*

 *

 *

 *

 * The Original Code is the elliptic curve math library.

 *

 * 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):

 *   Stephen Fung <fungstep@hotmail.com> and

 *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories

 *

 *********************************************************************** */

#include "mpi.h"

#include "mp_gf2m.h"

#include "ecl-priv.h"

#include "mpi-priv.h"

#ifndef _KERNEL

#include <stdlib.h>

#endif

/* Allocate memory for a new GFMethod object. */

GFMethod *

GFMethod_new(int kmflag)

{

        mp_err res = MP_OKAY;

        GFMethod *meth;

#ifdef _KERNEL

        meth = (GFMethod *) kmem_alloc(sizeof(GFMethod), kmflag);

#else

        meth = (GFMethod *) malloc(sizeof(GFMethod));

        if (meth == NULL)

                return NULL;

#endif

        meth->constructed = MP_YES;

        MP_DIGITS(&meth->irr) = 0;

        meth->extra_free = NULL;

        MP_CHECKOK(mp_init(&meth->irr, kmflag));

  CLEANUP:

        if (res != MP_OKAY) {

                GFMethod_free(meth);

                return NULL;

        }

        return meth;

}

/* Construct a generic GFMethod for arithmetic over prime fields with

 * irreducible irr. */

GFMethod *

GFMethod_consGFp(const mp_int *irr)

{

        mp_err res = MP_OKAY;

        GFMethod *meth = NULL;

        meth = GFMethod_new(FLAG(irr));

        if (meth == NULL)

                return NULL;

        MP_CHECKOK(mp_copy(irr, &meth->irr));

        meth->irr_arr[0] = mpl_significant_bits(irr);

        meth->irr_arr[1] = meth->irr_arr[2] = meth->irr_arr[3] =

                meth->irr_arr[4] = 0;

        switch(MP_USED(&meth->irr)) {

        /* maybe we need 1 and 2 words here as well?*/

        case 3:

                meth->field_add = &ec_GFp_add_3;

                meth->field_sub = &ec_GFp_sub_3;

                break;

        case 4:

                meth->field_add = &ec_GFp_add_4;

                meth->field_sub = &ec_GFp_sub_4;

                break;

        case 5:

                meth->field_add = &ec_GFp_add_5;

                meth->field_sub = &ec_GFp_sub_5;

                break;

        case 6:

                meth->field_add = &ec_GFp_add_6;

                meth->field_sub = &ec_GFp_sub_6;

                break;

        default:

                meth->field_add = &ec_GFp_add;

                meth->field_sub = &ec_GFp_sub;

        }

        meth->field_neg = &ec_GFp_neg;

        meth->field_mod = &ec_GFp_mod;

        meth->field_mul = &ec_GFp_mul;

        meth->field_sqr = &ec_GFp_sqr;

        meth->field_div = &ec_GFp_div;

        meth->field_enc = NULL;

        meth->field_dec = NULL;

        meth->extra1 = NULL;

        meth->extra2 = NULL;

        meth->extra_free = NULL;

  CLEANUP:

        if (res != MP_OKAY) {

                GFMethod_free(meth);

                return NULL;

        }

        return meth;

}

/* Construct a generic GFMethod for arithmetic over binary polynomial

 * fields with irreducible irr that has array representation irr_arr (see

 * ecl-priv.h for description of the representation).  If irr_arr is NULL,

 * then it is constructed from the bitstring representation. */

GFMethod *

GFMethod_consGF2m(const mp_int *irr, const unsigned int irr_arr[5])

{

        mp_err res = MP_OKAY;

        int ret;

        GFMethod *meth = NULL;

        meth = GFMethod_new(FLAG(irr));

        if (meth == NULL)

                return NULL;

        MP_CHECKOK(mp_copy(irr, &meth->irr));

        if (irr_arr != NULL) {

                /* Irreducible polynomials are either trinomials or pentanomials. */

                meth->irr_arr[0] = irr_arr[0];

                meth->irr_arr[1] = irr_arr[1];

                meth->irr_arr[2] = irr_arr[2];

                if (irr_arr[2] > 0) {

                        meth->irr_arr[3] = irr_arr[3];

                        meth->irr_arr[4] = irr_arr[4];

                } else {

                        meth->irr_arr[3] = meth->irr_arr[4] = 0;

                }

        } else {

                ret = mp_bpoly2arr(irr, meth->irr_arr, 5);

                /* Irreducible polynomials are either trinomials or pentanomials. */

                if ((ret != 5) && (ret != 3)) {

                        res = MP_UNDEF;

                        goto CLEANUP;

                }

        }

        meth->field_add = &ec_GF2m_add;

        meth->field_neg = &ec_GF2m_neg;

        meth->field_sub = &ec_GF2m_add;

        meth->field_mod = &ec_GF2m_mod;

        meth->field_mul = &ec_GF2m_mul;

        meth->field_sqr = &ec_GF2m_sqr;

        meth->field_div = &ec_GF2m_div;

        meth->field_enc = NULL;

        meth->field_dec = NULL;

        meth->extra1 = NULL;

        meth->extra2 = NULL;

        meth->extra_free = NULL;

  CLEANUP:

        if (res != MP_OKAY) {

                GFMethod_free(meth);

                return NULL;

        }

        return meth;

}

/* Free the memory allocated (if any) to a GFMethod object. */

void

GFMethod_free(GFMethod *meth)

{

        if (meth == NULL)

                return;

        if (meth->constructed == MP_NO)

                return;

        mp_clear(&meth->irr);

        if (meth->extra_free != NULL)

                meth->extra_free(meth);

#ifdef _KERNEL

        kmem_free(meth, sizeof(GFMethod));

#else

        free(meth);

#endif

}

/* Wrapper functions for generic prime field arithmetic. */

/* Add two field elements.  Assumes that 0 <= a, b < meth->irr */

mp_err

ec_GFp_add(const mp_int *a, const mp_int *b, mp_int *r,

                   const GFMethod *meth)

{

        /* PRE: 0 <= a, b < p = meth->irr POST: 0 <= r < p, r = a + b (mod p) */

        mp_err res;

        if ((res = mp_add(a, b, r)) != MP_OKAY) {

                return res;

        }

        if (mp_cmp(r, &meth->irr) >= 0) {

                return mp_sub(r, &meth->irr, r);

        }

        return res;

}

/* Negates a field element.  Assumes that 0 <= a < meth->irr */

mp_err

ec_GFp_neg(const mp_int *a, mp_int *r, const GFMethod *meth)

{

        /* PRE: 0 <= a < p = meth->irr POST: 0 <= r < p, r = -a (mod p) */

        if (mp_cmp_z(a) == 0) {

                mp_zero(r);

                return MP_OKAY;

        }

        return mp_sub(&meth->irr, a, r);

}

/* Subtracts two field elements.  Assumes that 0 <= a, b < meth->irr */

mp_err

ec_GFp_sub(const mp_int *a, const mp_int *b, mp_int *r,

                   const GFMethod *meth)

{

        mp_err res = MP_OKAY;

        /* PRE: 0 <= a, b < p = meth->irr POST: 0 <= r < p, r = a - b (mod p) */

        res = mp_sub(a, b, r);

        if (res == MP_RANGE) {

                MP_CHECKOK(mp_sub(b, a, r));

                if (mp_cmp_z(r) < 0) {

                        MP_CHECKOK(mp_add(r, &meth->irr, r));

                }

                MP_CHECKOK(ec_GFp_neg(r, r, meth));

        }

        if (mp_cmp_z(r) < 0) {

                MP_CHECKOK(mp_add(r, &meth->irr, r));

        }

  CLEANUP:

        return res;

}

/*

 * Inline adds for small curve lengths.

 */

/* 3 words */

mp_err

ec_GFp_add_3(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);

        case 2:

                a1 = MP_DIGIT(a,1);

        case 1:

                a0 = MP_DIGIT(a,0);

        }

        switch(MP_USED(b)) {

        case 3:

                r2 = MP_DIGIT(b,2);

        case 2:

                r1 = MP_DIGIT(b,1);

        case 1:

                r0 = MP_DIGIT(b,0);

        }

#ifndef MPI_AMD64_ADD

        MP_ADD_CARRY_ZERO(a0, r0, r0, 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

        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;

        /* Do quick 'subract' if we've gone over

         * (add the 2's complement of the curve field) */

         a2 = MP_DIGIT(&meth->irr,2);

        if (carry ||  r2 >  a2 ||

                ((r2 == a2) && mp_cmp(r,&meth->irr) != MP_LT)) {

                a1 = MP_DIGIT(&meth->irr,1);

                a0 = MP_DIGIT(&meth->irr,0);

#ifndef MPI_AMD64_ADD

                MP_SUB_BORROW(r0, a0, r0, 0,     carry);

                MP_SUB_BORROW(r1, a1, r1, carry, carry);

                MP_SUB_BORROW(r2, a2, r2, carry, carry);

#else

                __asm__ (

                        "subq   %3,%0           \n\t"

                        "sbbq   %4,%1           \n\t"

                        "sbbq   %5,%2           \n\t"

                        : "=r"(r0), "=r"(r1), "=r"(r2)

                        : "r" (a0), "r" (a1), "r" (a2),

                          "0" (r0), "1" (r1), "2" (r2)

                        : "%cc" );

#endif

                MP_DIGIT(r, 2) = r2;

                MP_DIGIT(r, 1) = r1;

                MP_DIGIT(r, 0) = r0;

        }

        s_mp_clamp(r);

  CLEANUP:

        return res;

}

/* 4 words */

mp_err

ec_GFp_add_4(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, a3 = 0;

        mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0;

        mp_digit carry;

        switch(MP_USED(a)) {

        case 4:

                a3 = MP_DIGIT(a,3);

        case 3:

                a2 = MP_DIGIT(a,2);

        case 2:

                a1 = MP_DIGIT(a,1);

        case 1:

                a0 = MP_DIGIT(a,0);

        }

        switch(MP_USED(b)) {

        case 4:

                r3 = MP_DIGIT(b,3);

        case 3:

                r2 = MP_DIGIT(b,2);

        case 2:

                r1 = MP_DIGIT(b,1);

        case 1:

                r0 = MP_DIGIT(b,0);

        }

#ifndef MPI_AMD64_ADD

        MP_ADD_CARRY_ZERO(a0, r0, r0, carry);

        MP_ADD_CARRY(a1, r1, r1, carry, carry);

        MP_ADD_CARRY(a2, r2, r2, carry, carry);

        MP_ADD_CARRY(a3, r3, r3, carry, carry);

#else

        __asm__ (

                "xorq   %4,%4           \n\t"

                "addq   %5,%0           \n\t"

                "adcq   %6,%1           \n\t"

                "adcq   %7,%2           \n\t"

                "adcq   %8,%3           \n\t"

                "adcq   $0,%4           \n\t"

                : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(carry)

                : "r" (a0), "r" (a1), "r" (a2), "r" (a3),

                  "0" (r0), "1" (r1), "2" (r2), "3" (r3)

                : "%cc" );

#endif

        MP_CHECKOK(s_mp_pad(r, 4));

        MP_DIGIT(r, 3) = r3;

        MP_DIGIT(r, 2) = r2;

        MP_DIGIT(r, 1) = r1;

        MP_DIGIT(r, 0) = r0;

        MP_SIGN(r) = MP_ZPOS;

        MP_USED(r) = 4;

        /* Do quick 'subract' if we've gone over

         * (add the 2's complement of the curve field) */

         a3 = MP_DIGIT(&meth->irr,3);

        if (carry ||  r3 >  a3 ||

                ((r3 == a3) && mp_cmp(r,&meth->irr) != MP_LT)) {

                a2 = MP_DIGIT(&meth->irr,2);

                a1 = MP_DIGIT(&meth->irr,1);

                a0 = MP_DIGIT(&meth->irr,0);

#ifndef MPI_AMD64_ADD

                MP_SUB_BORROW(r0, a0, r0, 0,     carry);

                MP_SUB_BORROW(r1, a1, r1, carry, carry);

                MP_SUB_BORROW(r2, a2, r2, carry, carry);

                MP_SUB_BORROW(r3, a3, r3, carry, carry);

#else

                __asm__ (

                        "subq   %4,%0           \n\t"

                        "sbbq   %5,%1           \n\t"

                        "sbbq   %6,%2           \n\t"

                        "sbbq   %7,%3           \n\t"

                        : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3)

                        : "r" (a0), "r" (a1), "r" (a2), "r" (a3),

                          "0" (r0), "1" (r1), "2" (r2), "3" (r3)

                        : "%cc" );

#endif

                MP_DIGIT(r, 3) = r3;

                MP_DIGIT(r, 2) = r2;

                MP_DIGIT(r, 1) = r1;

                MP_DIGIT(r, 0) = r0;

        }

        s_mp_clamp(r);

  CLEANUP:

        return res;

}

/* 5 words */

mp_err

ec_GFp_add_5(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, a3 = 0, a4 = 0;

        mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0;

        mp_digit carry;

        switch(MP_USED(a)) {

        case 5:

                a4 = MP_DIGIT(a,4);

        case 4:

                a3 = MP_DIGIT(a,3);

        case 3:

                a2 = MP_DIGIT(a,2);

        case 2:

                a1 = MP_DIGIT(a,1);

        case 1:

                a0 = MP_DIGIT(a,0);

        }

        switch(MP_USED(b)) {

        case 5:

                r4 = MP_DIGIT(b,4);

        case 4:

                r3 = MP_DIGIT(b,3);

        case 3:

                r2 = MP_DIGIT(b,2);

        case 2:

                r1 = MP_DIGIT(b,1);

        case 1:

                r0 = MP_DIGIT(b,0);

        }

        MP_ADD_CARRY_ZERO(a0, r0, r0, carry);

        MP_ADD_CARRY(a1, r1, r1, carry, carry);

        MP_ADD_CARRY(a2, r2, r2, carry, carry);

        MP_ADD_CARRY(a3, r3, r3, carry, carry);

        MP_ADD_CARRY(a4, r4, r4, carry, carry);

        MP_CHECKOK(s_mp_pad(r, 5));

        MP_DIGIT(r, 4) = r4;

        MP_DIGIT(r, 3) = r3;

        MP_DIGIT(r, 2) = r2;

        MP_DIGIT(r, 1) = r1;

        MP_DIGIT(r, 0) = r0;

        MP_SIGN(r) = MP_ZPOS;

        MP_USED(r) = 5;

        /* Do quick 'subract' if we've gone over

         * (add the 2's complement of the curve field) */

         a4 = MP_DIGIT(&meth->irr,4);

        if (carry ||  r4 >  a4 ||

                ((r4 == a4) && mp_cmp(r,&meth->irr) != MP_LT)) {

                a3 = MP_DIGIT(&meth->irr,3);

                a2 = MP_DIGIT(&meth->irr,2);

                a1 = MP_DIGIT(&meth->irr,1);

                a0 = MP_DIGIT(&meth->irr,0);

                MP_SUB_BORROW(r0, a0, r0, 0,     carry);

                MP_SUB_BORROW(r1, a1, r1, carry, carry);

                MP_SUB_BORROW(r2, a2, r2, carry, carry);

                MP_SUB_BORROW(r3, a3, r3, carry, carry);

                MP_SUB_BORROW(r4, a4, r4, carry, carry);

                MP_DIGIT(r, 4) = r4;

                MP_DIGIT(r, 3) = r3;

                MP_DIGIT(r, 2) = r2;

                MP_DIGIT(r, 1) = r1;

                MP_DIGIT(r, 0) = r0;

        }

        s_mp_clamp(r);

  CLEANUP:

        return res;

}

/* 6 words */

mp_err

ec_GFp_add_6(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, a3 = 0, a4 = 0, a5 = 0;

        mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0;

        mp_digit carry;

        switch(MP_USED(a)) {

        case 6: