michael@0: /* This Source Code Form is subject to the terms of the Mozilla Public
michael@0:  * License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0:  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
michael@0: 
michael@0: #include "ecp.h"
michael@0: #include "mpi.h"
michael@0: #include "mplogic.h"
michael@0: #include "mpi-priv.h"
michael@0: 
michael@0: #define ECP224_DIGITS ECL_CURVE_DIGITS(224)
michael@0: 
michael@0: /* Fast modular reduction for p224 = 2^224 - 2^96 + 1.  a can be r. Uses
michael@0:  * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
michael@0:  * Implementation of the NIST Elliptic Curves over Prime Fields. */
michael@0: static mp_err
michael@0: ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 	mp_size a_used = MP_USED(a);
michael@0: 
michael@0: 	int    r3b;
michael@0: 	mp_digit carry;
michael@0: #ifdef ECL_THIRTY_TWO_BIT
michael@0:         mp_digit a6a = 0, a6b = 0,
michael@0:                 a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
michael@0:         mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a;
michael@0: #else
michael@0: 	mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0;
michael@0:         mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0;
michael@0:         mp_digit r0, r1, r2, r3;
michael@0: #endif
michael@0: 
michael@0: 	/* reduction not needed if a is not larger than field size */
michael@0: 	if (a_used < ECP224_DIGITS) {
michael@0: 		if (a == r) return MP_OKAY;
michael@0: 		return mp_copy(a, r);
michael@0: 	}
michael@0: 	/* for polynomials larger than twice the field size, use regular
michael@0: 	 * reduction */
michael@0: 	if (a_used > ECL_CURVE_DIGITS(224*2)) {
michael@0: 		MP_CHECKOK(mp_mod(a, &meth->irr, r));
michael@0: 	} else {
michael@0: #ifdef ECL_THIRTY_TWO_BIT
michael@0: 		/* copy out upper words of a */
michael@0: 		switch (a_used) {
michael@0: 		case 14:
michael@0: 			a6b = MP_DIGIT(a, 13);
michael@0: 		case 13:
michael@0: 			a6a = MP_DIGIT(a, 12);
michael@0: 		case 12:
michael@0: 			a5b = MP_DIGIT(a, 11);
michael@0: 		case 11:
michael@0: 			a5a = MP_DIGIT(a, 10);
michael@0: 		case 10:
michael@0: 			a4b = MP_DIGIT(a, 9);
michael@0: 		case 9:
michael@0: 			a4a = MP_DIGIT(a, 8);
michael@0: 		case 8:
michael@0: 			a3b = MP_DIGIT(a, 7);
michael@0: 		}
michael@0: 		r3a = MP_DIGIT(a, 6);
michael@0: 		r2b= MP_DIGIT(a, 5);
michael@0: 		r2a= MP_DIGIT(a, 4);
michael@0: 		r1b = MP_DIGIT(a, 3);
michael@0: 		r1a = MP_DIGIT(a, 2);
michael@0: 		r0b = MP_DIGIT(a, 1);
michael@0: 		r0a = MP_DIGIT(a, 0);
michael@0: 
michael@0: 
michael@0: 		/* implement r = (a3a,a2,a1,a0)
michael@0: 			+(a5a, a4,a3b,  0)
michael@0: 			+(  0, a6,a5b,  0)
michael@0: 			-(  0	 0,    0|a6b, a6a|a5b )
michael@0: 			-(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
michael@0: 		MP_ADD_CARRY (r1b, a3b, r1b, 0,     carry);
michael@0: 		MP_ADD_CARRY (r2a, a4a, r2a, carry, carry);
michael@0: 		MP_ADD_CARRY (r2b, a4b, r2b, carry, carry);
michael@0: 		MP_ADD_CARRY (r3a, a5a, r3a, carry, carry);
michael@0: 		r3b = carry;
michael@0: 		MP_ADD_CARRY (r1b, a5b, r1b, 0,     carry);
michael@0: 		MP_ADD_CARRY (r2a, a6a, r2a, carry, carry);
michael@0: 		MP_ADD_CARRY (r2b, a6b, r2b, carry, carry);
michael@0: 		MP_ADD_CARRY (r3a,   0, r3a, carry, carry);
michael@0: 		r3b += carry;
michael@0: 		MP_SUB_BORROW(r0a, a3b, r0a, 0,     carry);
michael@0: 		MP_SUB_BORROW(r0b, a4a, r0b, carry, carry);
michael@0: 		MP_SUB_BORROW(r1a, a4b, r1a, carry, carry);
michael@0: 		MP_SUB_BORROW(r1b, a5a, r1b, carry, carry);
michael@0: 		MP_SUB_BORROW(r2a, a5b, r2a, carry, carry);
michael@0: 		MP_SUB_BORROW(r2b, a6a, r2b, carry, carry);
michael@0: 		MP_SUB_BORROW(r3a, a6b, r3a, carry, carry);
michael@0: 		r3b -= carry;
michael@0: 		MP_SUB_BORROW(r0a, a5b, r0a, 0,     carry);
michael@0: 		MP_SUB_BORROW(r0b, a6a, r0b, carry, carry);
michael@0: 		MP_SUB_BORROW(r1a, a6b, r1a, carry, carry);
michael@0: 		if (carry) {
michael@0: 			MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
michael@0: 			MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
michael@0: 			MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
michael@0: 			MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
michael@0: 			r3b -= carry;
michael@0: 		}
michael@0: 
michael@0: 		while (r3b > 0) {
michael@0: 			int tmp;
michael@0: 			MP_ADD_CARRY(r1b, r3b, r1b, 0,     carry);
michael@0: 			if (carry) {
michael@0: 				MP_ADD_CARRY(r2a,  0, r2a, carry, carry);
michael@0: 				MP_ADD_CARRY(r2b,  0, r2b, carry, carry);
michael@0: 				MP_ADD_CARRY(r3a,  0, r3a, carry, carry);
michael@0: 			}
michael@0: 			tmp = carry;
michael@0: 			MP_SUB_BORROW(r0a, r3b, r0a, 0,     carry);
michael@0: 			if (carry) {
michael@0: 				MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
michael@0: 				MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
michael@0: 				MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
michael@0: 				MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
michael@0: 				MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
michael@0: 				MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
michael@0: 				tmp -= carry;
michael@0: 			}
michael@0: 			r3b = tmp;
michael@0: 		}
michael@0: 
michael@0: 		while (r3b < 0) {
michael@0: 			mp_digit maxInt = MP_DIGIT_MAX;
michael@0:                 	MP_ADD_CARRY (r0a, 1, r0a, 0,     carry);
michael@0:                 	MP_ADD_CARRY (r0b, 0, r0b, carry, carry);
michael@0:                 	MP_ADD_CARRY (r1a, 0, r1a, carry, carry);
michael@0:                 	MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry);
michael@0:                 	MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry);
michael@0:                 	MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry);
michael@0:                 	MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry);
michael@0: 			r3b += carry;
michael@0: 		}
michael@0: 		/* check for final reduction */
michael@0: 		/* now the only way we are over is if the top 4 words are all ones */
michael@0: 		if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX)
michael@0: 			&& (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) &&
michael@0: 			 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) {
michael@0: 			/* one last subraction */
michael@0: 			MP_SUB_BORROW(r0a, 1, r0a, 0,     carry);
michael@0: 			MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
michael@0: 			MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
michael@0: 			r1b = r2a = r2b = r3a = 0;
michael@0: 		}
michael@0: 
michael@0: 
michael@0: 		if (a != r) {
michael@0: 			MP_CHECKOK(s_mp_pad(r, 7));
michael@0: 		}
michael@0: 		/* set the lower words of r */
michael@0: 		MP_SIGN(r) = MP_ZPOS;
michael@0: 		MP_USED(r) = 7;
michael@0: 		MP_DIGIT(r, 6) = r3a;
michael@0: 		MP_DIGIT(r, 5) = r2b;
michael@0: 		MP_DIGIT(r, 4) = r2a;
michael@0: 		MP_DIGIT(r, 3) = r1b;
michael@0: 		MP_DIGIT(r, 2) = r1a;
michael@0: 		MP_DIGIT(r, 1) = r0b;
michael@0: 		MP_DIGIT(r, 0) = r0a;
michael@0: #else
michael@0: 		/* copy out upper words of a */
michael@0: 		switch (a_used) {
michael@0: 		case 7:
michael@0: 			a6 = MP_DIGIT(a, 6);
michael@0: 			a6b = a6 >> 32;
michael@0: 			a6a_a5b = a6 << 32;
michael@0: 		case 6:
michael@0: 			a5 = MP_DIGIT(a, 5);
michael@0: 			a5b = a5 >> 32;
michael@0: 			a6a_a5b |= a5b;
michael@0: 			a5b = a5b << 32;
michael@0: 			a5a_a4b = a5 << 32;
michael@0: 			a5a = a5 & 0xffffffff;
michael@0: 		case 5:
michael@0: 			a4 = MP_DIGIT(a, 4);
michael@0: 			a5a_a4b |= a4 >> 32;
michael@0: 			a4a_a3b = a4 << 32;
michael@0: 		case 4:
michael@0: 			a3b = MP_DIGIT(a, 3) >> 32;
michael@0: 			a4a_a3b |= a3b;
michael@0: 			a3b = a3b << 32;
michael@0: 		}
michael@0: 
michael@0: 		r3 = MP_DIGIT(a, 3) & 0xffffffff;
michael@0: 		r2 = MP_DIGIT(a, 2);
michael@0: 		r1 = MP_DIGIT(a, 1);
michael@0: 		r0 = MP_DIGIT(a, 0);
michael@0: 
michael@0: 		/* implement r = (a3a,a2,a1,a0)
michael@0: 			+(a5a, a4,a3b,  0)
michael@0: 			+(  0, a6,a5b,  0)
michael@0: 			-(  0	 0,    0|a6b, a6a|a5b )
michael@0: 			-(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
michael@0: 		MP_ADD_CARRY (r1, a3b, r1, 0,     carry);
michael@0: 		MP_ADD_CARRY (r2, a4 , r2, carry, carry);
michael@0: 		MP_ADD_CARRY (r3, a5a, r3, carry, carry);
michael@0: 		MP_ADD_CARRY (r1, a5b, r1, 0,     carry);
michael@0: 		MP_ADD_CARRY (r2, a6 , r2, carry, carry);
michael@0: 		MP_ADD_CARRY (r3,   0, r3, carry, carry);
michael@0: 
michael@0: 		MP_SUB_BORROW(r0, a4a_a3b, r0, 0,     carry);
michael@0: 		MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry);
michael@0: 		MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry);
michael@0: 		MP_SUB_BORROW(r3, a6b    , r3, carry, carry);
michael@0: 		MP_SUB_BORROW(r0, a6a_a5b, r0, 0,     carry);
michael@0: 		MP_SUB_BORROW(r1, a6b    , r1, carry, carry);
michael@0: 		if (carry) {
michael@0: 			MP_SUB_BORROW(r2, 0, r2, carry, carry);
michael@0: 			MP_SUB_BORROW(r3, 0, r3, carry, carry);
michael@0: 		}
michael@0: 
michael@0: 
michael@0: 		/* if the value is negative, r3 has a 2's complement 
michael@0: 		 * high value */
michael@0: 		r3b = (int)(r3 >>32);
michael@0: 		while (r3b > 0) {
michael@0: 			r3 &= 0xffffffff;
michael@0: 			MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry);
michael@0: 			if (carry) {
michael@0: 				MP_ADD_CARRY(r2,  0, r2, carry, carry);
michael@0: 				MP_ADD_CARRY(r3,  0, r3, carry, carry);
michael@0: 			}
michael@0: 			MP_SUB_BORROW(r0, r3b, r0, 0, carry);
michael@0: 			if (carry) {
michael@0: 				MP_SUB_BORROW(r1, 0, r1, carry, carry);
michael@0: 				MP_SUB_BORROW(r2, 0, r2, carry, carry);
michael@0: 				MP_SUB_BORROW(r3, 0, r3, carry, carry);
michael@0: 			}
michael@0: 			r3b = (int)(r3 >>32);
michael@0: 		}
michael@0: 
michael@0: 		while (r3b < 0) {
michael@0:                 	MP_ADD_CARRY (r0, 1, r0, 0,     carry);
michael@0:                 	MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry);
michael@0:                 	MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry);
michael@0:                 	MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry);
michael@0: 			r3b = (int)(r3 >>32);
michael@0: 		}
michael@0: 		/* check for final reduction */
michael@0: 		/* now the only way we are over is if the top 4 words are 
michael@0: 		 * all ones. Subtract the curve. (curve is 2^224 - 2^96 +1)
michael@0: 		 */
michael@0: 		if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX)
michael@0: 			&& ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) &&
michael@0: 			 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) {
michael@0: 			/* one last subraction */
michael@0: 			MP_SUB_BORROW(r0, 1, r0, 0,     carry);
michael@0: 			MP_SUB_BORROW(r1, MP_DIGIT_MAX << 32, r1, carry, carry);
michael@0: 			r2 = r3 = 0;
michael@0: 		}
michael@0: 
michael@0: 
michael@0: 		if (a != r) {
michael@0: 			MP_CHECKOK(s_mp_pad(r, 4));
michael@0: 		}
michael@0: 		/* set the lower words of r */
michael@0: 		MP_SIGN(r) = MP_ZPOS;
michael@0: 		MP_USED(r) = 4;
michael@0: 		MP_DIGIT(r, 3) = r3;
michael@0: 		MP_DIGIT(r, 2) = r2;
michael@0: 		MP_DIGIT(r, 1) = r1;
michael@0: 		MP_DIGIT(r, 0) = r0;
michael@0: #endif
michael@0: 	}
michael@0: 	s_mp_clamp(r);
michael@0: 
michael@0:   CLEANUP:
michael@0: 	return res;
michael@0: }
michael@0: 
michael@0: /* Compute the square of polynomial a, reduce modulo p224. Store the
michael@0:  * result in r.  r could be a.  Uses optimized modular reduction for p224. 
michael@0:  */
michael@0: static mp_err
michael@0: ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 
michael@0: 	MP_CHECKOK(mp_sqr(a, r));
michael@0: 	MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
michael@0:   CLEANUP:
michael@0: 	return res;
michael@0: }
michael@0: 
michael@0: /* Compute the product of two polynomials a and b, reduce modulo p224.
michael@0:  * Store the result in r.  r could be a or b; a could be b.  Uses
michael@0:  * optimized modular reduction for p224. */
michael@0: static mp_err
michael@0: ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r,
michael@0: 					const GFMethod *meth)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 
michael@0: 	MP_CHECKOK(mp_mul(a, b, r));
michael@0: 	MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
michael@0:   CLEANUP:
michael@0: 	return res;
michael@0: }
michael@0: 
michael@0: /* Divides two field elements. If a is NULL, then returns the inverse of
michael@0:  * b. */
michael@0: static mp_err
michael@0: ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r,
michael@0: 		   const GFMethod *meth)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 	mp_int t;
michael@0: 
michael@0: 	/* If a is NULL, then return the inverse of b, otherwise return a/b. */
michael@0: 	if (a == NULL) {
michael@0: 		return  mp_invmod(b, &meth->irr, r);
michael@0: 	} else {
michael@0: 		/* MPI doesn't support divmod, so we implement it using invmod and 
michael@0: 		 * mulmod. */
michael@0: 		MP_CHECKOK(mp_init(&t));
michael@0: 		MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
michael@0: 		MP_CHECKOK(mp_mul(a, &t, r));
michael@0: 		MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
michael@0: 	  CLEANUP:
michael@0: 		mp_clear(&t);
michael@0: 		return res;
michael@0: 	}
michael@0: }
michael@0: 
michael@0: /* Wire in fast field arithmetic and precomputation of base point for
michael@0:  * named curves. */
michael@0: mp_err
michael@0: ec_group_set_gfp224(ECGroup *group, ECCurveName name)
michael@0: {
michael@0: 	if (name == ECCurve_NIST_P224) {
michael@0: 		group->meth->field_mod = &ec_GFp_nistp224_mod;
michael@0: 		group->meth->field_mul = &ec_GFp_nistp224_mul;
michael@0: 		group->meth->field_sqr = &ec_GFp_nistp224_sqr;
michael@0: 		group->meth->field_div = &ec_GFp_nistp224_div;
michael@0: 	}
michael@0: 	return MP_OKAY;
michael@0: }