wolfssl/wolfcrypt/src/sakke.c

/* sakke.c
 *
 * Copyright (C) 2006-2022 wolfSSL Inc.
 *
 * This file is part of wolfSSL.
 *
 * wolfSSL is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * wolfSSL is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
 */



#ifdef HAVE_CONFIG_H
    #include <config.h>
#endif

#include <wolfssl/wolfcrypt/settings.h>

#ifdef NO_INLINE
    #include <wolfssl/wolfcrypt/misc.h>
#else
    #define WOLFSSL_MISC_INCLUDED
    #include <wolfcrypt/src/misc.c>
#endif

#ifdef WOLFSSL_HAVE_SP_ECC
    #include <wolfssl/wolfcrypt/sp.h>
#endif

#ifdef WOLFCRYPT_HAVE_SAKKE

#include <wolfssl/wolfcrypt/error-crypt.h>
#include <wolfssl/wolfcrypt/sakke.h>
#include <wolfssl/wolfcrypt/asn_public.h>

/* SAKKE Build Options:
 * WOLFSSL_SAKKE_SMALL:          Small code size version of SAKKE.
 * WOLFSSL_SAKKE_SMALL_MODEXP:   Small code size for just SAKKE modexp.
 */


#ifdef WOLFCRYPT_SAKKE_CLIENT
/*
 * Initialize the client components of the SAKKE key.
 *
 * @param  [in]  key      SAKKE key to initialize.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_init_client(SakkeKey* key)
{
    int err = 0;

    key->tmp.p1 = wc_ecc_new_point_h(key->ecc.heap);
    if (key->tmp.p1 == NULL) {
        err = MEMORY_E;
    }
    if (err == 0) {
        key->tmp.p2 = wc_ecc_new_point_h(key->ecc.heap);
        if (key->tmp.p2 == NULL) {
            err = MEMORY_E;
        }
    }
    if (err == 0) {
        key->tmp.p3 = wc_ecc_new_point_h(key->ecc.heap);
        if (key->tmp.p3 == NULL) {
            err = MEMORY_E;
        }
    }
    if (err == 0) {
        key->rsk.rsk = wc_ecc_new_point_h(key->ecc.heap);
        if (key->rsk.rsk == NULL) {
            err = MEMORY_E;
        }
    }
    if (err == 0) {
        key->i.i = wc_ecc_new_point_h(key->ecc.heap);
        if (key->i.i == NULL) {
            err = MEMORY_E;
        }
    }

    return err;
}
#endif

/**
 * Initialize the components of the SAKKE key.
 *
 * Must be called before performing any operations.
 * Free the SAKKE key with wc_FreeSakkeKey() when no longer needed.
 *
 * @param  [in]  key      SAKKE key to initialize.
 * @param  [in]  keySize  Size of the curve. For SAKKE set 1, use 128.
 * @param  [in]  curveId  ID of curve. For SAKKE set 1, use ECC_SAKKE_1.
 * @param  [in]  heap     Heap hint.
 * @param  [in]  devId    Device identifier.
 *                        Use INVALID_DEVID when no device used.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key is NULL.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
int wc_InitSakkeKey_ex(SakkeKey* key, int keySize, int curveId, void* heap,
        int devId)
{
    int err = 0;
    SakkeKeyParams* params = NULL;

    if (key == NULL) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        XMEMSET(key, 0, sizeof(*key));
        key->heap = heap;
        params = &key->params;

        err = wc_ecc_init_ex(&key->ecc, heap, devId);
    }
    if (err == 0) {
        err = wc_ecc_set_curve(&key->ecc, keySize, curveId);
    }
    if (err == 0) {
        params->base = wc_ecc_new_point_h(key->ecc.heap);
        if (params->base == NULL) {
            err = MEMORY_E;
        }
#ifdef WOLFCRYPT_SAKKE_CLIENT
        if (err == 0) {
            err = sakke_init_client(key);
        }
#endif
        if (err == 0) {
            err = mp_init_multi(&params->prime, &params->q, &params->g,
                    &params->a, &key->tmp.m1,
#ifdef WOLFCRYPT_SAKKE_CLIENT
                    &key->tmp.m2
#else
                    NULL
#endif
                    );
        }
        if (err == 0) {
            key->mpInit = 1;
        }

        if (err != 0) {
            wc_FreeSakkeKey(key);
        }
    }

    return err;
}

/**
 * Initialize the components of the SAKKE key.
 *
 * Must be called before performing any operations.
 * Free the SAKKE key with wc_FreeSakkeKey() when no longer needed.
 *
 * @param  [in]  key      SAKKE key to initialize.
 * @param  [in]  heap     Heap hint.
 * @param  [in]  devId    Device identifier.
 *                        Use INVALID_DEVID when no device used.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key is NULL.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
int wc_InitSakkeKey(SakkeKey* key, void* heap, int devId)
{
    return wc_InitSakkeKey_ex(key, 128, ECC_SAKKE_1, heap, devId);
}

/**
 * Frees memory associated with components of the SAKKE key.
 *
 * Must be called when finished with the SAKKE key.
 *
 * @param  [in]  key  SAKKE key.
 */
void wc_FreeSakkeKey(SakkeKey* key)
{
    if (key != NULL) {
        SakkeKeyParams* params = &key->params;

        if (key->mpInit) {
            mp_free(&params->prime);
            mp_free(&params->q);
            mp_free(&params->g);
            mp_free(&params->a);
            mp_free(&key->tmp.m1);
#ifdef WOLFCRYPT_SAKKE_CLIENT
            mp_free(&key->tmp.m2);
#endif
        }
#ifdef WOLFCRYPT_SAKKE_CLIENT
        if (key->i.i != NULL) {
            wc_ecc_del_point_h(key->i.i, key->ecc.heap);
        }
        if (key->rsk.rsk != NULL) {
            wc_ecc_del_point_h(key->rsk.rsk, key->ecc.heap);
        }
        if (key->tmp.p3 != NULL) {
            wc_ecc_del_point_h(key->tmp.p3, key->ecc.heap);
        }
        if (key->tmp.p2 != NULL) {
            wc_ecc_del_point_h(key->tmp.p2, key->ecc.heap);
        }
        if (key->tmp.p1 != NULL) {
            wc_ecc_del_point_h(key->tmp.p1, key->ecc.heap);
        }
#endif
        if (params->base != NULL) {
            wc_ecc_del_point_h(params->base, key->ecc.heap);
        }
        wc_ecc_free(&key->ecc);
    }
}

/*
 * Load order (q), prime (p) and a, hex strings in ECC object, into fields of
 * key.
 *
 * Flags that the p, q and a are available so it isn't loaded multiple times.
 *
 * @param  [in]  key  SAKKE key.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_load_params(SakkeKey* key)
{
    int err = 0;
    SakkeKeyParams* params = &key->params;

    if (!params->havePrime) {
        /* Load prime or modulus from string. */
        err = mp_read_radix(&params->prime, key->ecc.dp->prime, MP_RADIX_HEX);
        if (err == 0) {
            params->havePrime = 1;
        }
    }
    if (!params->haveQ) {
        /* Load order from string. */
        err = mp_read_radix(&params->q, key->ecc.dp->order, MP_RADIX_HEX);
        if (err == 0) {
            params->haveQ = 1;
        }
    }
    if (!params->haveA) {
        /* Load parameter A from string. */
        err = mp_read_radix(&params->a, key->ecc.dp->Af, MP_RADIX_HEX);
        if (err == 0) {
            params->haveA = 1;
        }
    }

    return err;
}

/*
 * Load the base point, hex encoded in the ECC object, as an ecc_point.
 *
 * @param  [in]   key   SAKKE key.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_load_base_point(SakkeKey* key)
{
    int err = 0;
    SakkeKeyParams* params = &key->params;

    if (!params->haveBase) {
        /* Load base point modulus from string. */
        err = mp_read_radix(params->base->x, key->ecc.dp->Gx, MP_RADIX_HEX);
        if (err == 0) {
            err = mp_read_radix(params->base->y, key->ecc.dp->Gy, MP_RADIX_HEX);
        }
        if (err == 0) {
            /* Affine co-ordinates have a Z of 1 in Jacobian. */
            err = mp_set(params->base->z, 1);
        }
        if (err == 0) {
            /* Base point loaded. */
            params->haveBase = 1;
        }
    }

    return err;
}

#ifdef WOLFSSL_HAVE_SP_ECC
/*
 * Scalar multiply the base point.
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   n     MP integer that is the scalar.
 * @param  [out]  res   ECC point to hold the result.
 * @param  [in]   map   Map the result to affine co-ordinates.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_mulmod_base(SakkeKey* key, const mp_int* n, ecc_point* res,
        int map)
{
    int err = NOT_COMPILED_IN;

#ifdef WOLFSSL_SP_1024
    if ((key->ecc.idx != ECC_CUSTOM_IDX) &&
            (ecc_sets[key->ecc.idx].id == ECC_SAKKE_1)) {
        err = sp_ecc_mulmod_base_1024(n, res, map, key->heap);
    }
#endif

    return err;
}

/*
 * Scalar multiply the base point and add a point.
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   n     MP integer that is the scalar.
 * @param  [in]   a     ECC point to add.
 * @param  [out]  res   ECC point to hold the result.
 * @param  [in]   map   Map the result to affine co-ordinates.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_mulmod_base_add(SakkeKey* key, const mp_int* n,
        const ecc_point* a, ecc_point* res, int map)
{
    int err = NOT_COMPILED_IN;

#ifdef WOLFSSL_SP_1024
    if ((key->ecc.idx != ECC_CUSTOM_IDX) &&
            (ecc_sets[key->ecc.idx].id == ECC_SAKKE_1)) {
        err = sp_ecc_mulmod_base_add_1024(n, a, 0, res, map, key->heap);
    }
#endif

    return err;
}
#else
/*
 * Scalar multiply the base point.
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   n     MP integer that is the scalar.
 * @param  [out]  res   ECC point to hold the result.
 * @param  [in]   map   Map the result to affine co-ordinates.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_mulmod_base(SakkeKey* key, const mp_int* n, ecc_point* res,
        int map)
{
    int err;
    SakkeKeyParams* params = &key->params;

    err = wc_ecc_mulmod(n, params->base, res, &params->a, &params->prime, map);

    return err;
}

/*
 * Scalar multiply the base point and add a point.
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   n     MP integer that is the scalar.
 * @param  [in]   a     ECC point to add. Point ordinates must be in Montgomery
 *                      form.
 * @param  [out]  res   ECC point to hold the result.
 * @param  [in]   map   Map the result to affine co-ordinates.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_mulmod_base_add(SakkeKey* key, const mp_int* n, ecc_point* a,
        ecc_point* res, int map)
{
    int err;
    mp_digit mp = 0;
    SakkeKeyParams* params = &key->params;

    /* Scalar multiply base by n - leaves ordinates in Montgomery form. */
    err = wc_ecc_mulmod(n, params->base, res, &params->a, &params->prime, 0);
    if (err == 0) {
        err = mp_montgomery_setup(&params->prime, &mp);
    }
    if (err == 0) {
        /* Add a to result. */
        err = ecc_projective_add_point(res, a, res, &params->a,
                &params->prime, mp);
    }
    if ((err == 0) && map) {
        /* Map result back to affine co-ordinates. */
        err = ecc_map(res, &params->prime, mp);
    }

    return err;
}
#endif

#ifdef WOLFSSL_HAVE_SP_ECC
/*
 * Scalar multiply a point.
 *
 * @param  [in]   key    SAKKE key.
 * @param  [in]   n      MP integer that is the scalar.
 * @param  [in]   p      ECC point to multiply.
 * @param  [in]   table  Precomputation table for p. May be NULL.
 * @param  [out]  res    ECC point to hold the result.
 * @param  [in]   map    Map the result to affine co-ordinates.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_mulmod_point(SakkeKey* key, const mp_int* n,
        const ecc_point* p, byte* table, ecc_point* res, int map)
{
    int err = NOT_COMPILED_IN;

#ifdef WOLFSSL_SP_1024
    if ((key->ecc.idx != ECC_CUSTOM_IDX) &&
            (ecc_sets[key->ecc.idx].id == ECC_SAKKE_1)) {
        if (table == NULL) {
            err = sp_ecc_mulmod_1024(n, p, res, map, key->heap);
        }
        else {
            err = sp_ecc_mulmod_table_1024(n, p, table, res, map, key->heap);
        }
    }
#endif

    return err;
}
#else
/*
 * Scalar multiply a point.
 *
 * @param  [in]   key    SAKKE key.
 * @param  [in]   n      MP integer that is the scalar.
 * @param  [in]   p      ECC point to multiply.
 * @param  [in]   table  Precomputation table for p. May be NULL.
 * @param  [out]  res    ECC point to hold the result.
 * @param  [in]   map    Map the result to affine co-ordinates.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_mulmod_point(SakkeKey* key, const mp_int* n, ecc_point* p,
        const byte* table, ecc_point* res, int map)
{
    int err;
    SakkeKeyParams* params = &key->params;

    err = wc_ecc_mulmod(n, p, res, &params->a, &params->prime, map);

    (void)table;
    return err;
}
#endif

#ifdef WOLFCRYPT_SAKKE_KMS
/**
 * Generate KMS Master Secret (z_T) and KMS Public Key (Z_T).
 *
 * RFC 6508, Section 4.1
 *
 * Called when establishing a new KMS.\n
 * z_T must be kept secret while Z_T is required by clients for encapsulating
 * and deriving.
 * Export key using wc_ExportSakkeKey(), once generated, to reuse the key.\n
 * Export KPAK using wc_ExportSakkePublicKey(), once generate to send to
 * clients.
 *
 * @param  [in]  key      SAKKE key.
 * @param  [in]  rng      Random number generator.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or rng is NULL.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 * @return  Other value when an an internal operation fails.
 */
int wc_MakeSakkeKey(SakkeKey* key, WC_RNG* rng)
{
    int err = 0;
    int digits = 0;

    if ((key == NULL) || (rng == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        digits = (key->ecc.dp->size * 8 + DIGIT_BIT - 1) / DIGIT_BIT;

        err = sakke_load_params(key);
    }
    if (err == 0) {
        err = sakke_load_base_point(key);
    }
    if (err == 0) {
        int genTryCnt = 0;

        /* Generate a random number that is not 0 - master secret. */
        do {
            /* Don't infinitely loop on random number generation failure. */
            if ((++genTryCnt) > SAKKE_MAX_GEN_COUNT) {
                err = RNG_FAILURE_E;
            }
            if (err == 0) {
                err = mp_rand(&key->ecc.k, digits, rng);
            }
            if (err == 0) {
                err = mp_mod(&key->ecc.k, &key->params.q, &key->ecc.k);
            }
        }
        while ((err == 0) && mp_iszero(&key->ecc.k));
    }
    if (err == 0) {
        /* Calculate public key by multiply master secret by base point. */
        err = sakke_mulmod_base(key, &key->ecc.k, &key->ecc.pubkey, 1);
    }
    if (err == 0) {
        key->ecc.type = ECC_PRIVATEKEY;
    }

    return err;
}

/**
 * Generates the KMS Public Key (Z_T) from the KMS Master Secret (z_T).
 *
 * Only z_T is required to calculate Receiver Secret Key (RSK).
 *
 * @param  [in]   key  SAKKE key.
 * @param  [out]  pub  ECC point containing KPAK.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or pub is NULL.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 * @return  Other value when an an internal operation fails.
 */
int wc_MakeSakkePublicKey(SakkeKey* key, ecc_point* pub)
{
    int err = 0;

    if ((key == NULL) || (pub == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        err = sakke_load_base_point(key);
    }
    if (err == 0) {
        err = sakke_mulmod_base(key, &key->ecc.k, pub, 1);
    }

    return err;
}

/**
 * Export the SAKKE key as encoded public/private ECC key.
 *
 * Use when saving the KMS key pair.
 *
 * Private key, x ordinate of public key and y ordinate of public key
 * concatenated. Each number is zero padded to key size.
 *
 * @param  [in]      key   SAKKE key.
 * @param  [out]     data  Buffer to hold encoded SAKKE key.
 * @param  [in,out]  sz    In, size of buffer in bytes.
 *                         Out, size of encoded SAKKE key in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or sz is NULL.
 * @return  LENGTH_ONLY_E when data is NULL - sz is set.
 * @return  BUFFER_E when size of buffer is too small.
 */
int wc_ExportSakkeKey(SakkeKey* key, byte* data, word32* sz)
{
    int err = 0;

    if ((key == NULL) || (sz == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if ((err == 0) && (data == NULL)) {
        *sz = 3 * key->ecc.dp->size;
        err = LENGTH_ONLY_E;
    }
    if ((err >= 0) && (*sz < (word32)(3 * key->ecc.dp->size))) {
        err = BUFFER_E;
    }
    if (err == 0) {
        /* Write out the secret value into key size bytes. */
        err = mp_to_unsigned_bin_len(&key->ecc.k, data, key->ecc.dp->size);
    }
    if (err == 0) {
        data += key->ecc.dp->size;
        /* Write out the public key point's x ordinate into key size bytes. */
        err = mp_to_unsigned_bin_len(key->ecc.pubkey.x, data,
                key->ecc.dp->size);
    }
    if (err == 0) {
        data += key->ecc.dp->size;
        /* Write out the public key point's y ordinate into key size bytes. */
        err = mp_to_unsigned_bin_len(key->ecc.pubkey.y, data,
                key->ecc.dp->size);
    }
    if (err == 0) {
        *sz = 3 * key->ecc.dp->size;
    }

    return err;
}

/**
 * Import the SAKKE key as DER encoded public/private ECC key.
 *
 * Use when restoring the KMS key pair.
 *
 * Private key, x ordinate of public key and y ordinate of public key
 * concatenated. Each number is zero padded to key size.
 *
 * @param  [in]  key   SAKKE key.
 * @param  [in]  data  Buffer holding encoded SAKKE key.
 * @param  [in]  sz    Size of encoded SAKKE key in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or data is NULL.
 * @return  BUFFER_E when size of data is not equal to the expected size.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 */
int wc_ImportSakkeKey(SakkeKey* key, const byte* data, word32 sz)
{
    int err = 0;

    if ((key == NULL) || (data == NULL)) {
        err = BAD_FUNC_ARG;
    }
    if ((err == 0) && (sz != (word32)key->ecc.dp->size * 3)) {
        err = BUFFER_E;
    }

    if (err == 0) {
        /* Read the secret value from key size bytes. */
        err = mp_read_unsigned_bin(&key->ecc.k, data, key->ecc.dp->size);
    }
    if (err == 0) {
        data += key->ecc.dp->size;
        /* Read the public key point's x value from key size bytes. */
        err = mp_read_unsigned_bin(key->ecc.pubkey.x, data, key->ecc.dp->size);
    }
    if (err == 0) {
        data += key->ecc.dp->size;
        /* Read the public key point's y value from key size bytes. */
        err = mp_read_unsigned_bin(key->ecc.pubkey.y, data, key->ecc.dp->size);
    }
    if (err == 0) {
        err = mp_set(key->ecc.pubkey.z, 1);
    }
    if (err == 0) {
        key->ecc.type = ECC_PRIVATEKEY;
    }

    return err;
}

/**
 * Export the SAKKE key as DER encoded private ECC key.
 *
 * Use when saving the KMS private key.
 *
 * Private key zero padded to key size.
 *
 * @param  [in]      key   SAKKE key.
 * @param  [out]     data  Buffer to hold encoded SAKKE key.
 * @param  [in,out]  sz    In, size of buffer in bytes.
 *                         Out, size of encoded SAKKE key in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or sz is NULL.
 * @return  LENGTH_ONLY_E when data is NULL - sz is set.
 * @return  BUFFER_E when size of buffer is too small.
 */
int wc_ExportSakkePrivateKey(SakkeKey* key, byte* data, word32* sz)
{
    int err = 0;

    if ((key == NULL) || (sz == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if ((err == 0) && (data == NULL)) {
        *sz = key->ecc.dp->size;
        err = LENGTH_ONLY_E;
    }
    if ((err >= 0) && (*sz < (word32)key->ecc.dp->size)) {
        err = BUFFER_E;
    }
    if (err == 0) {
        /* Write out the secret value into key size bytes. */
        err = mp_to_unsigned_bin_len(&key->ecc.k, data, key->ecc.dp->size);
    }
    if (err == 0) {
        *sz = key->ecc.dp->size;
    }

    return err;
}

/**
 * Import the SAKKE key as DER encoded private ECC key.
 *
 * Use when restoring the KMS private key.
 * Use wc_MakeSakkePublicKey() to recalculate the public key.
 *
 * Private key zero padded to key size.
 *
 * @param  [in]  key   SAKKE key.
 * @param  [in]  data  Buffer holding encoded SAKKE key.
 * @param  [in]  sz    Size of encoded SAKKE key in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or data is NULL.
 * @return  BUFFER_E when size of data is not equal to the expected size.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 */
int wc_ImportSakkePrivateKey(SakkeKey* key, const byte* data, word32 sz)
{
    int err = 0;

    if ((key == NULL) || (data == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if ((err == 0) && (sz != (word32)key->ecc.dp->size)) {
        err = BUFFER_E;
    }

    if (err == 0) {
        /* Read the secret value from key size bytes. */
        err = mp_read_unsigned_bin(&key->ecc.k, data, key->ecc.dp->size);
    }

    return err;
}

/*
 * Convert the public key from montgomery form.
 *
 * The public key is needed in Montgomery form for validation and derivation.
 *
 * @param  [in]  key      SAKKE key.
 * @return  0 on success.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 * @return  Other value when an an internal operation fails.
 */
static int sakke_z_from_mont(SakkeKey* key)
{
    int err = 0;
    mp_digit mp;
    ecc_point* z = &key->ecc.pubkey;
    mp_int* prime = &key->params.prime;

    if (key->zMont) {
        err = mp_montgomery_setup(prime, &mp);
        if (err == 0) {
            err = mp_montgomery_reduce(z->x, prime, mp);
        }
        if (err == 0) {
            err = mp_montgomery_reduce(z->y, prime, mp);
        }
        if (err == 0) {
            err = mp_montgomery_reduce(z->z, prime, mp);
        }
        if (err == 0) {
            key->zMont = 0;
        }
    }

    return err;
}

/*
 * Encode a point into a buffer.
 *
 * X and y ordinate of point concatenated. Each number is zero padded tosize.
 * Descriptor byte (0x04) is prepended when not raw.
 *
 * @param  [in]      point    ECC point to encode.
 * @param  [in]      size     Size of prime in bytes - maximum ordinate length.
 * @param  [out]     data     Buffer to hold encoded data.
 *                            NULL when needing length of encoded data.
 * @param  [in,out]  sz       In, the size of the buffer in bytes.
 *                            Out, the size of the encoded data in bytes.
 * @param  [in]      raw      On 0, prepend descriptor byte.
 *                            On 1, only include ordinates.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or sz is NULL.
 * @return  LENGTH_ONLY_E when data is NULL - sz will hold the size in bytes of
 *          the encoded data.
 * @return  BUFFER_E when size of buffer is too small.
 */
static int sakke_encode_point(ecc_point* point, word32 size, byte* data,
        word32* sz, int raw)
{
    int err = 0;

    if (data == NULL) {
        *sz = size * 2 + !raw;
        err = LENGTH_ONLY_E;
    }
    if ((err == 0) && (*sz < size * 2 + !raw)) {
        err = BUFFER_E;
    }

    if (err == 0) {
        if (!raw) {
            data[0] = 0x04;
            data++;
        }

        /* Write out the point's x ordinate into key size bytes. */
        err = mp_to_unsigned_bin_len(point->x, data, size);
    }
    if (err == 0) {
        data += size;
        /* Write out the point's y ordinate into key size bytes. */
        err = mp_to_unsigned_bin_len(point->y, data, size);
    }
    if (err == 0) {
        *sz = size * 2 + !raw;
    }

    return err;
}

/*
 * Decode the data into an ECC point.
 *
 * X and y ordinate of point concatenated. Each number is zero padded to
 * key size. Supports prepended descriptor byte (0x04).
 *
 * @param  [out]  point  ECC point to encode.
 * @param  [in]   size   Size of prime in bytes - maximum ordinate length.
 * @param  [in]   data   Encoded public key.
 * @param  [in]   sz     Size of the encoded public key in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or z is NULL.
 * @return  BUFFER_E when size of data is not equal to the expected size.
 * @return  ASN_PARSE_E when format byte is invalid.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 */
static int sakke_decode_point(ecc_point* point, word32 size, const byte* data,
        word32 sz)
{
    int err = 0;

    if ((sz != size * 2) && (sz != size * 2 + 1)) {
        err = BUFFER_E;
    }

    if ((err == 0) && (sz & 1)) {
        if (data[0] != 0x04) {
            err = ASN_PARSE_E;
        }
        data++;
    }

    if (err == 0) {
        /* Read the public key point's x value from key size bytes. */
        err = mp_read_unsigned_bin(point->x, data, size);
    }
    if (err == 0) {
        data += size;
        /* Read the public key point's y value from key size bytes. */
        err = mp_read_unsigned_bin(point->y, data, size);
    }
    if (err == 0) {
        err = mp_set(point->z, 1);
    }

    return err;
}


/**
 * Encode the KMS public key (Z_T) into a buffer.
 *
 * Z_T is required by all clients in order to perform cryptographic operations.
 *
 * X and y ordinate of public key concatenated. Each number is zero padded to
 * key size.
 * Descriptor byte (0x04) is prepended when not raw.
 *
 * @param  [in]      key      SAKKE key.
 * @param  [out]     data     Buffer to hold encoded data.
 *                            NULL when needing length of encoded data.
 * @param  [in,out]  sz       In, the size of the buffer in bytes.
 *                            Out, the size of the encoded data in bytes.
 * @param  [in]      raw      On 0, prepend descriptor byte.
 *                            On 1, only include ordinates.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or sz is NULL.
 * @return  LENGTH_ONLY_E when data is NULL - sz will hold the size in bytes of
 *          the encoded data.
 * @return  BUFFER_E when size of buffer is too small.
 */
int wc_ExportSakkePublicKey(SakkeKey* key, byte* data, word32* sz, int raw)
{
    int err = 0;

    if ((key == NULL) || (sz == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if ((err == 0) && (data != NULL)) {
        err = sakke_z_from_mont(key);
    }

    if (err == 0) {
        err = sakke_encode_point(&key->ecc.pubkey, (word32)key->ecc.dp->size,
                data, sz, raw);
    }

    return err;
}

/**
 * Calculates the Receiver Secret Key (RSK) for the identity.
 *
 * RFC 6508, Section 6.1.1
 *
 * RSK = [ (a + z_T) ^ 1 modulo q ]P\n
 * RSK is required by receiver to derive SSV.
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   id    Identity to create hash for.
 * @param  [in]   idSz  Length of identity in bytes.
 * @param  [out]  rsk   Receiver Secret Key as an ECC point.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, id, or rsk is NULL.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 * @return  Other value when an an internal operation fails.
 */
int wc_MakeSakkeRsk(SakkeKey* key, const byte* id, word16 idSz, ecc_point* rsk)
{
    int err = 0;
    mp_int* a = NULL;

    if ((key == NULL) || (id == NULL) || (rsk == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        err = sakke_load_base_point(key);
    }

    /* Compute RSK = [ (a + z_T) ^ 1 modulo q ]P */
    if (err == 0) {
        a = &key->tmp.m1;
        err = mp_read_unsigned_bin(a, id, idSz);
    }
    /* a + z_T */
    if (err == 0) {
        err = mp_addmod(a, &key->ecc.k, &key->params.q, a);
    }
    /* (a + z_T) ^ 1 modulo q */
    if (err == 0) {
        err = mp_invmod(a, &key->params.q, a);
    }

    /* [ (a + z_T) ^ 1 modulo q ]P */
    if (err == 0) {
        err = sakke_mulmod_base(key, a, rsk, 1);
    }

    return err;
}

/**
 * Encode the SAKKE Receiver Secret Key (RSK) as DER encoded public ECC key.
 *
 * Encode the RSK to send to ther receiving client.
 *
 * X and y ordinate of RSK point concatenated. Each number is zero padded to
 * key size.
 * Descriptor byte (0x04) is prepended when not raw.
 *
 * @param  [in]      key   SAKKE key.
 * @param  [in]      rsk   ECC point that is the Receiver Secret Key (RSK).
 * @param  [out]     out   Buffer to hold encoded RSK.
 * @param  [in,out]  sz    In, size of buffer in bytes.
 *                         Out, size of encoded RSK in bytes.
 * @param  [in]      raw   On 0, prepend descriptor byte.
 *                         On 1, only include ordinates.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, rsk, or sz is NULL.
 * @return  LENGTH_ONLY_E when data is NULL - sz will hold the size in bytes of
 *          the encoded data.
 * @return  BUFFER_E when size of buffer is too small.
 */
int wc_EncodeSakkeRsk(const SakkeKey* key, ecc_point* rsk, byte* out,
        word32* sz, int raw)
{
    int err = 0;

    if ((key == NULL) || (rsk == NULL) || (sz == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        err = sakke_encode_point(rsk, (word32)key->ecc.dp->size, out, sz, raw);
    }

    return err;
}

#endif /* WOLFCRYPT_SAKKE_KMS */

#ifdef WOLFCRYPT_SAKKE_CLIENT

/**
 * Decode the KMS public key (Z_T) into the key.
 *
 * A client imports Z_T to perform derivation of SSV.
 *
 * X and y ordinate of public key concatenated. Each number is zero padded to
 * key size. Supports prepended descriptor byte (0x04).
 *
 * @param  [in]  key   SAKKE key.
 * @param  [in]  data  Encoded public key.
 * @param  [in]  sz    Size of the encoded public key in bytes.
 * @param  [in]  trusted  1 when public key is trusted.
 *                        0 when validation is required to be performed.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or z is NULL.
 * @return  BUFFER_E when size of data is not equal to the expected size.
 * @return  ASN_PARSE_E when format byte is invalid.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 * @return  ECC_OUT_OF_RANGE_E when point is invalid.
 * @return  ECC_INF_E when point is at infinity and invalid.
 */
int wc_ImportSakkePublicKey(SakkeKey* key, const byte* data, word32 sz,
        int trusted)
{
    int err = 0;

    if ((key == NULL) || (data == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        err = sakke_decode_point(&key->ecc.pubkey, (word32)key->ecc.dp->size,
                data, sz);
    }
    if (err == 0) {
        key->ecc.type = ECC_PUBLICKEY;
        key->zMont = 0;
    }
    if ((err == 0) && (!trusted)) {
        err = wc_ecc_check_key(&key->ecc);
    }

    return err;
}

/**
 * Decode the SAKKE Receiver Secret Key (RSK) as DER encoded public ECC key.
 *
 * A receiving client needs the RSK for deriving SSV.
 *
 * X and y ordinate of RSK point concatenated. Each number is zero padded to
 * key size. Supports prepended descriptor byte (0x04).
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   data  Buffer holding encoded SAKKE key.
 * @param  [in]   sz    Size of encoded RSK in bytes.
 * @param  [out]  rsk   ECC point to hold the Receiver Secret Key (RSK).
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, data or rsk is NULL.
 * @return  BUFFER_E when size of data is not equal to the expected size.
 * @return  ASN_PARSE_E when format byte is invalid.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 */
int wc_DecodeSakkeRsk(const SakkeKey* key, const byte* data, word32 sz,
        ecc_point* rsk)
{
    int err = 0;

    if ((key == NULL) || (data == NULL) || (rsk == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        err = sakke_decode_point(rsk, (word32)key->ecc.dp->size, data, sz);
    }

    return err;
}

/**
 * Decode the SAKKE Receiver Secret Key (RSK) as DER encoded public ECC key and
 * stores internally.
 *
 * A receiving client needs the RSK for deriving SSV.
 *
 * X and y ordinate of RSK point concatenated. Each number is zero padded to
 * key size. Supports prepended descriptor byte (0x04).
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   data  Buffer holding encoded SAKKE key.
 * @param  [in]   sz    Size of encoded RSK in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or data is NULL.
 * @return  BUFFER_E when size of data is not equal to the expected size.
 * @return  MP_MEM or MEMORY_E when dynamic memory allocation fails.
 */
int wc_ImportSakkeRsk(SakkeKey* key, const byte* data, word32 sz)
{
    int err = 0;

    if ((key == NULL) || (data == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        err = wc_DecodeSakkeRsk(key, data, sz, key->rsk.rsk);
    }

    return err;
}

/* Base (g) for SAKKE parameter set 1. */
static const byte sakke_param_set_1_base[] = {
    0x66, 0xFC, 0x2A, 0x43, 0x2B, 0x6E, 0xA3, 0x92,
    0x14, 0x8F, 0x15, 0x86, 0x7D, 0x62, 0x30, 0x68,
    0xC6, 0xA8, 0x7B, 0xD1, 0xFB, 0x94, 0xC4, 0x1E,
    0x27, 0xFA, 0xBE, 0x65, 0x8E, 0x01, 0x5A, 0x87,
    0x37, 0x1E, 0x94, 0x74, 0x4C, 0x96, 0xFE, 0xDA,
    0x44, 0x9A, 0xE9, 0x56, 0x3F, 0x8B, 0xC4, 0x46,
    0xCB, 0xFD, 0xA8, 0x5D, 0x5D, 0x00, 0xEF, 0x57,
    0x70, 0x72, 0xDA, 0x8F, 0x54, 0x17, 0x21, 0xBE,
    0xEE, 0x0F, 0xAE, 0xD1, 0x82, 0x8E, 0xAB, 0x90,
    0xB9, 0x9D, 0xFB, 0x01, 0x38, 0xC7, 0x84, 0x33,
    0x55, 0xDF, 0x04, 0x60, 0xB4, 0xA9, 0xFD, 0x74,
    0xB4, 0xF1, 0xA3, 0x2B, 0xCA, 0xFA, 0x1F, 0xFA,
    0xD6, 0x82, 0xC0, 0x33, 0xA7, 0x94, 0x2B, 0xCC,
    0xE3, 0x72, 0x0F, 0x20, 0xB9, 0xB7, 0xB0, 0x40,
    0x3C, 0x8C, 0xAE, 0x87, 0xB7, 0xA0, 0x04, 0x2A,
    0xCD, 0xE0, 0xFA, 0xB3, 0x64, 0x61, 0xEA, 0x46
};

/*
 * Load Pairing Base (g), hex strings in ECC object, into field of key.
 *
 * Flags that the g is available so it isn't loaded multiple times.
 *
 * @param  [in]  key  SAKKE key.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_load_pairing_base(SakkeKey* key)
{
    int err = 0;
    SakkeKeyParams* params = &key->params;

    if (!params->haveG) {
        if (key->ecc.dp->id != ECC_SAKKE_1) {
            err = NOT_COMPILED_IN;
        }
        if (err == 0) {
            err = mp_read_unsigned_bin(&params->g, sakke_param_set_1_base,
                    sizeof(sakke_param_set_1_base));
            if (err == 0) {
                params->haveG = 1;
            }
        }
    }

    return err;
}

#ifndef WOLFSSL_HAVE_SP_ECC
/*
 * Put point into Montgomery form.
 *
 * @param  [in]  p      ECC point.
 * @param  [in]  prime  Prime modulus.
 * @param  [in]  mu     Temporary MP integer to hold mu.
 * @param  [in]  set    1 when mu is set and 0 when it needs to be calculated.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_point_to_mont(ecc_point* p, mp_int* prime, mp_int* mu, int set)
{
    int err = 0;

    if (!set) {
        /* Calculate multiplier that converts to Montgomery form. */
        err = mp_montgomery_calc_normalization(mu, prime);
    }
    if (err == 0) {
        err = mp_mulmod(p->x, mu, prime, p->x);
    }
    if (err == 0) {
        err = mp_mulmod(p->y, mu, prime, p->y);
    }
    if (err == 0) {
        err = mp_mulmod(p->z, mu, prime, p->z);
    }

    return err;
}

/*
 * Take point out of Montgomery form.
 *
 * @param  [in]  p      ECC point.
 * @param  [in]  prime  Prime modulus.
 * @param  [in]  mp     Multiplier to use when converting from Montgomery form.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_point_from_mont(ecc_point* p, mp_int* prime, mp_digit mp)
{
    int err;

    err = mp_montgomery_reduce(p->x, prime, mp);
    if (err == 0) {
        err = mp_montgomery_reduce(p->y, prime, mp);
    }
    if (err == 0) {
        err = mp_montgomery_reduce(p->z, prime, mp);
    }

    return err;
}

/*
 * Put Z into Montgomery form.
 *
 * @param  [in]  key  SAKKE key.
 * @param  [in]  mu   Temporary MP integer.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_z_to_mont(SakkeKey* key, mp_int* tmp)
{
    int err = 0;
    ecc_point* z = &key->ecc.pubkey;

    if (!key->zMont) {
        err = sakke_point_to_mont(z, &key->params.prime, tmp, 0);
        if (err == 0) {
            key->zMont = 1;
        }
    }

    return err;
}
#endif

#ifdef WOLFSSL_HAVE_SP_ECC
/**
 * Generate a pre-computation table for the RSK point.
 *
 * The table contains sensitive data.
 *
 * @param  [in]      key    SAKKE key.
 * @param  [in]      rsk    Point to generate table for.
 * @param  [out]     table  Pre-generated values. Passing NULL indicates that
 *                          the length of the table is required.
 * @param  [in,out]  len    On in, the size of table buffer in bytes.
 *                          On out, the size of the pre-generated data in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, rsk or len is NULL.
 * @return  LENGTH_ONLY_E when table is NULL.
 * @return  BAD_LENGTH_E when table is specified and len is too small.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
int wc_GenerateSakkeRskTable(const SakkeKey* key, const ecc_point* rsk,
        byte* table, word32* len)
{
    int err = 0;

    if ((key == NULL) || (rsk == NULL) || (len == 0)) {
        err = BAD_FUNC_ARG;
    }
    if (err == 0) {
        SAVE_VECTOR_REGISTERS(return _svr_ret;);
#ifdef WOLFSSL_SP_1024
        err = sp_Pairing_gen_precomp_1024(rsk, table, len);
#else
        err = NOT_COMPILED_IN;
#endif
        RESTORE_VECTOR_REGISTERS();
    }

    return err;
}

/*
 * Calculate r = pairing <P, Q>.
 *
 * That is, multiply base in PF_p[q] by the scalar s, such that s.P = Q.
 *
 * @param  [in]   key  SAKKE key.
 * @param  [in]   p    First point on E(F_p)[q].
 * @param  [in]   q    Second point on E(F_p)[q].
 * @param  [out]  r    Result of calculation.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_pairing(const SakkeKey* key, const ecc_point* p,
    const ecc_point* q, mp_int* r, const byte* table, word32 len)
{
    int err = NOT_COMPILED_IN;

#ifdef WOLFSSL_SP_1024
    if ((key->ecc.idx != ECC_CUSTOM_IDX) &&
            (ecc_sets[key->ecc.idx].id == ECC_SAKKE_1)) {
        if (table == NULL) {
            err = sp_Pairing_1024(p, q, r);
        }
        else {
            err = sp_Pairing_precomp_1024(p, q, r, table, len);
        }
    }
#else
    (void)key;
    (void)p;
    (void)q;
    (void)r;
    (void)table;
    (void)len;
#endif

    return err;
}

#else /* WOLFSSL_HAVE_SP_ECC */
/**
 * Generate a pre-computation table for the RSK point.
 *
 * Empty table as not supported in this implementation.
 *
 * @param  [in]      key    SAKKE key.
 * @param  [in]      rsk    Point to generate table for.
 * @param  [out]     table  Pre-generated values. Passing NULL indicates that
 *                          the length of the table is required.
 * @param  [in,out]  len    On in, the size of table buffer in bytes.
 *                          On out, the size of the pre-generated data in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, rsk or len is NULL.
 * @return  LENGTH_ONLY_E when table is NULL.
 * @return  BAD_LENGTH_E when table is specified and len is too small.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
int wc_GenerateSakkeRskTable(const SakkeKey* key, const ecc_point* rsk,
        byte* table, word32* len)
{
    int err = 0;

    if ((key == NULL) || (rsk == NULL) || (len == 0)) {
        err = BAD_FUNC_ARG;
    }
    if ((err == 0) && (table == NULL)) {
        *len = 0;
        err = LENGTH_ONLY_E;
    }
    if ((err == 0) && (*len != 0)) {
        err = BUFFER_E;
    }
    if (err == 0) {
        *len = 0;
    }

    (void)table;

    return err;
}

/*
 * Square a modulo m in Montgomery.
 *
 * @param  [in]   a   MP integer that is number to square.
 * @param  [in]   m   MP integer that is modulus.
 * @param  [out]  r   MP integer that is the result.
 * @param  [in]   mp  Multiplier to use when converting from Montgomery form.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_mont_sqrmod(mp_int* a, mp_int* m, mp_int* r, mp_digit mp)
{
    int err;

    err = mp_sqr(a, r);
    if (err == 0) {
        err = mp_montgomery_reduce(r, m, mp);
    }

    return err;
}

/*
 * Multiply a by b modulo m in Montgomery.
 *
 * @param  [in]   a   MP integer that is first number to multiply.
 * @param  [in]   b   MP integer that is second number to multiply.
 * @param  [in]   m   MP integer that is modulus.
 * @param  [out]  r   MP integer that is the result.
 * @param  [in]   mp  Multiplier to use when converting from Montgomery form.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_mont_mulmod(mp_int* a, mp_int* b, mp_int* m, mp_int* r,
        mp_digit mp)
{
    int err;

    err = mp_mul(a, b, r);
    if (err == 0) {
        err = mp_montgomery_reduce(r, m, mp);
    }

    return err;
}

/*
 * Add a and b modulo m. r = a + b % m
 *
 * @param  [in]   a   MP integer that is first number to add.
 * @param  [in]   b   MP integer that is second number to add.
 * @param  [out]  m   MP integer that is modulus.
 * @param  [in]   r   MP integer that is the result.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_addmod(mp_int* a, mp_int* b, mp_int* m, mp_int* r)
{
    int err;

    err = mp_add(a, b, r);
    if ((err == 0) && (mp_cmp(r, m) != MP_LT)) {
        err = mp_sub(r, m, r);
    }

    return err;
}

/*
 * Triple a modulo m. r = 3.a % m
 *
 * @param  [in]   a   MP integer that is number to triple
 * @param  [out]  m   MP integer that is modulus.
 * @param  [in]   r   MP integer that is the result.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_tplmod(mp_int* a, mp_int* m, mp_int* r)
{
    int err;

    err = mp_mul_d(a, 3, r);
    if ((err == 0) && (mp_cmp(r, m) != MP_LT)) {
        err = mp_sub(r, m, r);
    }
    if ((err == 0) && (mp_cmp(r, m) != MP_LT)) {
        err = mp_sub(r, m, r);
    }
    if ((err == 0) && (mp_cmp(r, m) != MP_LT)) {
        err = mp_sub(r, m, r);
    }

    return err;
}

/*
 * Subtract b from a modulo m. r = a - b % m
 *
 * @param  [in]   a   MP integer that is first number to add.
 * @param  [in]   b   MP integer that is second number to add.
 * @param  [in]   m   MP integer that is modulus.
 * @param  [out]  r   MP integer that is the result.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_submod(mp_int* a, mp_int* b, mp_int* m, mp_int* r)
{
    int err;

#if !defined(WOLFSSL_SP_MATH_ALL) || defined(WOLFSSL_SP_INT_NEGATIVE)
    err = mp_sub(a, b, r);
    if ((err == 0) && mp_isneg(r)) {
        err = mp_add(r, m, r);
    }
#else
    err = sp_submod_ct(a, b, m, r);
#endif

    return err;
}

/*
 * Square the element of PF_p[q] (projectivization of F_p with order q).
 *
 * Calculation:
 *   r.x = (p.x + p.y) * (p.x - p.y)
 *   r.y = (p.x * p.y) * 2
 *
 * @param  [in]   p      MP projective integer - value to square.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  r      MP projective integer - Result of square.
 * @param  [in]   t1     MP integer temporary.
 * @param  [in]   t2     MP integer temporary.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_proj_sqr(mp_proj* p, mp_int* prime, mp_digit mp, mp_proj* r,
        mp_int* t1, mp_int* t2)
{
    int err;

    /* t1 = p.x + p.y */
    err = sakke_addmod(p->x, p->y, prime, t1);
    /* t2 = p.x - p.y */
    if (err == 0) {
        err = sakke_submod(p->x, p->y, prime, t2);
    }
    /* r.y = p.x * p.y */
    if (err == 0) {
        err = sakke_mont_mulmod(p->x, p->y, prime, r->y, mp);
    }
    /* r.x = (p.x + p.y) * (p.x - p.y) */
    if (err == 0) {
        err = sakke_mont_mulmod(t1, t2, prime, r->x, mp);
    }
    /* r.y = (p.x * p.y) * 2 */
    if (err == 0) {
        err = sakke_addmod(r->y, r->y, prime, r->y);
    }

    return err;
}

/*
 * Multiply two elements of PF_p[q] (projectivization of F_p with order q).
 *
 * q must not be the same object as r.
 * Calculation:
 *   r.x = (p.x * q.x) - (p.y * q.y)
 *   r.y = (p.x * q.y) + (p.y * q.x)
 *
 * @param  [in]   p      MP projective integer - first value to multiply.
 * @param  [in]   q      MP projective integer - second value to multiply.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  r      Result of operation.
 * @param  [in]   t1     MP integer temporary.
 * @param  [in]   t2     MP integer temporary.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_proj_mul(mp_proj* p, mp_proj* q, mp_int* prime, mp_digit mp,
        mp_proj* r, mp_int* t1, mp_int* t2)
{
    int err;

    /* t1 = p.x * q.y */
    err = sakke_mont_mulmod(p->x, q->y, prime, t1, mp);
    /* r->x = p.x * q.x */
    if (err == 0) {
        err = sakke_mont_mulmod(p->x, q->x, prime, r->x, mp);
    }
    /* t2 = p.y * q.y */
    if (err == 0) {
        err = sakke_mont_mulmod(p->y, q->y, prime, t2, mp);
    }
    /* r.x = (p.x * q.x) - (p.y * q.y) */
    if (err == 0) {
        err = sakke_submod(r->x, t2, prime, r->x);
    }
    /* r.y = p.y * q.x */
    if (err == 0) {
        err = sakke_mont_mulmod(p->y, q->x, prime, r->y, mp);
    }
    /* r.y = (p.x * q.y) + (p.y * q.x) */
    if (err == 0) {
        err = sakke_addmod(t1, r->y, prime, r->y);
    }

    return err;
}

/*
 * Multiply two elements of PF_p[q] (projectivization of F_p with order q).
 *
 * q must not be the same object as r.
 * Calculation:
 *   r.x = (p.x * q.x) - (p.y * q.y)
 *   r.y = (p.x * q.y) + (p.y * q.x)
 * But qx = 1
 *   r.x = p.x - (p.y * q.y)
 *   r.y = (p.x * q.y) + p.y
 *
 * @param  [in]   p      MP projective integer - first value to multiply.
 * @param  [in]   q      MP projective integer - second value to multiply.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  r      Result of operation.
 * @param  [in]   t1     MP integer temporary.
 * @param  [in]   t2     MP integer temporary.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_proj_mul_qx1(mp_proj* p, mp_int* q, mp_int* prime, mp_digit mp,
        mp_proj* r, mp_int* t1, mp_int* t2)
{
    int err;

    /* t1 = p.x * q.y */
    err = sakke_mont_mulmod(p->x, q, prime, t1, mp);
    /* t2 = p.y * q.y */
    if (err == 0) {
        err = sakke_mont_mulmod(p->y, q, prime, t2, mp);
    }
    /* r.x = p.x - (p.y * q.y) */
    if (err == 0) {
        err = sakke_submod(p->x, t2, prime, r->x);
    }
    /* r.y = (p.x * q.y) + p.y */
    if (err == 0) {
        err = sakke_addmod(t1, p->y, prime, r->y);
    }

    return err;
}

/*
 * Calculate the gradient of line through P, P and [-2]P.
 *
 * @param  [in]   p      ECC point - first point on the elliptic curve.
 * @param  [in]   t2     MP integer temporary.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  l      MP integer representing gradient.
 * @param  [out]  z2     MP integer representing p.z^2.
 */
static int sakke_calc_dbl_rx(ecc_point* p, ecc_point* q, mp_int* prime,
        mp_digit mp, mp_proj* r, mp_int* l, mp_int* z2)
{
    int err;
    mp_int* t = r->y;

    /* z2 = p.z^2 */
    err = sakke_mont_sqrmod(p->z, prime, z2, mp);
    /* t = p.x + p.z^2 */
    if (err == 0) {
        err = sakke_addmod(p->x, z2, prime, l);
    }
    /* r1 = p.x - p.z^2 */
    if (err == 0) {
        err = sakke_submod(p->x, z2, prime, t);
    }
    /* l = ((p.x - p.z^2) * (p.x + p.z^2) = p.x ^ 2 - p.z^4  */
    if (err == 0) {
        err = sakke_mont_mulmod(l, t, prime, l, mp);
    }
    /* l = ((p.x ^ 2) - p.z^4) * 3 */
    if (err == 0) {
        err = sakke_tplmod(l, prime, l);
    }
    /* t = q.x * p.z^2 */
    if (err == 0) {
        err = sakke_mont_mulmod(q->x, z2, prime, t, mp);
    }
    /* t = p.x + q.x * p.z^2 */
    if (err == 0) {
        err = sakke_addmod(p->x, t, prime, t);
    }
    /* r.x = l * (p.x + q.x * p.z^2) */
    if (err == 0) {
        err = sakke_mont_mulmod(l, t, prime, r->x, mp);
    }

    return err;
}

#ifdef WOLFSSL_SAKKE_SMALL
/*
 * Calculate gradient of line through P, P and [-2]P and accumulate line.
 *
 * Calculation:
 *   l = 3 * (p.x^2 - p.z^4) = 3 * (p.x - p.z^2) * (p.x + p.z^2)
 *   r.x = l * (p.x + q.x * p.z^2) - 2 * p.y^2
 *   r.y = 2 * p.y * p.z^3 * q.y
 *   v* = v*^2 * r*
 *
 * @param  [in]   p      ECC point - first point on the elliptic curve.
 * @param  [in]   q      ECC point - second point on the elliptic curve.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  r      MP projective integer - gradient in PF_p[q].
 * @param  [in]   t1     MP integer temporary.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_accumulate_line_dbl(mp_proj* v, ecc_point* p, ecc_point* q,
        mp_int* prime, mp_digit mp, mp_proj* r, mp_int** t)
{
    int err;
    mp_int* t1 = t[0];
    mp_int* t2 = r->z;
    mp_int* z2 = t[1];
    mp_int* l = t1;

    /* v = v^2 */
    err = sakke_proj_sqr(v, prime, mp, v, t1, t2);
    /* l = 3 * (p.x^2 - p.z^4), z2 = p.z^2, rx = l * (p.x + q.x * p.z^2) */
    if (err == 0) {
        err = sakke_calc_dbl_rx(p, q, prime, mp, r, l, z2);
    }
    /* t1 = p.y ^ 2 */
    if (err == 0) {
        err = sakke_mont_sqrmod(p->y, prime, t1, mp);
    }
    /* t1 = 2 * (p.y ^ 2) */
    if (err == 0) {
        err = sakke_addmod(t1, t1, prime, t1);
    }
    /* r.x -= 2 * (p.y ^ 2) */
    if (err == 0) {
        err = sakke_submod(r->x, t1, prime, r->x);
    }
    /* r.y = p.y * 2 */
    if (err == 0) {
        err = sakke_addmod(p->y, p->y, prime, r->y);
    }
    /* r.y = (p.y * 2) * q.y */
    if (err == 0) {
        err = sakke_mont_mulmod(r->y, q->y, prime, r->y, mp);
    }
    /* t2 = p.z^3 */
    if (err == 0) {
        err = sakke_mont_mulmod(p->z, z2, prime, t2, mp);
    }
    /* r.y *= p.z^3 */
    if (err == 0) {
        err = sakke_mont_mulmod(r->y, t2, prime, r->y, mp);
    }
    /* v = v^2 * r */
    if (err == 0) {
        err = sakke_proj_mul(v, r, prime, mp, v, t1, t2);
    }

    return err;
}

/*
 * Calculate gradient of line through C, P and -C-P and accumulate line.
 *
 * Calculations:
 *   r.x = (q.x + p.x) * c.y - (q.x * c.z^2 + c.x) * p.y * c.z
 *   r.y = (c.x - p.x * c.z^2) * q.y * c.z
 *   v* = v* * r*
 *
 * @param  [in]   p      First point on elliptic curve.
 * @param  [in]   q      Second point on elliptic curve.
 * @param  [in]   c      Third point on elliptic curve.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  r      Resulting gradient in PF_p[q].
 * @param  [in]   t      MP integer temporary.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_accumulate_line_add_one(mp_proj* v, mp_int* prime, mp_digit mp,
        ecc_point* p, ecc_point* q, ecc_point* c, mp_proj* r, mp_int* t1)
{
    int err;
    mp_int* t2 = r->z;

    /* r.x = (q.x + p.x) * c.y */
    err = sakke_addmod(q->x, p->x, prime, r->x);
    if (err == 0) {
        err = sakke_mont_mulmod(r->x, c->y, prime, r->x, mp);
    }
    /* t2 = c.z^2 */
    if (err == 0) {
        err = sakke_mont_sqrmod(c->z, prime, t2, mp);
    }
    /* t = q.x * c.z^2 */
    if (err == 0) {
        err = sakke_mont_mulmod(q->x, t2, prime, t1, mp);
    }
    /* t = q.x * c.z^2 + c.x */
    if (err == 0) {
        err = sakke_addmod(t1, c->x, prime, t1);
    }
    /* t = (q.x * c.z^2 + c.x) * p.y */
    if (err == 0) {
        err = sakke_mont_mulmod(t1, p->y, prime, t1, mp);
    }
    /* t *= c.z */
    if (err == 0) {
        err = sakke_mont_mulmod(t1, c->z, prime, t1, mp);
    }
    /* r.x -= t */
    if (err == 0) {
        err = sakke_submod(r->x, t1, prime, r->x);
    }
    /* t = p.x * c.z^2 */
    if (err == 0) {
        err = sakke_mont_mulmod(p->x, t2, prime, t1, mp);
    }
    /* r.y = c.x - p.x * c.z^2 */
    if (err == 0) {
        err = sakke_submod(c->x, t1, prime, r->y);
    }
    /* r.y = (c.x - p.x) * q.y */
    if (err == 0) {
        err = sakke_mont_mulmod(r->y, q->y, prime, r->y, mp);
    }
    /* r.y = c.x - p.x) * q.y * c.z */
    if (err == 0) {
        err = sakke_mont_mulmod(r->y, c->z, prime, r->y, mp);
    }
    /* v = v * r */
    if (err == 0) {
        err = sakke_proj_mul(v, r, prime, mp, v, t1, t2);
    }

    return err;
}
#else
/*
 * Calculate gradient of line through P, P and [-2]P and accumulate line.
 * Double the point p.
 *
 * Calculation:
 *   l = 3 * (p.x^2 - p.z^4) = 3 * (p.x - p.z^2) * (p.x + p.z^2)
 *   r.x = l * (p.x + q.x * p.z^2) - 2 * p.y^2
 *   r.y = 2 * p.y * p.z^3 * q.y
 *   v* = v*^2 * r*
 *   p'.x = l^2 - 8 * p.y^2 * p.x
 *   p'.y = (4 * p.y^2 * p.x - p'.x) * l - 8 * p.y^4
 *   p'.z = 2 * p.y * p.z
 *
 * @param  [in]   p      ECC point - first point on the elliptic curve.
 * @param  [in]   q      ECC point - second point on the elliptic curve.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  r      MP projective integer - gradient in PF_p[q].
 * @param  [in]   t1     MP integer temporary.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_accumulate_line_dbl(mp_proj* v, ecc_point* p, ecc_point* q,
        mp_int* prime, mp_digit mp, mp_proj* r, mp_int** t)
{
    int err = 0;
    mp_int* t1 = t[0];
    mp_int* t2 = r->z;
    mp_int* z2 = t[1];
#ifdef WOLFSSL_SMALL_STACK
    mp_int* l = NULL;
    mp_int* ty = NULL;
    l = (mp_int *)XMALLOC(sizeof(*l), NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (l == NULL)
        err = 1;
    ty = (mp_int *)XMALLOC(sizeof(*ty), NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (ty == NULL)
        err = 1;
#else
    mp_int tmp[2];
    mp_int* l = &tmp[0];
    mp_int* ty = &tmp[1];
#endif

    if (err == 0)
        err = mp_init(l);
    if (err == 0) {
        err = mp_init(ty);
    }

    /* v = v^2 */
    if (err == 0) {
        err = sakke_proj_sqr(v, prime, mp, v, t1, t2);
    }
    /* l = 3 * (p.x^2 - p.z^4), z2 = p.z^2, rx = l * (p.x + q.x * p.z^2) */
    if (err == 0) {
        err = sakke_calc_dbl_rx(p, q, prime, mp, r, l, z2);
    }
    /* ty = p.y ^ 2 */
    if (err == 0) {
        err = sakke_mont_sqrmod(p->y, prime, ty, mp);
    }
    /* ty = 2 * (p.y ^ 2) */
    if (err == 0) {
        err = sakke_addmod(ty, ty, prime, ty);
    }
    /* r.x -= 2 * (p.y ^ 2) */
    if (err == 0) {
        err = sakke_submod(r->x, ty, prime, r->x);
    }
    /* r.y = p.y * 2 */
    if (err == 0) {
        err = sakke_addmod(p->y, p->y, prime, r->y);
    }
    /* r.y = p.y * 2 * p.z */
    if (err == 0) {
        err = sakke_mont_mulmod(r->y, p->z, prime, p->z, mp);
    }
    /* r.y = p.y * 2 * p.z^3 */
    if (err == 0) {
        err = sakke_mont_mulmod(p->z, z2, prime, r->y, mp);
    }
    /* r.y = (p.y * 2 * p.z^3) * q.y */
    if (err == 0) {
        err = sakke_mont_mulmod(r->y, q->y, prime, r->y, mp);
    }
    /* v = v^2 * r */
    if (err == 0) {
        err = sakke_proj_mul(v, r, prime, mp, v, t1, t2);
    }

    /* Double point using previously calculated values
     *   l = 3 * (X - Z^2).(X + Z^2)
     *   ty = 2 * Y^2
     *   Z = 2 * Y * Z
     */
    /* Y = 2 * 2 * Y^2 */
    if (err == 0) {
        err = sakke_addmod(ty, ty, prime, p->y);
    }
    /* T2 = 4 * Y^4 */
    if (err == 0) {
        err = sakke_mont_sqrmod(ty, prime, t2, mp);
    }
    /* T2 = 8 * Y^4 */
    if (err == 0) {
        err = sakke_addmod(t2, t2, prime, t2);
    }
    /* Y = Y * X */
    if (err == 0) {
        err = sakke_mont_mulmod(p->y, p->x, prime, p->y, mp);
    }
    /* X = l * l */
    if (err == 0) {
        err = sakke_mont_sqrmod(l, prime, p->x, mp);
    }
    /* X = X - Y */
    if (err == 0) {
        err = sakke_submod(p->x, p->y, prime, p->x);
    }
    /* X = X - Y */
    if (err == 0) {
        err = sakke_submod(p->x, p->y, prime, p->x);
    }
    /* Y = Y - X */
    if (err == 0) {
        err = sakke_submod(p->y, p->x, prime, p->y);
    }
    /* Y = Y * l */
    if (err == 0) {
        err = sakke_mont_mulmod(p->y, l, prime, p->y, mp);
    }
    /* Y = Y - T2 */
    if (err == 0) {
        err = sakke_submod(p->y, t2, prime, p->y);
    }

#ifdef WOLFSSL_SMALL_STACK
    if (ty != NULL) {
        mp_free(ty);
        XFREE(ty, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    }
    if (l != NULL) {
        mp_free(l);
        XFREE(l, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    }
#else
    mp_free(ty);
    mp_free(l);
#endif

    return err;
}

/*
 * Calculate gradient of line through C, P and -C-P and accumulate line.
 * Add point p into c.
 *
 * Calculations:
 *   r.x = (q.x + p.x) * c.y - (q.x * c.z^2 + c.x) * p.y * c.z
 *   r.y = (c.x - p.x * c.z^2) * q.y * c.z
 *   v* = v* * r*
 *   r = p.y * c.z^3 - c.y
 *   c'.x = r^2 + h^3 - 2 * c.x * h^2
 *   c'.y = r * (c'.x - c.x * h^2) - c.y * h^3
 *   c'.z = (c.x - p.x * c.z^2) * c.z
 *
 * @param  [in]   p      First point on elliptic curve.
 * @param  [in]   q      Second point on elliptic curve.
 * @param  [in]   c      Third point on elliptic curve.
 * @param  [in]   prime  MP integer that is the modulus of the field.
 * @param  [in]   mp     Multiplier to use when converting from Montgomery form.
 * @param  [out]  r      Resulting gradient in PF_p[q].
 * @param  [in]   t      MP integer temporary.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_accumulate_line_add_one(mp_proj* v, mp_int* prime, mp_digit mp,
        ecc_point* p, ecc_point* q, ecc_point* c, mp_proj* r, mp_int** t)
{
    int err = 0;
    mp_int* t1 = t[0];
    mp_int* t2 = t[1];
#ifdef WOLFSSL_SMALL_STACK
    mp_int* h = NULL;
    mp_int* ty = NULL;
    mp_int* tz = NULL;
    mp_int* t3 = NULL;
    h = (mp_int *)XMALLOC(sizeof(*h), NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (h == NULL)
        err = 1;
    ty = (mp_int *)XMALLOC(sizeof(*ty), NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (ty == NULL)
        err = 1;
    tz = (mp_int *)XMALLOC(sizeof(*tz), NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (tz == NULL)
        err = 1;
    t3 = (mp_int *)XMALLOC(sizeof(*t3), NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (t3 == NULL)
        err = 1;
#else
    mp_int tmp[4];
    mp_int* h = &tmp[0];
    mp_int* ty = &tmp[1];
    mp_int* tz = &tmp[2];
    mp_int* t3 = &tmp[3];
#endif

    if (err == 0)
        err = mp_init_multi(h, ty, tz, t3, NULL, NULL);

    /* r.x = (q.x + p.x) * c.y */
    if (err == 0) {
        err = sakke_addmod(q->x, p->x, prime, r->x);
    }
    if (err == 0) {
        err = sakke_mont_mulmod(r->x, c->y, prime, r->x, mp);
    }
    /* tz = c.z^2 */
    if (err == 0) {
        err = sakke_mont_sqrmod(c->z, prime, tz, mp);
    }
    /* t = q.x * c.z^2 */
    if (err == 0) {
        err = sakke_mont_mulmod(q->x, tz, prime, t1, mp);
    }
    /* t = q.x * c.z^2 + c.x */
    if (err == 0) {
        err = sakke_addmod(t1, c->x, prime, t1);
    }
    /* ty = p.y * c.z */
    if (err == 0) {
        err = sakke_mont_mulmod(p->y, c->z, prime, ty, mp);
    }
    /* t = (q.x * c.z^2 + c.x) * p.y * c.z */
    if (err == 0) {
        err = sakke_mont_mulmod(t1, ty, prime, t1, mp);
    }
    /* r.x -= t */
    if (err == 0) {
        err = sakke_submod(r->x, t1, prime, r->x);
    }
    /* t = p.x * c.z^2 */
    if (err == 0) {
        err = sakke_mont_mulmod(p->x, tz, prime, t1, mp);
    }
    /* h = c.x - p.x * c.z^2 */
    if (err == 0) {
        err = sakke_submod(c->x, t1, prime, h);
    }
    /* t3 = (c.x - p.x * c.z^2 ) * c.z*/
    if (err == 0) {
        err = sakke_mont_mulmod(h, c->z, prime, t3, mp);
    }
    /* r.y = (c.x - p.x * c.z^2) * c.z * q.y */
    if (err == 0) {
        err = sakke_mont_mulmod(t3, q->y, prime, r->y, mp);
    }
    /* v = v * r */
    if (err == 0) {
        err = sakke_proj_mul(v, r, prime, mp, v, t1, t2);
    }

    /* Add p to c using previously calculated values.
     *   h = c.x - p.x * c.z^2
     *   ty = p.y * c.z
     *   tz = c.z^2
     *   t3 = (c.x - p.x * c.z^2) * c.z
     */

    /* R = p.y * c.z^3 - c.y */
    if (err == 0) {
        err = sakke_mont_mulmod(ty, tz, prime, ty, mp);
    }
    if (err == 0) {
        err = sakke_submod(ty, c->y, prime, ty);
    }
    /* c'.z = -H * c.z */
    if (err == 0) {
        err = sakke_submod(prime, t3, prime, c->z);
    }
    /* c'.x = R^2 + H^3 - 2 * c.x * H^2 */
    if (err == 0) {
        err = sakke_mont_sqrmod(ty, prime, t1, mp);
    }
    if (err == 0) {
        err = sakke_mont_sqrmod(h, prime, t2, mp);
    }
    if (err == 0) {
        err = sakke_mont_mulmod(c->x, t2, prime, t3, mp);
    }
    if (err == 0) {
        err = sakke_mont_mulmod(t2, h, prime, t2, mp);
    }
    if (err == 0) {
        err = sakke_addmod(t1, t2, prime, c->x);
    }
    if (err == 0) {
        err = sakke_addmod(t3, t3, prime, t1);
    }
    if (err == 0) {
        err = sakke_submod(c->x, t1, prime, c->x);
    }
    /* c'.y = R * (c.x * H^2 - c'.x) + c.y * H^3 */
    if (err == 0) {
        err = sakke_submod(t3, c->x, prime, t3);
    }
    if (err == 0) {
        err = sakke_mont_mulmod(t3, ty, prime, t3, mp);
    }
    if (err == 0) {
        err = sakke_mont_mulmod(t2, c->y, prime, t2, mp);
    }
    if (err == 0) {
        err = sakke_addmod(t3, t2, prime, c->y);
    }

#ifdef WOLFSSL_SMALL_STACK
    if (t3 != NULL) {
        mp_free(t3);
        XFREE(t3, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    }
    if (tz != NULL) {
        mp_free(tz);
        XFREE(tz, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    }
    if (ty != NULL) {
        mp_free(ty);
        XFREE(ty, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    }
    if (h != NULL) {
        mp_free(h);
        XFREE(h, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    }
#else
    mp_free(t3);
    mp_free(tz);
    mp_free(ty);
    mp_free(h);
#endif

    return err;
}
#endif /* WOLFSSL_SAKKE_SMALL */

/*
 * Calculate r = pairing <P, Q>.
 *
 * That is, multiply base in PF_p[q] by the scalar s, such that s.P = Q.
 *
 * @param  [in]   key  SAKKE key.
 * @param  [in]   p    First point on E(F_p)[q].
 * @param  [in]   q    Second point on E(F_p)[q].
 * @param  [out]  r    Result of calculation.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_pairing(SakkeKey* key, ecc_point* p, ecc_point* q, mp_int* r,
    const byte* table, word32 len)
{
    int err;
    ecc_point* v = key->params.base;
    ecc_point* c = key->tmp.p1;
    mp_proj* t2 = key->tmp.p3;
    mp_int* t3 = &key->tmp.m2;
    mp_int* prime = &key->params.prime;
    mp_int* t[] = { &key->tmp.m1, t3 };
    int i;
    mp_digit mp = 0;
    SakkeKeyParams* params = &key->params;

    (void)table;
    (void)len;

    err = sakke_point_to_mont(p, prime, &key->tmp.m1, 0);
    if (err == 0) {
        err = sakke_point_to_mont(q, prime, &key->tmp.m1, 1);
    }
    if (err == 0) {
        err = wc_ecc_copy_point(p, c);
    }
    /* Set v to 1. */
    if (err == 0) {
        params->haveBase = 0;
        err = mp_set(v->x, 1);
    }
    if (err == 0) {
        err = mp_set(v->y, 0);
    }
    if (err == 0) {
        err = mp_montgomery_setup(prime, &mp);
    }

    for (i = mp_count_bits(&params->q) - 2; (err == 0) && (i >= 0); i--) {
#ifdef WOLFSSL_SAKKE_SMALL
        /* Accumulate line into v and double point. */
        err = sakke_accumulate_line_dbl(v, c, q, prime, mp, t2, t);
        if (err == 0) {
            err = ecc_projective_dbl_point(c, c, NULL, prime, mp);
        }

        if ((err == 0) && (i > 0) && mp_is_bit_set(&params->q, i)) {
            /* Accumulate line into v and add P into C. */
            err = sakke_accumulate_line_add_one(v, prime, mp, p, q, c, t2,
                    &key->tmp.m1);
            if (err == 0) {
                err = ecc_projective_add_point(p, c, c, NULL, prime, mp);
            }
        }
#else
        /* Accumulate line into v and double point. */
        err = sakke_accumulate_line_dbl(v, c, q, prime, mp, t2, t);

        if ((err == 0) && (i > 0) && mp_is_bit_set(&params->q, i)) {
            /* Accumulate line into v and add P into C. */
            err = sakke_accumulate_line_add_one(v, prime, mp, p, q, c, t2, t);
        }
#endif /* WOLFSSL_SAKKE_SMALL */
    }

    /* Final exponentiation */
    if (err == 0) {
        err = sakke_proj_sqr(v, prime, mp, v, &key->tmp.m1, t3);
    }
    if (err == 0) {
        err = sakke_proj_sqr(v, prime, mp, v, &key->tmp.m1, t3);
    }
    /* Convert from PF_p[q] to F_p */
    if (err == 0) {
        err = mp_invmod(v->x, prime, r);
    }
    if (err == 0) {
        err = mp_mulmod(r, v->y, prime, r);
    }

    if (err == 0) {
        err = sakke_point_from_mont(p, prime, mp);
    }
    if (err == 0) {
        err = sakke_point_from_mont(q, prime, mp);
    }

    return err;
}
#endif /* WOLFSSL_HAVE_SP_ECC */

/**
 * Set the Receiver Secret Key (RSK) and any table associated with it.
 *
 * @param  [in]  key    SAKKE key.
 * @param  [in]  rsk    Receiver Secret Key (RSK) as an ECC point.
 * @param  [in]  table  Pre-computation table. May be NULL.
 * @param  [in]  len    Size of pre-computation table in bytes.
 * @return  0 on success.
 * @return BAD_FUNC_ARG when key or rsk is NULL.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
int wc_SetSakkeRsk(SakkeKey* key, const ecc_point* rsk, byte* table, word32 len)
{
    int err = 0;

    if ((key == NULL) || (rsk == NULL)) {
        err = BAD_FUNC_ARG;
    }
    if (err == 0) {
        key->rsk.set = 0;
        err = wc_ecc_copy_point(rsk, key->rsk.rsk);
    }
    if (err == 0) {
        key->rsk.table = table;
        key->rsk.tableLen = len;
        key->rsk.set = 1;
    }

    return err;
}

/*
 * Compute the elliptic curve point I for device B. Partial for point R.
 *
 * RFC 6508, Section 6.2.1, Step 3.\n
 * RFC 6508, Section 6.2.2, Step 5.\n
 * I = [b]P + Z_S
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   id    Identifier to of device B.
 * @param  [in]   idSz  Size of identifier in bytes.
 * @param  [out]  i     ECC point - partial for point R.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_compute_point_i(SakkeKey* key, const byte* id, word16 idSz,
        ecc_point* i)
{
    int err;
    mp_int* b = &key->ecc.k;

    /* Load b - ID of receiver */
    err = mp_read_unsigned_bin(b, id, idSz);
    if (err == 0) {
        err = sakke_load_base_point(key);
    }
#ifndef WOLFSSL_HAVE_SP_ECC
    /* Convert to montgomery form for add operation. */
    if (err == 0) {
        err = sakke_z_to_mont(key, &key->tmp.m2);
    }
#endif
    /* [b]P + Z_S */
    if (err == 0) {
        ecc_point* z = &key->ecc.pubkey;
        err = sakke_mulmod_base_add(key, b, z, i, 1);
    }
    return err;
}

/**
 * Validate the Receiver Secret Key (RSK) with the identity.
 *
 * RFC 6508, Section 6.1.2
 *
 * A receiving client should validate an RSK before use.
 *
 * @param  [in]   key    SAKKE key.
 * @param  [in]   id     Identity to use.
 * @param  [in]   idSz   Size of identity in bytes.
 * @param  [in]   rsk    Receiver Secret Key as an ECC point.
 * @param  [out]  valid  1 indicates RSK is valid for identity.
 *                       0 otherwise.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, id, rsk or valid is NULL.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
int wc_ValidateSakkeRsk(SakkeKey* key, const byte* id, word16 idSz,
        ecc_point* rsk, int* valid)
{
    int err = 0;
    mp_int* a = NULL;

    if ((key == NULL) || (id == NULL) || (rsk == NULL) || (valid == NULL)) {
        err = BAD_FUNC_ARG;
    }

    SAVE_VECTOR_REGISTERS(return _svr_ret;);

    /* Load elliptic curve parameters */
    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        err = sakke_load_base_point(key);
    }
    /* Load pairing base - g */
    if (err == 0) {
        err = sakke_load_pairing_base(key);
    }
    /* Load a - identifier */
    if (err == 0) {
        a = &key->tmp.m1;
        err = mp_read_unsigned_bin(a, id, idSz);
    }

    if (err == 0) {
        /* I = [b]P + Z_S */
        err = sakke_compute_point_i(key, id, idSz, key->i.i);
        if ((err == 0) && (idSz <= SAKKE_ID_MAX_SIZE)) {
            XMEMCPY(key->i.id, id, idSz);
            key->i.idSz = idSz;
        }
    }
    /* < [a]P + Z, K_(a,T) > = < K_(a,T), [a]P + Z > = < rsk, i >*/
    if (err == 0) {
        err = sakke_pairing(key, rsk, key->i.i, a, NULL, 0);
    }

    /* Compare pairing result with generator. */
    if (valid != NULL) {
        *valid = ((err == 0) && (mp_cmp(a, &key->params.g) == MP_EQ));
    }

    RESTORE_VECTOR_REGISTERS();

    return err;
}

/**
 * Get the size of the authentication data that is the first part of the
 * encapsulated data.
 *
 * Clients need to know how long the authentication data so as the SSV starts
 * after the authentication data in a buffer.\n
 * For SAKKE parameter set 1: 257 bytes
 *
 * @param  [in]   key     SAKKE key.
 * @param  [out]  authSz  Size of authentication data in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or authSz is NULL.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
int wc_GetSakkeAuthSize(SakkeKey* key, word16* authSz)
{
    int err = 0;

    if ((key == NULL) || (authSz == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        word16 n = (word16)((mp_count_bits(&key->params.prime) + 7) / 8);
        *authSz = 1 + 2 * n;
    }

    return err;
}

#ifdef WOLFSSL_HAVE_SP_ECC
/*
 * Modular exponentiate the value in F_p*.
 *
 * @param  [in]   key  SAKKE key.
 * @param  [in]   b    MP integer that is the base to exponentiate.
 * @param  [in]   e    MP integer that is the exponent.
 * @param  [out]  r    Result of exponentiation.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_modexp(const SakkeKey* key, const mp_int* b, mp_int* e,
        mp_int* r)
{
    int err = NOT_COMPILED_IN;

#ifdef WOLFSSL_SP_1024
    if ((key->ecc.idx != ECC_CUSTOM_IDX) &&
            (ecc_sets[key->ecc.idx].id == ECC_SAKKE_1)) {
        err = sp_ModExp_Fp_star_1024(b, e, r);
    }
#endif

    return err;
}
#else
#ifdef WOLFSSL_SAKKE_SMALL
/*
 * Modular exponentiate the value in F_p*.
 *
 * @param  [in]   key  SAKKE key.
 * @param  [in]   b    MP integer that is the base to exponentiate.
 * @param  [in]   e    MP integer that is the exponent.
 * @param  [out]  c    Result of exponentiation.
 * @param  [in]   mp   Multiplier to use when converting from Montgomery form.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_modexp_loop(SakkeKey* key, mp_int* b, mp_int* e, mp_proj* c,
        mp_digit mp)
{
    int err;
    mp_int* t1 = &key->tmp.m1;
    mp_int* t2 = &key->tmp.m2;
    mp_int* by = key->tmp.p1->z;
    mp_int* prime = &key->params.prime;
    int i;

    /* Set the working value to the base in PF_p[q] */
    err = mp_montgomery_calc_normalization(c->x, prime);
    /* Set c->y as montgomery form of b - base */
    if (err == 0) {
        err = mp_mulmod(b, c->x, prime, by);
    }
    /* Set by as montgomery form of b - base */
    if (err == 0) {
        err = mp_copy(by, c->y);
    }
    /* Simple non-constant time exponentiation over a field. */
    for (i = mp_count_bits(e) - 2; (err == 0) && (i >= 0); i--) {
        err = sakke_proj_sqr(c, prime, mp, c, t1, t2);
        if (err == 0) {
            if (mp_is_bit_set(e, i)) {
                err = sakke_proj_mul_qx1(c, by, prime, mp, c, t1, t2);
            }
        }
    }

    return err;
}

#elif defined(WOLFSSL_SAKKE_SMALL_MODEXP) || !defined(USE_FAST_MATH)

/*
 * Modular exponentiate the value in F_p*.
 *
 * @param  [in]   key  SAKKE key.
 * @param  [in]   b    MP integer that is the base to exponentiate.
 * @param  [in]   e    MP integer that is the exponent.
 * @param  [out]  r    Result of exponentiation.
 * @param  [in]   mp   Multiplier to use when converting from Montgomery form.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_modexp_loop(SakkeKey* key, mp_int* b, mp_int* e, mp_proj* r,
        mp_digit mp)
{
    int err;
#ifdef WC_NO_CACHE_RESISTANT
    mp_proj* c[2] = { r, key->tmp.p2 };
#else
    mp_proj* c[3] = { r, key->tmp.p3, key->tmp.p2 };
#endif
    mp_int* t1 = &key->tmp.m1;
    mp_int* t2 = &key->tmp.m2;
    mp_int* by = key->tmp.p1->z;
    mp_int* prime = &key->params.prime;
    int i;

    /* Set the working value to the base in PF_p[q] */
    err = mp_montgomery_calc_normalization(c[0]->x, prime);
    /* Set c[0] to [mont_one, zero] */
    if (err == 0) {
        mp_zero(c[0]->y);

        /* Set 'by' to montgomery form of 'b' - base */
        err = mp_mulmod(b, c[0]->x, prime, by);
    }
    for (i = mp_count_bits(&key->params.q) - 1; (err == 0) && (i >= 0); i--) {
        int j = mp_is_bit_set(e, i);
        err = sakke_proj_sqr(c[0], prime, mp, c[0], t1, t2);
        if (err == 0) {
#ifdef WC_NO_CACHE_RESISTANT
            err = sakke_proj_mul_qx1(c[0], by, prime, mp, c[j^1], t1, t2);
#else
            err = sakke_proj_mul_qx1(c[0], by, prime, mp, c[2], t1, t2);
            mp_copy(c[2]->x,
            (mp_int*) ( ((wc_ptr_t)c[0]->x & wc_off_on_addr[j]) +
                        ((wc_ptr_t)c[1]->x & wc_off_on_addr[j^1]) ) );
            mp_copy(c[2]->y,
            (mp_int*) ( ((wc_ptr_t)c[0]->y & wc_off_on_addr[j]) +
                        ((wc_ptr_t)c[1]->y & wc_off_on_addr[j^1]) ) );
#endif
        }
    }

    return err;
}

#else

/* Table for 8-bit striping exponentiation. */
static const byte sakke_1024_g_table[256][128] = {
    { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
      0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
    { 0x59, 0xe9, 0x3c, 0x6a, 0x6b, 0xd3, 0xba, 0xf4, 0xaf, 0xd5,
      0x88, 0x91, 0xe8, 0x6c, 0xb2, 0x21, 0x61, 0x52, 0xba, 0x02,
      0xc7, 0x27, 0xc9, 0x8e, 0x21, 0xf1, 0x1c, 0x06, 0x7d, 0x3b,
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    { 0x54, 0xff, 0x78, 0x84, 0x79, 0xb2, 0x5d, 0x71, 0xa1, 0xc9,
      0x98, 0x13, 0xff, 0x22, 0x25, 0xab, 0xae, 0x80, 0x45, 0x3f,
      0xbb, 0x1e, 0x5b, 0xd8, 0xa7, 0xf0, 0x44, 0x0c, 0x9f, 0x68,
      0x4f, 0x25, 0x33, 0x5c, 0xc4, 0xf8, 0x5d, 0x15, 0xdf, 0xbf,
      0xff, 0x3a, 0xba, 0x5c, 0x69, 0x62, 0x80, 0x46, 0x55, 0xce,
      0x84, 0x91, 0x58, 0x80, 0xcd, 0xaf, 0x8e, 0xe0, 0x0e, 0x1a,
      0x8e, 0xef, 0x6c, 0xc9, 0x4e, 0x01, 0x41, 0xae, 0x85, 0x02,
      0xaa, 0x89, 0x20, 0x73, 0x95, 0x4c, 0xd2, 0xe9, 0x6d, 0xdf,
      0x14, 0x42, 0xbf, 0x36, 0x7d, 0xd4, 0xc5, 0x31, 0x46, 0x71,
      0x6f, 0x79, 0xa9, 0x25, 0xe7, 0xe7, 0xbb, 0x48, 0x27, 0xfa,
      0x4e, 0xb2, 0x1f, 0x6b, 0x4c, 0x93, 0x46, 0x89, 0x2f, 0xe3,
      0x74, 0xcb, 0x4b, 0x9f, 0xd0, 0x33, 0x04, 0x8b, 0x5d, 0xe9,
      0xea, 0xb2, 0x1f, 0xf0, 0xe1, 0xd0, 0xfa, 0x79 },
    { 0x8a, 0xdb, 0xad, 0x85, 0x3f, 0x18, 0x30, 0xfe, 0x4e, 0x4e,
      0x45, 0x73, 0xee, 0x30, 0xb2, 0x86, 0x8a, 0xcd, 0xa9, 0x65,
      0x9f, 0xa1, 0x01, 0xe6, 0x17, 0x87, 0x55, 0x00, 0x28, 0xc9,
      0x30, 0x2c, 0x06, 0x9e, 0x82, 0xdc, 0x36, 0x78, 0xa4, 0x27,
      0xd6, 0xa2, 0xc0, 0x1d, 0x8b, 0x6a, 0x6c, 0x6b, 0x28, 0x94,
      0x5e, 0x31, 0xc9, 0x55, 0xae, 0xad, 0x91, 0x53, 0x62, 0xdc,
      0xb7, 0x86, 0xea, 0x9f, 0x33, 0x9d, 0xf0, 0x81, 0x0c, 0xcd,
      0x9e, 0xc9, 0xc6, 0x8f, 0x1b, 0x3b, 0x4a, 0x2c, 0x08, 0xe3,
      0xbb, 0x74, 0xe5, 0x8f, 0xdc, 0xb0, 0xc0, 0x0f, 0xe3, 0x28,
      0x54, 0x41, 0x8d, 0xf9, 0x0d, 0x2b, 0x50, 0xa5, 0xa5, 0xad,
      0xc0, 0x41, 0x81, 0x15, 0xe2, 0x4a, 0x46, 0x04, 0xfa, 0x3b,
      0x21, 0xf6, 0x92, 0x26, 0x46, 0x5b, 0xe6, 0xf3, 0xa5, 0x1e,
      0x27, 0xc6, 0xee, 0x30, 0xde, 0x40, 0xb0, 0x68 },
    { 0x73, 0x93, 0x00, 0x36, 0xc0, 0x94, 0x5e, 0x5f, 0xf3, 0x42,
      0xc1, 0xaa, 0x02, 0x7e, 0x71, 0xc1, 0xb7, 0x5c, 0x41, 0xa6,
      0x66, 0xcb, 0xc9, 0x6c, 0xf5, 0x88, 0xb4, 0xf8, 0x17, 0x17,
      0xe1, 0xaf, 0x14, 0xeb, 0x86, 0xf3, 0x58, 0x40, 0x7a, 0x1d,
      0xdb, 0xe3, 0x86, 0xcb, 0x81, 0x6c, 0x07, 0x30, 0x40, 0x3f,
      0x16, 0x8c, 0x30, 0x26, 0xcd, 0x41, 0x95, 0xb1, 0x6c, 0xcc,
      0xcd, 0x5e, 0x87, 0xe7, 0x40, 0xd8, 0x6f, 0x30, 0x12, 0x43,
      0xf3, 0xef, 0x40, 0x90, 0xcf, 0xa6, 0x1b, 0x46, 0x4b, 0x28,
      0xcd, 0xbc, 0x2a, 0xd2, 0x09, 0x84, 0xfb, 0x0e, 0x6a, 0xa1,
      0xf5, 0xde, 0x8e, 0x1c, 0x0f, 0x7f, 0x45, 0x6b, 0x9c, 0xf2,
      0xe2, 0x33, 0x6d, 0x4f, 0x3c, 0xec, 0x67, 0x66, 0x7c, 0xc1,
      0xfc, 0xc2, 0xf4, 0x2f, 0xda, 0xf7, 0xf3, 0x9b, 0xcc, 0x79,
      0x06, 0x0a, 0xe1, 0x1f, 0x09, 0x69, 0xd5, 0x24 },
    { 0x8b, 0xc6, 0xec, 0x4a, 0xe4, 0x29, 0x65, 0xe2, 0x5b, 0xd1,
      0x01, 0x82, 0xaa, 0x7c, 0x99, 0xd3, 0x9c, 0x28, 0xa9, 0x67,
      0x73, 0xea, 0xf2, 0x23, 0xcf, 0x56, 0x13, 0x48, 0xe0, 0x96,
      0x1b, 0x31, 0x45, 0xb9, 0xe6, 0x1b, 0x73, 0x1f, 0xc4, 0x47,
      0x61, 0xa5, 0x14, 0xe1, 0xb5, 0x24, 0x63, 0x2f, 0x43, 0x4a,
      0xc7, 0xb1, 0x64, 0xac, 0x8f, 0x15, 0x70, 0x5d, 0xdd, 0x5a,
      0xd9, 0x11, 0x08, 0xcc, 0xda, 0xcd, 0xfd, 0x5d, 0xd2, 0x9c,
      0x01, 0xaa, 0x4b, 0xd7, 0xd6, 0x9d, 0x61, 0x17, 0x9c, 0xae,
      0x17, 0x15, 0x90, 0x3e, 0x6a, 0x4f, 0x69, 0x85, 0x92, 0xb3,
      0x05, 0xd1, 0x02, 0x2c, 0xeb, 0x91, 0x69, 0x64, 0x2e, 0x08,
      0xf1, 0x8f, 0xd5, 0xbc, 0x8b, 0x98, 0x68, 0x19, 0xf5, 0x51,
      0x4f, 0x25, 0x78, 0x8b, 0x59, 0x1d, 0xf4, 0x18, 0x1a, 0xab,
      0x95, 0x4f, 0x75, 0x7d, 0x22, 0xcd, 0xaf, 0x42 },
    { 0x8e, 0x85, 0x43, 0x7d, 0xbe, 0x9c, 0x7e, 0x15, 0x2b, 0x3c,
      0x8f, 0x71, 0xdc, 0xeb, 0x89, 0x55, 0xab, 0x01, 0x2c, 0x2c,
      0x58, 0x47, 0xa4, 0xd7, 0x28, 0x44, 0xd9, 0x6a, 0x98, 0x2f,
      0xc0, 0xd4, 0xd6, 0xa7, 0xdf, 0x0d, 0xaa, 0x60, 0xaa, 0x6a,
      0xd3, 0x08, 0xfc, 0x21, 0xae, 0x9b, 0x2a, 0xa8, 0xfc, 0x9a,
      0xc3, 0xb9, 0x48, 0xd6, 0x5c, 0xbb, 0xe5, 0x65, 0x43, 0x1c,
      0x8b, 0x65, 0xc9, 0xa1, 0xe3, 0x14, 0x71, 0xee, 0x6b, 0xe6,
      0xc8, 0xca, 0x73, 0x24, 0x83, 0xe3, 0x51, 0xb7, 0xda, 0x61,
      0xa0, 0xac, 0xfc, 0xa2, 0x2b, 0x29, 0xb2, 0xb7, 0x51, 0x0e,
      0x18, 0x60, 0x84, 0x57, 0xaa, 0x6e, 0x66, 0x55, 0xfc, 0x9c,
      0xbb, 0x60, 0x54, 0xa6, 0x06, 0xfe, 0x43, 0x7c, 0x40, 0x1e,
      0x36, 0x0c, 0xff, 0x54, 0x80, 0x0c, 0x09, 0x38, 0x8a, 0x30,
      0xd0, 0x96, 0xe5, 0xc0, 0xe7, 0xf2, 0xa3, 0x2b },
};

/*
 * Loop for modular exponentiate the value in F_p*.
 *
 * Using 8-bit stripe table.
 *
 * @param  [in]   key  SAKKE key.
 * @param  [in]   b    MP integer that is the base to exponentiate.
 * @param  [in]   e    MP integer that is the exponent.
 * @param  [out]  c    Result of exponentiation.
 * @param  [in]   mp   Multiplier to use when converting from Montgomery form.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_modexp_loop(SakkeKey* key, const mp_int* b, mp_int* e,
        mp_proj* c, mp_digit mp)
{
    int err = 0;
    mp_int* t1 = &key->tmp.m1;
    mp_int* t2 = &key->tmp.m2;
    mp_int* by = key->tmp.p1->z;
    mp_int* prime = &key->params.prime;
    unsigned char eb[128];
    int i;
    int y;

    /* Use table for values of b exponentiated. */
    (void)b;

    (void)mp_to_unsigned_bin_len(e, eb, sizeof(eb));

    /* Set the working value to the base in PF_p[q] */
    err = mp_montgomery_calc_normalization(c->x, prime);
    if (err == 0) {
        y  =  (eb[112] >> 7) & 1;
        y |= ((eb[ 96] >> 7) & 1) << 1;
        y |= ((eb[ 80] >> 7) & 1) << 2;
        y |= ((eb[ 64] >> 7) & 1) << 3;
        y |= ((eb[ 48] >> 7) & 1) << 4;
        y |= ((eb[ 32] >> 7) & 1) << 5;
        y |= ((eb[ 16] >> 7) & 1) << 6;
        y |= ((eb[  0] >> 7) & 1) << 7;

        (void)mp_read_unsigned_bin(c->y, sakke_1024_g_table[y], 128);
    }
    for (i = 128 - 2; (err == 0) && (i >= 0); i--) {
        y  =  (eb[127 -  i / 8       ] >> (i & 0x7)) & 1;
        y |= ((eb[127 - (i / 8 +  16)] >> (i & 0x7)) & 1) << 1;
        y |= ((eb[127 - (i / 8 +  32)] >> (i & 0x7)) & 1) << 2;
        y |= ((eb[127 - (i / 8 +  48)] >> (i & 0x7)) & 1) << 3;
        y |= ((eb[127 - (i / 8 +  64)] >> (i & 0x7)) & 1) << 4;
        y |= ((eb[127 - (i / 8 +  80)] >> (i & 0x7)) & 1) << 5;
        y |= ((eb[127 - (i / 8 +  96)] >> (i & 0x7)) & 1) << 6;
        y |= ((eb[127 - (i / 8 + 112)] >> (i & 0x7)) & 1) << 7;

        err = sakke_proj_sqr(c, prime, mp, c, t1, t2);
        if (err == 0) {
            (void)mp_read_unsigned_bin(by, sakke_1024_g_table[y], 128);
            err = sakke_proj_mul_qx1(c, by, prime, mp, c, t1, t2);
        }
    }

    return err;
}
#endif /* WOLFSSL_SAKKE_SMALL */

/*
 * Modular exponentiate the value in F_p*.
 *
 * @param  [in]   key  SAKKE key.
 * @param  [in]   b    MP integer that is the base to exponentiate.
 * @param  [in]   e    MP integer that is the exponent.
 * @param  [out]  r    Result of exponentiation.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_modexp(SakkeKey* key, mp_int* b, mp_int* e, mp_int* r)
{
    int err;
    mp_digit mp;
    mp_int* prime = &key->params.prime;
    mp_proj* c = key->tmp.p1;

    (void)b;

    err = mp_montgomery_setup(prime, &mp);
    if (err == 0) {
        err = sakke_modexp_loop(key, b, e, c, mp);
    }

    if (err == 0) {
        err = mp_montgomery_reduce(c->x, prime, mp);
    }
    if (err == 0) {
        err = mp_montgomery_reduce(c->y, prime, mp);
    }
    /* Convert value back from PF_p[q] to F_p* */
    if (err == 0) {
        err = mp_invmod(c->x, prime, c->x);
    }
    if (err == 0) {
        err = mp_mulmod(c->x, c->y, prime, r);
    }

    return err;
}
#endif /* WOLFSSL_HAVE_SP_ECC */

/*
 * Calculate the hash values h and v.
 *
 * RFC 6508, section 5.1, Steps 4.a and 4.b.
 *
 * @param  [in]   key       SAKKE key.
 * @param  [in]   hashType  Hash algorithm to use.
 * @param  [in]   hashSz    Size of output of hash algorithm in bytes.
 * @param  [in]   a         Hash of data and extra.
 * @param  [in]   h         Rolling hash result.
 * @param  [out]  v         Output bytes of hashing.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when hashType is not supported.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_calc_h_v(SakkeKey* key, enum wc_HashType hashType,
        word32 hashSz, const byte* a, byte* h, byte* v)
{
    int err;

    /* Step 4.a: h_i = hashfn(h_(i - 1)) */
    err = wc_HashUpdate(&key->hash, hashType, h, hashSz);
    if (err == 0) {
        err = wc_HashFinal(&key->hash, hashType, h);
    }

    /* Step 4.b: v_i = hashfn(h_i | A) */
    if (err == 0) {
        err = wc_HashUpdate(&key->hash, hashType, h, hashSz);
    }
    if (err == 0) {
        err = wc_HashUpdate(&key->hash, hashType, a, hashSz);
    }
    if (err == 0) {
        err = wc_HashFinal(&key->hash, hashType, v);
    }

    return err;
}

/*
 * XOR hash output v into output, with length n, starting at index i.
 *
 * @param  [in]      v       Output bytes of hashing.
 * @param  [in]      hashSz  Size of output of hash algorithm in bytes.
 * @param  [in,out]  out     Data to be XORed.
 * @param  [in]      idx     Index to start XORing into.
 * @param  [in]      n       Length of data to XOR (mask) in bytes.
 */
static void sakke_xor_in_v(const byte* v, word32 hashSz, byte* out, int idx,
        int n)
{
    int o;
    word32 i;

    if (idx == 0) {
        i = hashSz - (n % hashSz);
        if (i == hashSz) {
            i = 0;
        }
    }
    else {
        i = 0;
    }
    o = i;
    for (; i < hashSz; i++) {
        out[idx + i - o] ^= v[i];
    }
}

/*
 * Hash octet strings to an integer range.
 *
 * RFC 6508, section 5.1, Steps 1 to 4.
 *
 * @param  [in]   key       SAKKE key.
 * @param  [in]   hashType  Hash algorithm to use.
 * @param  [in]   data      First block of data.
 * @param  [in]   sz        Size of first block of data in bytes.
 * @param  [in]   extra     Extra block of data.
 * @param  [in]   extraSz   Size of extra block of data in bytes.
 * @param  [out]  a         Output bytes of hashing.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when hashType is not supported.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_calc_a(SakkeKey* key, enum wc_HashType hashType,
        const byte* data, word32 sz, const byte* extra, word32 extraSz, byte* a)
{
    int err;
    int hash_inited = 0;

    /* Step 1: A = hashfn( s ), where s = data | extra */
    err = wc_HashInit_ex(&key->hash, hashType, key->heap, INVALID_DEVID);
    if (err == 0) {
        hash_inited = 1;
        err = wc_HashUpdate(&key->hash, hashType, data, sz);
    }
    if ((err == 0) && (extra != NULL)) {
        err = wc_HashUpdate(&key->hash, hashType, extra, extraSz);
    }
    if (err == 0) {
        err = wc_HashFinal(&key->hash, hashType, a);
    }

    if (hash_inited) {
        (void)wc_HashFree(&key->hash, hashType);
    }

    return err;
}

/*
 * Hash octet strings to an integer range.
 *
 * RFC 6508, section 5.1, Steps 1 to 4.
 *
 * @param  [in]   key       SAKKE key.
 * @param  [in]   hashType  Hash algorithm to use.
 * @param  [in]   a         Hash of original data.
 * @param  [out]  out       Output bytes of hashing.
 * @param  [in]   n         Size of output buffer in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when hashType is not supported.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_hash_to_range(SakkeKey* key, enum wc_HashType hashType,
        const byte* a, byte* out, word32 n)
{
    int err = 0;
    byte h[WC_MAX_DIGEST_SIZE];
    byte v[WC_MAX_DIGEST_SIZE];
    word32 hashSz = 1;
    word32 i;
    int hash_inited = 0;

    err = wc_HashInit_ex(&key->hash, hashType, key->heap, INVALID_DEVID);
    if (err == 0)
        hash_inited = 1;

    /* Step 1: A = hashfn( s ), where s = data | extra
     * See sakke_calc_a (need function parameters to be 7 or less)
     */

    /* Step 2: h_0 = 00...00, a string of null bits of length hashlen bits */
    if (err == 0)
        err = wc_HashGetDigestSize(hashType);
    if (err > 0) {
        hashSz = (word32)err;
        XMEMSET(h, 0, hashSz);
        err = 0; /* reset err value after getting digest size */
    }
    else if (err == 0) {
        /* invalid hash digest size */
        err = BAD_FUNC_ARG;
    }

    /* Step 3: l = Ceiling(lg(n)/hashlen) */
    /* Step 4: For each i in 1 to l, do */
    for (i = 0; (err == 0) && (i < n); i += hashSz) {
        /* Steps 4.a and 4.b */
        err = sakke_calc_h_v(key, hashType, hashSz, a, h, v);

        /* XOR in the result into output buffer. */
        if (err == 0) {
            sakke_xor_in_v(v, hashSz, out, i, n);
        }
    }

    if (hash_inited) {
        (void)wc_HashFree(&key->hash, hashType);
    }

    return err;
}

/*
 * Hash octet strings to an integer range - RFC 6508 section 5.1.
 * Steps 1 to 6.
 *
 * @param  [in]   key       SAKKE key.
 * @param  [in]   hashType  Hash algorithm to use.
 * @param  [in]   a         Hash of original data.
 * @param  [in]   q         MP integer representing modulus.
 * @param  [in]   n         Size of output in bytes.
 * @param  [out]  r         MP integer representing modulo reduced hashes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when hashType is not supported.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_hash_to_range_int(SakkeKey* key, enum wc_HashType hashType,
        const byte* a, mp_int* q, word32 n, mp_int* r)
{
    int err;
    byte* rb = key->data;

    /* Make all zeros so that hash output can be XORed in. */
    XMEMSET(rb, 0, n);

    /* Steps 1-4 */
    err = sakke_hash_to_range(key, hashType, a, rb, n);
    if (err == 0) {
        /* Steps 5 v' = v_1 | ...  | v_l */
        err = mp_read_unsigned_bin(r, rb, n);
    }
    if (err == 0) {
        /* Steps 6 v = v' mod n */
        err = mp_mod(r, q, r);
    }

    return err;
}

/**
 * Set the identity to perform operations with.
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   id    Identity.
 * @param  [in]   idSz  Size of identity in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or id is NULL or idSz > SAKKE_ID_MAX_SIZE.
 */
int wc_SetSakkeIdentity(SakkeKey* key, const byte* id, word16 idSz)
{
    int err = 0;

    if ((key == NULL) || (id == NULL) || (idSz > SAKKE_ID_MAX_SIZE)) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        XMEMCPY(key->id, id, idSz);
        key->idSz = idSz;
    }

    return err;
}

/**
 * Compute the elliptic curve point I for identity. Partial for point R.
 *
 * RFC 6508, Section 6.2.1, Step 3.\n
 * RFC 6508, Section 6.2.2, Step 5.\n
 * I = [b]P + Z_S
 *
 * @param  [in]   key   SAKKE key.
 * @param  [in]   id    Identity.
 * @param  [in]   idSz  Size of identity in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or id is NULL or idSz > SAKKE_ID_MAX_SIZE.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
int wc_MakeSakkePointI(SakkeKey* key, const byte* id, word16 idSz)
{
    int err = 0;

    if ((key == NULL) || (id == NULL) || (idSz > SAKKE_ID_MAX_SIZE)) {
        err = BAD_FUNC_ARG;
    }

    SAVE_VECTOR_REGISTERS(return _svr_ret;);

    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        /* I = [b]P + Z_S */
        err = sakke_compute_point_i(key, id, idSz, key->i.i);
    }
    if (err == 0) {
        XMEMCPY(key->i.id, id, idSz);
        key->i.idSz = idSz;
    }

    RESTORE_VECTOR_REGISTERS();

    return err;
}

/**
 * Get the elliptic curve point I - a partial calculation for point R.
 *
 * RFC 6508, Section 6.2.1, Step 3.\n
 * RFC 6508, Section 6.2.2, Step 5.\n
 * I = [b]P + Z_S
 *
 * @param  [in]      key   SAKKE key.
 * @param  [out]     data  Encoding of point I.
 * @param  [in,out]  sz    On in, the size of data in bytes.
 *                         On out, the size of the encoding in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or sz is NULL.
 * @return  LENGTH_ONLY_E when data is NULL. Number of bytes required returned
 *          in sz.
 * @return  BUFFER_E when sz is too small to hold encoding.
 */
int wc_GetSakkePointI(SakkeKey* key, byte* data, word32* sz)
{
    int err = 0;

    if ((key == NULL) || (sz == NULL)) {
        err = BAD_FUNC_ARG;
    }

    if ((err == 0) && (data == NULL)) {
        *sz = key->ecc.dp->size * 2;
        err = LENGTH_ONLY_E;
    }
    if ((err == 0) && (*sz < (word32)key->ecc.dp->size * 2)) {
        err = BUFFER_E;
    }

    if (err == 0) {
        /* Write out the x ordinate into key size bytes. */
        err = mp_to_unsigned_bin_len(key->i.i->x, data, key->ecc.dp->size);
    }
    if (err == 0) {
        data += key->ecc.dp->size;
        /* Write data the y ordinate into key size bytes. */
        err = mp_to_unsigned_bin_len(key->i.i->y, data, key->ecc.dp->size);
    }
    if (err == 0) {
        *sz = key->ecc.dp->size * 2;
    }

    return err;
}

/**
 * Set the elliptic curve point I - a partial calculation for point R - and the
 * identity that it belongs to.
 *
 * RFC 6508, Section 6.2.1, Step 3.\n
 * RFC 6508, Section 6.2.2, Step 5.\n
 * I = [b]P + Z_S
 *
 * @param  [in]      key   SAKKE key.
 * @param  [out]     data  Encoding of point I.
 * @param  [in,out]  sz    On in, the size of data in bytes.
 *                         On out, the size of the encoding in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, id or data is NULL.
 * @return  BUFFER_E when idSz is too big to store or sz is not the required
 *          size.
 */
int wc_SetSakkePointI(SakkeKey* key, const byte* id, word16 idSz,
        const byte* data, word32 sz)
{
    int err = 0;

    if ((key == NULL) || (id == NULL) || (data == NULL)) {
        err = BAD_FUNC_ARG;
    }
    if ((err == 0) && ((idSz > SAKKE_ID_MAX_SIZE) ||
            (sz != (word32)key->ecc.dp->size * 2))) {
        err = BUFFER_E;
    }

    if (err == 0) {
        /* Read the x value from key size bytes. */
        err = mp_read_unsigned_bin(key->i.i->x, data, key->ecc.dp->size);
    }
    if (err == 0) {
        data += key->ecc.dp->size;
        /* Read the y value from key size bytes. */
        err = mp_read_unsigned_bin(key->i.i->y, data, key->ecc.dp->size);
    }
    if (err == 0) {
        err = mp_set(key->i.i->z, 1);
    }
    if (err == 0) {
        XMEMCPY(key->i.id, id, idSz);
        key->i.idSz = idSz;
    }

    return err;
}

/**
 * Generate the pre-computation table for point I.
 *
 * A reference to the table is stored if successfully generated.
 *
 * @param  [in]      key    SAKKE key.
 * @param  [in,out]  table  Pre-computation table.
 *                          NULL to indicate that only length required.
 * @param  [in,out]  len    On in, the size of table buffer in bytes.
 *                          On out, the size of table data in bytes.
 * @return  BAD_FUNC_ARG then key or len is NULL.
 * @return  LENGTH_ONLY_E when only the length is returned.
 * @return  BUFFER_E when len is too small.
 * @return  MEMORY_E when dynamic memory allocation fails.
 */
int wc_GenerateSakkePointITable(SakkeKey* key, byte* table, word32* len)
{
    int err = 0;

    if ((key == NULL) || (len == NULL)) {
        err = BAD_FUNC_ARG;
    }

#ifdef WOLFSSL_HAVE_SP_ECC
    if (err == 0) {
        SAVE_VECTOR_REGISTERS(return _svr_ret;);
        err = sp_ecc_gen_table_1024(key->i.i, table, len, key->heap);
        RESTORE_VECTOR_REGISTERS();
    }
    if (err == 0) {
        key->i.table = table;
        key->i.tableLen = *len;
    }
#else
    if ((err == 0) && (table == NULL)) {
        *len = 0;
        err = LENGTH_ONLY_E;
    }
    if ((err == 0) && (*len != 0)) {
        *len = 0;
        err = BUFFER_E;
    }
    if (err == 0) {
        *len = 0;
        key->i.table = table;
        key->i.tableLen = *len;
    }
    (void)table;
#endif

    return err;
}

/**
 * Sets the pre-computation table for point I.
 * Speeds up making and deriving the encapsulated SSV.
 *
 * @param  [in]  key    SAKKE key.
 * @param  [in]  table  Pre-computation table for Point I.
 * @param  [in]  len    Length of pre-computation table in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key or table is NULL.
 */
int wc_SetSakkePointITable(SakkeKey* key, byte* table, word32 len)
{
    int err = 0;
#ifdef WOLFSSL_HAVE_SP_ECC
    word32 sz = 0;
#endif

    if ((key == NULL) || (table == NULL)) {
        err = BAD_FUNC_ARG;
    }

#ifdef WOLFSSL_HAVE_SP_ECC
    if (err == 0) {
        err = sp_ecc_gen_table_1024(key->i.i, NULL, &sz, NULL);
        if (err == LENGTH_ONLY_E) {
            err = 0;
        }
    }
    if ((err == 0) && (len != sz)) {
        err = BUFFER_E;
    }
#else
    if ((err == 0) && (len != 0)) {
        err = BUFFER_E;
    }
#endif

    if (err == 0) {
        key->i.table = table;
        key->i.tableLen = len;
    }

    return err;
}

/**
 * Clears the pre-computation table for point I.
 *
 * Must be called once the table has been disposed of.
 *
 * @param  [in]  key    SAKKE key.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key is NULL.
 */
int wc_ClearSakkePointITable(SakkeKey* key)
{
    int err = 0;

    if (key == NULL) {
        err = BAD_FUNC_ARG;
    }

    if (err == 0) {
        key->i.table = NULL;
        key->i.tableLen = 0;
    }

    return err;
}

/*
 * Compute the elliptic curve point R for device B.
 *
 * RFC 6508, Section 6.2.1, Step 3.\n
 * RFC 6508, Section 6.2.2, Step 5.\n
 * R = [r]([b]P + Z_S)
 *
 * @param  [in]  key   SAKKE key.
 * @param  [in]  id    Identifier to of device B.
 * @param  [in]  idSz  Size of identifier in bytes.
 * @param  [in]  z     ECC point - KMS Public Key Z_S.
 * @param  [in]  n     Number of bytes in r.
 * @param  [in]  out   Result R encoded to bytes.
 * @return  0 on success.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
static int sakke_compute_point_r(SakkeKey* key, const byte* id, word16 idSz,
        const mp_int* r, word32 n, byte* out)
{
    int err = 0;
    ecc_point* i = key->i.i;
    ecc_point* rp = key->tmp.p2;
    word32 sz;

    if ((key->i.idSz == 0) || (key->i.idSz != idSz) ||
            (XMEMCMP(id, key->i.id, idSz) != 0)) {
        /* I = [b]P + Z_S */
        err = sakke_compute_point_i(key, id, idSz, i);
        if ((err == 0) && (idSz <= SAKKE_ID_MAX_SIZE)) {
            XMEMCPY(key->i.id, id, idSz);
            key->i.idSz = idSz;
        }
        key->i.table = NULL;
        key->i.tableLen = 0;
    }
    /* [r]([b]P + Z_S) */
    if (err == 0) {
        err = sakke_mulmod_point(key, r, i, key->i.table, rp, 1);
    }
    /* Export to canonical form */
    if (err == 0) {
        sz = n * 2 + 1;
        err = wc_ecc_export_point_der(wc_ecc_get_curve_idx(key->ecc.dp->id), rp,
                 out, &sz);
    }

    return err;
}

/**
 * Makes the Shared Secret Value (SSV) encapsulated and returns the
 * authentication data.
 *
 * RFC 6508, Section 6.2.1.
 *
 * SSV is overwritten with encapsulated SSV.
 *
 * Call wc_SetSakkeIdentity() to set the identity to use with operation.
 *
 * @param  [in]      key       SAKKE key.
 * @param  [in,out]  ssv       On in, Shared Secret Value (SSV) data.
 *                             On out, encrypted Shared Secret Value (SSV) data.
 * @param  [in]      ssvSz     Size of SSV in bytes.
 * @param  [in]      hashType  Hash algorithm to use.
 * @param  [out]     auth      Authentication data.
 * @param  [out]     authSz    Size of authentication data in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, ssv or encSz is NULL, ssvSz is to big or
 *          encSz is too small.
 * @return  BAD_STATE_E when identity not set.
 * @return  LENGTH_ONLY_E when auth is NULL. authSz contains required size of
 *          auth in bytes.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
int wc_MakeSakkeEncapsulatedSSV(SakkeKey* key, enum wc_HashType hashType,
        byte* ssv, word16 ssvSz, byte* auth, word16* authSz)
{
    int err = 0;
    mp_int* r = NULL;
    word16 n = 0;
    word16 outSz = 0;
    byte a[WC_MAX_DIGEST_SIZE];

    if ((key == NULL) || (ssv == NULL) || (authSz == NULL)) {
        err = BAD_FUNC_ARG;
    }
    if ((err == 0) && (key->idSz == 0)) {
        err = BAD_STATE_E;
    }

    SAVE_VECTOR_REGISTERS(return _svr_ret;);

    /* Load parameters */
    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        n = (word16)((mp_count_bits(&key->params.prime) + 7) / 8);

        /* Uncompressed point */
        outSz = 1 + 2 * n;

        if ((auth != NULL) && (*authSz < outSz)) {
            err = BAD_FUNC_ARG;
        }
    }
    if (err == 0) {
        *authSz = outSz;

        if (auth == NULL) {
            err = LENGTH_ONLY_E;
        }
    }

    if (err == 0) {
        err = sakke_load_base_point(key);
    }
    if (err == 0) {
        err = sakke_load_pairing_base(key);
    }

    /* Step 1: Generate a random SSV 0..(2^n)-1
     * Already generated - see wc_MakeSakkeEncapsulated()
     */
    /* Step 2: Compute r = HashToIntegerRange( SSV | b, q, Hash ) */
    if (err == 0) {
        err = sakke_calc_a(key, hashType, ssv, ssvSz, key->id, key->idSz, a);
    }
    if (err == 0) {
        r = key->tmp.p3->z;
        err = sakke_hash_to_range_int(key, hashType, a, &key->params.q, n, r);
    }
    /* Step 3: Compute R_(b,S) = [r]([b]P + Z_S) in E(F_p) */
    if (err == 0) {
        err = sakke_compute_point_r(key, key->id, key->idSz, r, n, auth);
    }

    /* Step 4.a: Compute g^r */
    if (err == 0) {
        err = sakke_modexp(key, &key->params.g, r, r);
    }

    /* Step 4.b: Compute H := SSV XOR HashToIntegerRange( g^r, 2^n, Hash ) */
    if (err == 0) {
        err = mp_to_unsigned_bin_len(r, key->data, n);
    }
    /* ssv ^= HashToIntegerRange( g^r, 2^n, Hash ) */
    if (err == 0) {
        err = sakke_calc_a(key, hashType, key->data, n, NULL, 0, a);
    }
    if (err == 0) {
        err = sakke_hash_to_range(key, hashType, a, ssv, ssvSz);
    }

    /* Step 5: Form the Encapsulated Data ( R_(b,S), H )
     * R_(b,S) encoded in sakke_compute_point_r, H is a pointer into enc.
     */

    /* Step 6: Output SSV - already encoded in buffer */

    RESTORE_VECTOR_REGISTERS();

    return err;
}

/**
 * Generate a random Shared Secret Value (SSV).
 *
 * RFC 6508, Section 6.2.1, Step 1.
 *
 * @param  [in]   key    SAKKE key.
 * @param  [in]   rng    Random number generator.
 * @param  [out]  ssv    Shared Secret Value (SSV) data.
 * @param  [out]  ssvSz  Size of SSV in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, rng or ssvSz is NULL or ssvSz is to small.
 * @return  LENGTH_ONLY_E when ssv is NULL. ssvSz contains the required size of
 *          in bytes.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
int wc_GenerateSakkeSSV(SakkeKey* key, WC_RNG* rng, byte* ssv, word16* ssvSz)
{
    int err = 0;
    word16 n = 0;

    if ((key == NULL) || (rng == NULL) || (ssvSz == NULL)) {
        err = BAD_FUNC_ARG;
    }

    /* Load parameters */
    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        n = (word16)((mp_count_bits(&key->params.prime) + 7) / 8);

        if ((ssv != NULL) && (*ssvSz > n)) {
            err = BAD_FUNC_ARG;
        }
    }
    if (err == 0) {
        /* Return length only if an ouput buffer is NULL. */
        if (ssv == NULL) {
            *ssvSz = (word16) (n / 8);
            err = LENGTH_ONLY_E;
        }
        else {
            n = *ssvSz;
        }
    }

    /* Step 1: Select a random ephemeral integer value. Range 0..(2^n - 1) */
    if (err == 0) {
        err = wc_RNG_GenerateBlock(rng, ssv, n);
    }

    return err;
}

/**
 * Derive the Shared Secret Value from the encapsulated data using the set
 * RSK
 *
 * RFC 6508, Section 6.2.2.
 *
 * Encapsulated SSV is overwritten with SSV.
 *
 * Call wc_SetSakkeIdentity() to set the identity to use with operation.
 *
 * Call wc_SetSakkeRSK() to set the Receiver Secret Key (RSK) to use with
 * operation.
 *
 * @param  [in]      key       SAKKE key.
 * @param  [in]      hashType  Hash algorithm to use.
 * @param  [in,out]  ssv       On in, encrypted Secret Shared Value (SSV) data.
 *                             On out, Secret Shared Value (SSV) data.
 * @param  [in]      ssvSz     Size of SSV in bytes.
 * @param  [in]      auth      Authentication data.
 * @param  [in]      authSz    Size of authentication data in bytes.
 * @return  0 on success.
 * @return  BAD_FUNC_ARG when key, ssv or auth is NULL.
 * @return  BAD_STATE_E when RSK or identity not set.
 * @return  SAKKE_VERIFY_FAIL_E when calculated R doesn't match the encapsulated
 *          data's R.
 * @return  MEMORY_E when dynamic memory allocation fails.
 * @return  Other -ve value on internal failure.
 */
int wc_DeriveSakkeSSV(SakkeKey* key, enum wc_HashType hashType, byte* ssv,
        word16 ssvSz, const byte* auth, word16 authSz)
{
    int err = 0;
    word16 n = 0;
    ecc_point* r = NULL;
    mp_int* w = NULL;
    mp_int* ri = NULL;
    byte* wb = NULL;
    byte* test = NULL;
    byte a[WC_MAX_DIGEST_SIZE] = {0};

    if ((key == NULL) || (ssv == NULL) || (auth == NULL)) {
        err = BAD_FUNC_ARG;
    }
    if ((err == 0) && (!key->rsk.set || (key->idSz == 0))) {
        err = BAD_STATE_E;
    }

    SAVE_VECTOR_REGISTERS(return _svr_ret;);

    /* Load parameters */
    if (err == 0) {
        err = sakke_load_params(key);
    }
    if (err == 0) {
        n = (word16)((mp_count_bits(&key->params.prime) + 7) / 8);

        if (authSz != 2 * n + 1) {
            err = BAD_FUNC_ARG;
        }
    }
    if (err == 0) {
        err = sakke_load_base_point(key);
    }

    /* Step 1: Parse the Encapsulated Data ( R_(b,S), H )
     * H = auth, so already extracted. */
    if (err == 0) {
        r = key->tmp.p2;

        err = wc_ecc_import_point_der(auth, n * 2 + 1,
                wc_ecc_get_curve_idx(key->ecc.dp->id), r);
    }

    /* Step 2: w = < R_(b,S), K_(b,S) > = < K_(b,S), R_(b,S) > = < rsk , r > */
    if (err == 0) {
        w = &key->tmp.m1;

        err = sakke_pairing(key, key->rsk.rsk, r, w, key->rsk.table,
                key->rsk.tableLen);
    }

    /* Step 3: Compute SSV = H XOR HashToIntegerRange( w, 2^n, Hash ) */
    if (err == 0) {
        wb = key->data;
        err = mp_to_unsigned_bin_len(w, wb, n);
    }
    /* HashToIntegerRange( w, 2^n, Hash ) */
    if (err == 0) {
        err = sakke_calc_a(key, hashType, wb, n, NULL, 0, a);
    }
    if (err == 0) {
        err = sakke_hash_to_range(key, hashType, a, ssv, ssvSz);
    }

    /* Step 4: r = HashToIntegerRange( SSV | b, q, Hash ) */
    if (err == 0) {
        err = sakke_calc_a(key, hashType, ssv, ssvSz, key->id, key->idSz, a);
    }
    if (err == 0) {
        ri = &key->tmp.m1;
        err = sakke_hash_to_range_int(key, hashType, a, &key->params.q, n, ri);
    }

    /* Step 5: Compute TEST = [r]([b]P + Z_S) == R_(b,S) */
    if (err == 0) {
        test = key->data;

        err = sakke_compute_point_r(key, key->id, key->idSz, ri, n, test);
    }
    if ((err == 0) && (XMEMCMP(auth, test, 2 * n + 1) != 0)) {
        err = SAKKE_VERIFY_FAIL_E;
    }

    RESTORE_VECTOR_REGISTERS();

    return err;
}
#endif /* WOLFCRYPT_SAKKE_CLIENT */

#endif /* WOLFCRYPT_HAVE_SAKKE */