xref: /illumos-gate/usr/src/common/crypto/ecc/ecp_192.c (revision 55fea89d)

/*
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is the elliptic curve math library for prime field curves.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 2003
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either the GNU General Public License Version 2 or later (the "GPL"), or
 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */
/*
 * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 *
 * Sun elects to use this software under the MPL license.
 */

#include "ecp.h"
#include "mpi.h"
#include "mplogic.h"
#include "mpi-priv.h"
#ifndef _KERNEL
#include <stdlib.h>
#endif

#define ECP192_DIGITS ECL_CURVE_DIGITS(192)

/* Fast modular reduction for p192 = 2^192 - 2^64 - 1.  a can be r. Uses
 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
 * Implementation of the NIST Elliptic Curves over Prime Fields. */
mp_err
ec_GFp_nistp192_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_size a_used = MP_USED(a);
	mp_digit r3;
#ifndef MPI_AMD64_ADD
	mp_digit carry;
#endif
#ifdef ECL_THIRTY_TWO_BIT
	mp_digit a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
        mp_digit r0a, r0b, r1a, r1b, r2a, r2b;
#else
	mp_digit a5 = 0, a4 = 0, a3 = 0;
        mp_digit r0, r1, r2;
#endif

	/* reduction not needed if a is not larger than field size */
	if (a_used < ECP192_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 > ECP192_DIGITS*2) {
		MP_CHECKOK(mp_mod(a, &meth->irr, r));
	} else {
		/* copy out upper words of a */

#ifdef ECL_THIRTY_TWO_BIT

		/* in all the math below,
		 * nXb is most signifiant, nXa is least significant */
		switch (a_used) {
		case 12:
			a5b = MP_DIGIT(a, 11);
			/* FALLTHROUGH */
		case 11:
			a5a = MP_DIGIT(a, 10);
			/* FALLTHROUGH */
		case 10:
			a4b = MP_DIGIT(a, 9);
			/* FALLTHROUGH */
		case 9:
			a4a = MP_DIGIT(a, 8);
			/* FALLTHROUGH */
		case 8:
			a3b = MP_DIGIT(a, 7);
			/* FALLTHROUGH */
		case 7:
			a3a = 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 = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
		MP_ADD_CARRY(r0a, a3a, r0a, 0,    carry);
		MP_ADD_CARRY(r0b, a3b, r0b, carry, carry);
		MP_ADD_CARRY(r1a, a3a, r1a, carry, carry);
		MP_ADD_CARRY(r1b, a3b, r1b, carry, carry);
		MP_ADD_CARRY(r2a, a4a, r2a, carry, carry);
		MP_ADD_CARRY(r2b, a4b, r2b, carry, carry);
		r3 = carry; carry = 0;
		MP_ADD_CARRY(r0a, a5a, r0a, 0,     carry);
		MP_ADD_CARRY(r0b, a5b, r0b, carry, carry);
		MP_ADD_CARRY(r1a, a5a, r1a, carry, carry);
		MP_ADD_CARRY(r1b, a5b, r1b, carry, carry);
		MP_ADD_CARRY(r2a, a5a, r2a, carry, carry);
		MP_ADD_CARRY(r2b, a5b, r2b, carry, carry);
		r3 += carry;
		MP_ADD_CARRY(r1a, a4a, r1a, 0,     carry);
		MP_ADD_CARRY(r1b, a4b, r1b, carry, carry);
		MP_ADD_CARRY(r2a,   0, r2a, carry, carry);
		MP_ADD_CARRY(r2b,   0, r2b, carry, carry);
		r3 += carry;

		/* reduce out the carry */
		while (r3) {
			MP_ADD_CARRY(r0a, r3, r0a, 0,     carry);
			MP_ADD_CARRY(r0b,  0, r0b, carry, carry);
			MP_ADD_CARRY(r1a, r3, r1a, carry, carry);
			MP_ADD_CARRY(r1b,  0, r1b, carry, carry);
			MP_ADD_CARRY(r2a,  0, r2a, carry, carry);
			MP_ADD_CARRY(r2b,  0, r2b, carry, carry);
			r3 = carry;
		}

		/* check for final reduction */
		/*
		 * our field is 0xffffffffffffffff, 0xfffffffffffffffe,
		 * 0xffffffffffffffff. That means we can only be over and need
		 * one more reduction
		 *  if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
		 *     and
		 *     r1 == 0xffffffffffffffffff   or
		 *     r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
		 * In all cases, we subtract the field (or add the 2's
		 * complement value (1,1,0)).  (r0, r1, r2)
		 */
		if (((r2b == 0xffffffff) && (r2a == 0xffffffff)
			&& (r1b == 0xffffffff) ) &&
			   ((r1a == 0xffffffff) ||
			    (r1a == 0xfffffffe) && (r0a == 0xffffffff) &&
					(r0b == 0xffffffff)) ) {
			/* do a quick subtract */
			MP_ADD_CARRY(r0a, 1, r0a, 0, carry);
			r0b += carry;
			r1a = r1b = r2a = r2b = 0;
		}

		/* set the lower words of r */
		if (a != r) {
			MP_CHECKOK(s_mp_pad(r, 6));
		}
		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;
		MP_USED(r) = 6;
#else
		switch (a_used) {
		case 6:
			a5 = MP_DIGIT(a, 5);
			/* FALLTHROUGH */
		case 5:
			a4 = MP_DIGIT(a, 4);
			/* FALLTHROUGH */
		case 4:
			a3 = MP_DIGIT(a, 3);
		}

                r2 = MP_DIGIT(a, 2);
                r1 = MP_DIGIT(a, 1);
                r0 = MP_DIGIT(a, 0);

		/* implement r = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
#ifndef MPI_AMD64_ADD
		MP_ADD_CARRY(r0, a3, r0, 0,     carry);
		MP_ADD_CARRY(r1, a3, r1, carry, carry);
		MP_ADD_CARRY(r2, a4, r2, carry, carry);
		r3 = carry;
		MP_ADD_CARRY(r0, a5, r0, 0,     carry);
		MP_ADD_CARRY(r1, a5, r1, carry, carry);
		MP_ADD_CARRY(r2, a5, r2, carry, carry);
		r3 += carry;
		MP_ADD_CARRY(r1, a4, r1, 0,     carry);
		MP_ADD_CARRY(r2,  0, r2, carry, carry);
		r3 += carry;

#else
                r2 = MP_DIGIT(a, 2);
                r1 = MP_DIGIT(a, 1);
                r0 = MP_DIGIT(a, 0);

                /* set the lower words of r */
                __asm__ (
                "xorq   %3,%3           \n\t"
                "addq   %4,%0           \n\t"
                "adcq   %4,%1           \n\t"
                "adcq   %5,%2           \n\t"
                "adcq   $0,%3           \n\t"
                "addq   %6,%0           \n\t"
                "adcq   %6,%1           \n\t"
                "adcq   %6,%2           \n\t"
                "adcq   $0,%3           \n\t"
                "addq   %5,%1           \n\t"
                "adcq   $0,%2           \n\t"
                "adcq   $0,%3           \n\t"
                : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3),
		  "=r"(a4), "=r"(a5)
                : "0" (r0), "1" (r1), "2" (r2), "3" (r3),
		  "4" (a3), "5" (a4), "6"(a5)
                : "%cc" );
#endif

		/* reduce out the carry */
		while (r3) {
#ifndef MPI_AMD64_ADD
			MP_ADD_CARRY(r0, r3, r0, 0,     carry);
			MP_ADD_CARRY(r1, r3, r1, carry, carry);
			MP_ADD_CARRY(r2,  0, r2, carry, carry);
			r3 = carry;
#else
			a3=r3;
              		__asm__ (
                	"xorq   %3,%3           \n\t"
                	"addq   %4,%0           \n\t"
                	"adcq   %4,%1           \n\t"
                	"adcq   $0,%2           \n\t"
                	"adcq   $0,%3           \n\t"
                	: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3)
                	: "0" (r0), "1" (r1), "2" (r2), "3" (r3), "4"(a3)
                	: "%cc" );
#endif
		}

		/* check for final reduction */
		/*
		 * our field is 0xffffffffffffffff, 0xfffffffffffffffe,
		 * 0xffffffffffffffff. That means we can only be over and need
		 * one more reduction
		 *  if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
		 *     and
		 *     r1 == 0xffffffffffffffffff   or
		 *     r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
		 * In all cases, we subtract the field (or add the 2's
		 * complement value (1,1,0)).  (r0, r1, r2)
		 */
		if (r3 || ((r2 == MP_DIGIT_MAX) &&
		      ((r1 == MP_DIGIT_MAX) ||
			((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
			/* do a quick subtract */
			r0++;
			r1 = r2 = 0;
		}
		/* set the lower words of r */
		if (a != r) {
			MP_CHECKOK(s_mp_pad(r, 3));
		}
		MP_DIGIT(r, 2) = r2;
		MP_DIGIT(r, 1) = r1;
		MP_DIGIT(r, 0) = r0;
		MP_USED(r) = 3;
#endif
	}

  CLEANUP:
	return res;
}

#ifndef ECL_THIRTY_TWO_BIT
/* Compute the sum of 192 bit curves. Do the work in-line since the
 * number of words are so small, we don't want to overhead of mp function
 * calls.  Uses optimized modular reduction for p192.
 */
mp_err
ec_GFp_nistp192_add(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit a0 = 0, a1 = 0, a2 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0;
	mp_digit carry;

	switch(MP_USED(a)) {
	case 3:
		a2 = MP_DIGIT(a,2);
		/* FALLTHROUGH */
	case 2:
		a1 = MP_DIGIT(a,1);
		/* FALLTHROUGH */
	case 1:
		a0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 3:
		r2 = MP_DIGIT(b,2);
		/* FALLTHROUGH */
	case 2:
		r1 = MP_DIGIT(b,1);
		/* FALLTHROUGH */
	case 1:
		r0 = MP_DIGIT(b,0);
	}

#ifndef MPI_AMD64_ADD
	MP_ADD_CARRY(a0, r0, r0, 0,     carry);
	MP_ADD_CARRY(a1, r1, r1, carry, carry);
	MP_ADD_CARRY(a2, r2, r2, carry, carry);
#else
	__asm__ (
                "xorq   %3,%3           \n\t"
                "addq   %4,%0           \n\t"
                "adcq   %5,%1           \n\t"
                "adcq   %6,%2           \n\t"
                "adcq   $0,%3           \n\t"
                : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(carry)
                : "r" (a0), "r" (a1), "r" (a2), "0" (r0),
		  "1" (r1), "2" (r2)
                : "%cc" );
#endif

	/* Do quick 'subract' if we've gone over
	 * (add the 2's complement of the curve field) */
	if (carry || ((r2 == MP_DIGIT_MAX) &&
		      ((r1 == MP_DIGIT_MAX) ||
			((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
#ifndef MPI_AMD64_ADD
		MP_ADD_CARRY(r0, 1, r0, 0,     carry);
		MP_ADD_CARRY(r1, 1, r1, carry, carry);
		MP_ADD_CARRY(r2, 0, r2, carry, carry);
#else
		__asm__ (
			"addq   $1,%0           \n\t"
			"adcq   $1,%1           \n\t"
			"adcq   $0,%2           \n\t"
			: "=r"(r0), "=r"(r1), "=r"(r2)
			: "0" (r0), "1" (r1), "2" (r2)
			: "%cc" );
#endif
	}


	MP_CHECKOK(s_mp_pad(r, 3));
	MP_DIGIT(r, 2) = r2;
	MP_DIGIT(r, 1) = r1;
	MP_DIGIT(r, 0) = r0;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 3;
	s_mp_clamp(r);


  CLEANUP:
	return res;
}

/* Compute the diff of 192 bit curves. Do the work in-line since the
 * number of words are so small, we don't want to overhead of mp function
 * calls.  Uses optimized modular reduction for p192.
 */
mp_err
ec_GFp_nistp192_sub(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit b0 = 0, b1 = 0, b2 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0;
	mp_digit borrow;

	switch(MP_USED(a)) {
	case 3:
		r2 = MP_DIGIT(a,2);
		/* FALLTHROUGH */
	case 2:
		r1 = MP_DIGIT(a,1);
		/* FALLTHROUGH */
	case 1:
		r0 = MP_DIGIT(a,0);
	}

	switch(MP_USED(b)) {
	case 3:
		b2 = MP_DIGIT(b,2);
		/* FALLTHROUGH */
	case 2:
		b1 = MP_DIGIT(b,1);
		/* FALLTHROUGH */
	case 1:
		b0 = MP_DIGIT(b,0);
	}

#ifndef MPI_AMD64_ADD
	MP_SUB_BORROW(r0, b0, r0, 0,     borrow);
	MP_SUB_BORROW(r1, b1, r1, borrow, borrow);
	MP_SUB_BORROW(r2, b2, r2, borrow, borrow);
#else
	__asm__ (
                "xorq   %3,%3           \n\t"
                "subq   %4,%0           \n\t"
                "sbbq   %5,%1           \n\t"
                "sbbq   %6,%2           \n\t"
                "adcq   $0,%3           \n\t"
                : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(borrow)
                : "r" (b0), "r" (b1), "r" (b2), "0" (r0),
		  "1" (r1), "2" (r2)
                : "%cc" );
#endif

	/* Do quick 'add' if we've gone under 0
	 * (subtract the 2's complement of the curve field) */
	if (borrow) {
#ifndef MPI_AMD64_ADD
		MP_SUB_BORROW(r0, 1, r0, 0,     borrow);
		MP_SUB_BORROW(r1, 1, r1, borrow, borrow);
		MP_SUB_BORROW(r2,  0, r2, borrow, borrow);
#else
		__asm__ (
			"subq   $1,%0           \n\t"
			"sbbq   $1,%1           \n\t"
			"sbbq   $0,%2           \n\t"
			: "=r"(r0), "=r"(r1), "=r"(r2)
			: "0" (r0), "1" (r1), "2" (r2)
			: "%cc" );
#endif
	}

	MP_CHECKOK(s_mp_pad(r, 3));
	MP_DIGIT(r, 2) = r2;
	MP_DIGIT(r, 1) = r1;
	MP_DIGIT(r, 0) = r0;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 3;
	s_mp_clamp(r);

  CLEANUP:
	return res;
}

#endif

/* Compute the square of polynomial a, reduce modulo p192. Store the
 * result in r.  r could be a.  Uses optimized modular reduction for p192.
 */
mp_err
ec_GFp_nistp192_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_nistp192_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Compute the product of two polynomials a and b, reduce modulo p192.
 * Store the result in r.  r could be a or b; a could be b.  Uses
 * optimized modular reduction for p192. */
mp_err
ec_GFp_nistp192_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_nistp192_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Divides two field elements. If a is NULL, then returns the inverse of
 * b. */
mp_err
ec_GFp_nistp192_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, FLAG(b)));
		MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
		MP_CHECKOK(mp_mul(a, &t, r));
		MP_CHECKOK(ec_GFp_nistp192_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_gfp192(ECGroup *group, ECCurveName name)
{
	if (name == ECCurve_NIST_P192) {
		group->meth->field_mod = &ec_GFp_nistp192_mod;
		group->meth->field_mul = &ec_GFp_nistp192_mul;
		group->meth->field_sqr = &ec_GFp_nistp192_sqr;
		group->meth->field_div = &ec_GFp_nistp192_div;
#ifndef ECL_THIRTY_TWO_BIT
		group->meth->field_add = &ec_GFp_nistp192_add;
		group->meth->field_sub = &ec_GFp_nistp192_sub;
#endif
	}
	return MP_OKAY;
}