUB_BORROW(r3, 0-r8_d,       r3, carry, carry);
andre@0: 			MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry, carry);
andre@0: 			MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry, carry);
andre@0: 			MP_SUB_BORROW(r6, 0-(r8_d+1),   r6, carry, carry);
andre@0: 			MP_SUB_BORROW(r7, (r8_d-1),     r7, carry, carry);
andre@0: 			r8 = 0-carry;
andre@0: 		}
andre@0: 		if (a != r) {
andre@0: 			MP_CHECKOK(s_mp_pad(r,8));
andre@0: 		}
andre@0: 		MP_SIGN(r) = MP_ZPOS;
andre@0: 		MP_USED(r) = 8;
andre@0: 
andre@0: 		MP_DIGIT(r,7) = r7;
andre@0: 		MP_DIGIT(r,6) = r6;
andre@0: 		MP_DIGIT(r,5) = r5;
andre@0: 		MP_DIGIT(r,4) = r4;
andre@0: 		MP_DIGIT(r,3) = r3;
andre@0: 		MP_DIGIT(r,2) = r2;
andre@0: 		MP_DIGIT(r,1) = r1;
andre@0: 		MP_DIGIT(r,0) = r0;
andre@0: 
andre@0: 		/* final reduction if necessary */
andre@0: 		if ((r7 == MP_DIGIT_MAX) &&
andre@0: 			((r6 > 1) || ((r6 == 1) &&
andre@0: 			(r5 || r4 || r3 || 
andre@0: 				((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX)
andre@0: 				  && (r0 == MP_DIGIT_MAX)))))) {
andre@0: 			MP_CHECKOK(mp_sub(r, &meth->irr, r));
andre@0: 		}
andre@0: 
andre@0: 		s_mp_clamp(r);
andre@0: #else
andre@0: 		switch (a_used) {
andre@0: 		case 8:
andre@0: 			a7 = MP_DIGIT(a,7);
andre@0: 		case 7:
andre@0: 			a6 = MP_DIGIT(a,6);
andre@0: 		case 6:
andre@0: 			a5 = MP_DIGIT(a,5);
andre@0: 		case 5:
andre@0: 			a4 = MP_DIGIT(a,4);
andre@0: 		}
andre@0: 		a7l = a7 << 32;
andre@0: 		a7h = a7 >> 32;
andre@0: 		a6l = a6 << 32;
andre@0: 		a6h = a6 >> 32;
andre@0: 		a5l = a5 << 32;
andre@0: 		a5h = a5 >> 32;
andre@0: 		a4l = a4 << 32;
andre@0: 		a4h = a4 >> 32;
andre@0: 		r3 = MP_DIGIT(a,3);
andre@0: 		r2 = MP_DIGIT(a,2);
andre@0: 		r1 = MP_DIGIT(a,1);
andre@0: 		r0 = MP_DIGIT(a,0);
andre@0: 
andre@0: 		/* sum 1 */
andre@0: 		MP_ADD_CARRY(r1, a5h << 32, r1, 0,     carry);
andre@0: 		MP_ADD_CARRY(r2, a6,        r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
andre@0: 		r4 = carry;
andre@0: 		MP_ADD_CARRY(r1, a5h << 32, r1, 0,     carry);
andre@0: 		MP_ADD_CARRY(r2, a6,        r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
andre@0: 		r4 += carry;
andre@0: 		/* sum 2 */
andre@0: 		MP_ADD_CARRY(r1, a6l,       r1, 0,     carry);
andre@0: 		MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a7h,       r3, carry, carry);
andre@0: 		r4 += carry;
andre@0: 		MP_ADD_CARRY(r1, a6l,       r1, 0,     carry);
andre@0: 		MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a7h,       r3, carry, carry);
andre@0: 		r4 += carry;
andre@0: 
andre@0: 		/* sum 3 */
andre@0: 		MP_ADD_CARRY(r0, a4,        r0, 0,     carry);
andre@0: 		MP_ADD_CARRY(r1, a5l >> 32, r1, carry, carry);
andre@0: 		MP_ADD_CARRY(r2, 0,         r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
andre@0: 		r4 += carry;
andre@0: 		/* sum 4 */
andre@0: 		MP_ADD_CARRY(r0, a4h | a5l,     r0, 0,     carry);
andre@0: 		MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry, carry);
andre@0: 		MP_ADD_CARRY(r2, a7,            r2, carry, carry);
andre@0: 		MP_ADD_CARRY(r3, a6h | a4l,     r3, carry, carry);
andre@0: 		r4 += carry;
andre@0: 		/* diff 5 */
andre@0: 		MP_SUB_BORROW(r0, a5h | a6l,    r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a6h,          r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, 0,            r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry, carry);
andre@0: 		r4 -= carry;
andre@0: 		/* diff 6 */
andre@0: 		MP_SUB_BORROW(r0, a6,  		r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a7,           r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, 0,            r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry, carry);
andre@0: 		r4 -= carry;
andre@0: 		/* diff 7 */
andre@0: 		MP_SUB_BORROW(r0, a6h|a7l,	r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a7h|a4l,      r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, a4h|a5l,      r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3, a6l,          r3, carry, carry);
andre@0: 		r4 -= carry;
andre@0: 		/* diff 8 */
andre@0: 		MP_SUB_BORROW(r0, a7,	        r0, 0,     carry);
andre@0: 		MP_SUB_BORROW(r1, a4h<<32,      r1, carry, carry);
andre@0: 		MP_SUB_BORROW(r2, a5,           r2, carry, carry);
andre@0: 		MP_SUB_BORROW(r3, a6h<<32,      r3, carry, carry);
andre@0: 		r4 -= carry;
andre@0: 
andre@0: 		/* reduce the overflows */
andre@0: 		while (r4 > 0) {
andre@0: 			mp_digit r4_long = r4;
andre@0: 			mp_digit r4l = (r4_long << 32);
andre@0: 			MP_ADD_CARRY(r0, r4_long,      r0, 0,     carry);
andre@0: 			MP_ADD_CARRY(r1, 0-r4l,        r1, carry, carry);
andre@0: 			MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry, carry);
andre@0: 			MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry, carry);
andre@0: 			r4 = carry;
andre@0: 		}
andre@0: 
andre@0: 		/* reduce the underflows */
andre@0: 		while (r4 < 0) {
andre@0: 			mp_digit r4_long = -r4;
andre@0: 			mp_digit r4l = (r4_long << 32);
andre@0: 			MP_SUB_BORROW(r0, r4_long,      r0, 0,     carry);
andre@0: 			MP_SUB_BORROW(r1, 0-r4l,        r1, carry, carry);
andre@0: 			MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry, carry);
andre@0: 			MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry, carry);
andre@0: 			r4 = 0-carry;
andre@0: 		}
andre@0: 
andre@0: 		if (a != r) {
andre@0: 			MP_CHECKOK(s_mp_pad(r,4));
andre@0: 		}
andre@0: 		MP_SIGN(r) = MP_ZPOS;
andre@0: 		MP_USED(r) = 4;
andre@0: 
andre@0: 		MP_DIGIT(r,3) = r3;
andre@0: 		MP_DIGIT(r,2) = r2;
andre@0: 		MP_DIGIT(r,1) = r1;
andre@0: 		MP_DIGIT(r,0) = r0;
andre@0: 
andre@0: 		/* final reduction if necessary */
andre@0: 		if ((r3 > 0xFFFFFFFF00000001ULL) ||
andre@0: 			((r3 == 0xFFFFFFFF00000001ULL) && 
andre@0: 			(r2 || (r1 >> 32)|| 
andre@0: 			       (r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) {
andre@0: 			/* very rare, just use mp_sub */
andre@0: 			MP_CHECKOK(mp_sub(r, &meth->irr, r));
andre@0: 		}
andre@0: 			
andre@0: 		s_mp_clamp(r);
andre@0: #endif
andre@0: 	}
andre@0: 
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Compute the square of polynomial a, reduce modulo p256. Store the
andre@0:  * result in r.  r could be a.  Uses optimized modular reduction for p256. 
andre@0:  */
andre@0: static mp_err
andre@0: ec_GFp_nistp256_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 
andre@0: 	MP_CHECKOK(mp_sqr(a, r));
andre@0: 	MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Compute the product of two polynomials a and b, reduce modulo p256.
andre@0:  * Store the result in r.  r could be a or b; a could be b.  Uses
andre@0:  * optimized modular reduction for p256. */
andre@0: static mp_err
andre@0: ec_GFp_nistp256_mul(const mp_int *a, const mp_int *b, mp_int *r,
andre@0: 					const GFMethod *meth)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 
andre@0: 	MP_CHECKOK(mp_mul(a, b, r));
andre@0: 	MP_CHECKOK(ec_GFp_nistp256_mod(r, r, meth));
andre@0:   CLEANUP:
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Wire in fast field arithmetic and precomputation of base point for
andre@0:  * named curves. */
andre@0: mp_err
andre@0: ec_group_set_gfp256(ECGroup *group, ECCurveName name)
andre@0: {
andre@0: 	if (name == ECCurve_NIST_P256) {
andre@0: 		group->meth->field_mod = &ec_GFp_nistp256_mod;
andre@0: 		group->meth->field_mul = &ec_GFp_nistp256_mul;
andre@0: 		group->meth->field_sqr = &ec_GFp_nistp256_sqr;
andre@0: 	}
andre@0: 	return MP_OKAY;
andre@0: }