DXR is a code search and navigation tool aimed at making sense of large projects. It supports full-text and regex searches as well as structural queries.

Mercurial (fddffdeab170)

VCS Links

Line Code
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352
/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

#include "ecp.h"
#include "mpi.h"
#include "mplogic.h"
#include "mpi-priv.h"

#define ECP224_DIGITS ECL_CURVE_DIGITS(224)

/* Fast modular reduction for p224 = 2^224 - 2^96 + 1.  a can be r. Uses
 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
 * Implementation of the NIST Elliptic Curves over Prime Fields. */
static mp_err
ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_size a_used = MP_USED(a);

	int    r3b;
	mp_digit carry;
#ifdef ECL_THIRTY_TWO_BIT
        mp_digit a6a = 0, a6b = 0,
                a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3b = 0;
        mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a;
#else
	mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0;
        mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0;
        mp_digit r0, r1, r2, r3;
#endif

	/* reduction not needed if a is not larger than field size */
	if (a_used < ECP224_DIGITS) {
		if (a == r) return MP_OKAY;
		return mp_copy(a, r);
	}
	/* for polynomials larger than twice the field size, use regular
	 * reduction */
	if (a_used > ECL_CURVE_DIGITS(224*2)) {
		MP_CHECKOK(mp_mod(a, &meth->irr, r));
	} else {
#ifdef ECL_THIRTY_TWO_BIT
		/* copy out upper words of a */
		switch (a_used) {
		case 14:
			a6b = MP_DIGIT(a, 13);
		case 13:
			a6a = MP_DIGIT(a, 12);
		case 12:
			a5b = MP_DIGIT(a, 11);
		case 11:
			a5a = MP_DIGIT(a, 10);
		case 10:
			a4b = MP_DIGIT(a, 9);
		case 9:
			a4a = MP_DIGIT(a, 8);
		case 8:
			a3b = MP_DIGIT(a, 7);
		}
		r3a = MP_DIGIT(a, 6);
		r2b= MP_DIGIT(a, 5);
		r2a= MP_DIGIT(a, 4);
		r1b = MP_DIGIT(a, 3);
		r1a = MP_DIGIT(a, 2);
		r0b = MP_DIGIT(a, 1);
		r0a = MP_DIGIT(a, 0);


		/* implement r = (a3a,a2,a1,a0)
			+(a5a, a4,a3b,  0)
			+(  0, a6,a5b,  0)
			-(  0	 0,    0|a6b, a6a|a5b )
			-(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
                carry = 0;
		MP_ADD_CARRY (r1b, a3b, r1b, carry);
		MP_ADD_CARRY (r2a, a4a, r2a, carry);
		MP_ADD_CARRY (r2b, a4b, r2b, carry);
		MP_ADD_CARRY (r3a, a5a, r3a, carry);
		r3b = carry; carry = 0;
		MP_ADD_CARRY (r1b, a5b, r1b, carry);
		MP_ADD_CARRY (r2a, a6a, r2a, carry);
		MP_ADD_CARRY (r2b, a6b, r2b, carry);
		MP_ADD_CARRY (r3a,   0, r3a, carry);
		r3b += carry; carry = 0;
		MP_SUB_BORROW(r0a, a3b, r0a, carry);
		MP_SUB_BORROW(r0b, a4a, r0b, carry);
		MP_SUB_BORROW(r1a, a4b, r1a, carry);
		MP_SUB_BORROW(r1b, a5a, r1b, carry);
		MP_SUB_BORROW(r2a, a5b, r2a, carry);
		MP_SUB_BORROW(r2b, a6a, r2b, carry);
		MP_SUB_BORROW(r3a, a6b, r3a, carry);
		r3b -= carry; carry = 0;
		MP_SUB_BORROW(r0a, a5b, r0a, carry);
		MP_SUB_BORROW(r0b, a6a, r0b, carry);
		MP_SUB_BORROW(r1a, a6b, r1a, carry);
		if (carry) {
			MP_SUB_BORROW(r1b, 0, r1b, carry);
			MP_SUB_BORROW(r2a, 0, r2a, carry);
			MP_SUB_BORROW(r2b, 0, r2b, carry);
			MP_SUB_BORROW(r3a, 0, r3a, carry);
			r3b -= carry;
		}

		while (r3b > 0) {
			int tmp;
                        carry = 0;
			MP_ADD_CARRY(r1b, r3b, r1b, carry);
			if (carry) {
				MP_ADD_CARRY(r2a,  0, r2a, carry);
				MP_ADD_CARRY(r2b,  0, r2b, carry);
				MP_ADD_CARRY(r3a,  0, r3a, carry);
			}
			tmp = carry; carry = 0;
			MP_SUB_BORROW(r0a, r3b, r0a, carry);
			if (carry) {
				MP_SUB_BORROW(r0b, 0, r0b, carry);
				MP_SUB_BORROW(r1a, 0, r1a, carry);
				MP_SUB_BORROW(r1b, 0, r1b, carry);
				MP_SUB_BORROW(r2a, 0, r2a, carry);
				MP_SUB_BORROW(r2b, 0, r2b, carry);
				MP_SUB_BORROW(r3a, 0, r3a, carry);
				tmp -= carry;
			}
			r3b = tmp;
		}

		while (r3b < 0) {
			mp_digit maxInt = MP_DIGIT_MAX;
                        carry = 0;
                	MP_ADD_CARRY (r0a, 1, r0a, carry);
                	MP_ADD_CARRY (r0b, 0, r0b, carry);
                	MP_ADD_CARRY (r1a, 0, r1a, carry);
                	MP_ADD_CARRY (r1b, maxInt, r1b, carry);
                	MP_ADD_CARRY (r2a, maxInt, r2a, carry);
                	MP_ADD_CARRY (r2b, maxInt, r2b, carry);
                	MP_ADD_CARRY (r3a, maxInt, r3a, carry);
			r3b += carry;
		}
		/* check for final reduction */
		/* now the only way we are over is if the top 4 words are all ones */
		if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX)
			&& (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) &&
			 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) {
			/* one last subraction */
                        carry = 0;
			MP_SUB_BORROW(r0a, 1, r0a, carry);
			MP_SUB_BORROW(r0b, 0, r0b, carry);
			MP_SUB_BORROW(r1a, 0, r1a, carry);
			r1b = r2a = r2b = r3a = 0;
		}


		if (a != r) {
			MP_CHECKOK(s_mp_pad(r, 7));
		}
		/* set the lower words of r */
		MP_SIGN(r) = MP_ZPOS;
		MP_USED(r) = 7;
		MP_DIGIT(r, 6) = r3a;
		MP_DIGIT(r, 5) = r2b;
		MP_DIGIT(r, 4) = r2a;
		MP_DIGIT(r, 3) = r1b;
		MP_DIGIT(r, 2) = r1a;
		MP_DIGIT(r, 1) = r0b;
		MP_DIGIT(r, 0) = r0a;
#else
		/* copy out upper words of a */
		switch (a_used) {
		case 7:
			a6 = MP_DIGIT(a, 6);
			a6b = a6 >> 32;
			a6a_a5b = a6 << 32;
		case 6:
			a5 = MP_DIGIT(a, 5);
			a5b = a5 >> 32;
			a6a_a5b |= a5b;
			a5b = a5b << 32;
			a5a_a4b = a5 << 32;
			a5a = a5 & 0xffffffff;
		case 5:
			a4 = MP_DIGIT(a, 4);
			a5a_a4b |= a4 >> 32;
			a4a_a3b = a4 << 32;
		case 4:
			a3b = MP_DIGIT(a, 3) >> 32;
			a4a_a3b |= a3b;
			a3b = a3b << 32;
		}

		r3 = MP_DIGIT(a, 3) & 0xffffffff;
		r2 = MP_DIGIT(a, 2);
		r1 = MP_DIGIT(a, 1);
		r0 = MP_DIGIT(a, 0);

		/* implement r = (a3a,a2,a1,a0)
			+(a5a, a4,a3b,  0)
			+(  0, a6,a5b,  0)
			-(  0	 0,    0|a6b, a6a|a5b )
			-(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
                carry = 0;
		MP_ADD_CARRY (r1, a3b, r1, carry);
		MP_ADD_CARRY (r2, a4 , r2, carry);
		MP_ADD_CARRY (r3, a5a, r3, carry);
                carry = 0;
		MP_ADD_CARRY (r1, a5b, r1, carry);
		MP_ADD_CARRY (r2, a6 , r2, carry);
		MP_ADD_CARRY (r3,   0, r3, carry);

		carry = 0;
		MP_SUB_BORROW(r0, a4a_a3b, r0, carry);
		MP_SUB_BORROW(r1, a5a_a4b, r1, carry);
		MP_SUB_BORROW(r2, a6a_a5b, r2, carry);
		MP_SUB_BORROW(r3, a6b    , r3, carry);
		carry = 0;
		MP_SUB_BORROW(r0, a6a_a5b, r0, carry);
		MP_SUB_BORROW(r1, a6b    , r1, carry);
		if (carry) {
			MP_SUB_BORROW(r2, 0, r2, carry);
			MP_SUB_BORROW(r3, 0, r3, carry);
		}


		/* if the value is negative, r3 has a 2's complement 
		 * high value */
		r3b = (int)(r3 >>32);
		while (r3b > 0) {
			r3 &= 0xffffffff;
                        carry = 0;
			MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, carry);
			if (carry) {
				MP_ADD_CARRY(r2,  0, r2, carry);
				MP_ADD_CARRY(r3,  0, r3, carry);
			}
			carry = 0;
			MP_SUB_BORROW(r0, r3b, r0, carry);
			if (carry) {
				MP_SUB_BORROW(r1, 0, r1, carry);
				MP_SUB_BORROW(r2, 0, r2, carry);
				MP_SUB_BORROW(r3, 0, r3, carry);
			}
			r3b = (int)(r3 >>32);
		}

		while (r3b < 0) {
                        carry = 0;
                	MP_ADD_CARRY (r0, 1, r0, carry);
                	MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry);
                	MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry);
                	MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry);
			r3b = (int)(r3 >>32);
		}
		/* check for final reduction */
		/* now the only way we are over is if the top 4 words are 
		 * all ones. Subtract the curve. (curve is 2^224 - 2^96 +1)
		 */
		if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX)
			&& ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) &&
			 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) {
			/* one last subraction */
			carry = 0;
			MP_SUB_BORROW(r0, 1, r0, carry);
			MP_SUB_BORROW(r1, MP_DIGIT_MAX << 32, r1, carry);
			r2 = r3 = 0;
		}


		if (a != r) {
			MP_CHECKOK(s_mp_pad(r, 4));
		}
		/* set the lower words of r */
		MP_SIGN(r) = MP_ZPOS;
		MP_USED(r) = 4;
		MP_DIGIT(r, 3) = r3;
		MP_DIGIT(r, 2) = r2;
		MP_DIGIT(r, 1) = r1;
		MP_DIGIT(r, 0) = r0;
#endif
	}
	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/* Compute the square of polynomial a, reduce modulo p224. Store the
 * result in r.  r could be a.  Uses optimized modular reduction for p224. 
 */
static mp_err
ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;

	MP_CHECKOK(mp_sqr(a, r));
	MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Compute the product of two polynomials a and b, reduce modulo p224.
 * Store the result in r.  r could be a or b; a could be b.  Uses
 * optimized modular reduction for p224. */
static mp_err
ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r,
					const GFMethod *meth)
{
	mp_err res = MP_OKAY;

	MP_CHECKOK(mp_mul(a, b, r));
	MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Divides two field elements. If a is NULL, then returns the inverse of
 * b. */
static mp_err
ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r,
		   const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_int t;

	/* If a is NULL, then return the inverse of b, otherwise return a/b. */
	if (a == NULL) {
		return  mp_invmod(b, &meth->irr, r);
	} else {
		/* MPI doesn't support divmod, so we implement it using invmod and 
		 * mulmod. */
		MP_CHECKOK(mp_init(&t));
		MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
		MP_CHECKOK(mp_mul(a, &t, r));
		MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
	  CLEANUP:
		mp_clear(&t);
		return res;
	}
}

/* Wire in fast field arithmetic and precomputation of base point for
 * named curves. */
mp_err
ec_group_set_gfp224(ECGroup *group, ECCurveName name)
{
	if (name == ECCurve_NIST_P224) {
		group->meth->field_mod = &ec_GFp_nistp224_mod;
		group->meth->field_mul = &ec_GFp_nistp224_mul;
		group->meth->field_sqr = &ec_GFp_nistp224_sqr;
		group->meth->field_div = &ec_GFp_nistp224_div;
	}
	return MP_OKAY;
}