path: root/crypto.c

/* This file is part of libbrandt.
 * Copyright (C) 2016 GNUnet e.V.
 *
 * libbrandt 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 3 of the License, or (at your option) any later
 * version.
 *
 * libbrandt 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
 * libbrandt.  If not, see <http://www.gnu.org/licenses/>.
 */

/**
 * @file crypto.c
 * @brief Implementation of the crypto primitives.
 * @author Markus Teich
 */

#include "platform.h"

#include <gcrypt.h>

#include "crypto.h"
#include "internals.h"
#include "util.h"


#define CURVE "Ed25519"


/**
 * Log an error message at log-level 'error' that indicates a failure of the
 * command 'cmd' with the message given by gcry_strerror(rc) and abort the
 * programm.
 */
#define ASSERT_GCRY(cmd, rc) do { \
		if (0 != rc) { \
			GNUNET_log_from (GNUNET_ERROR_TYPE_ERROR, \
			                 "libbrandt", \
			                 "`%s' failed at %s:%d with error: %s\n", \
			                 cmd, \
			                 __FILE__, \
			                 __LINE__, \
			                 gcry_strerror (rc)); \
			GNUNET_abort_ (); \
		} \
} while (0)


struct zkp_challenge_dl {
	struct ec_mpi g;
	struct ec_mpi v;
	struct ec_mpi a;
};

struct zkp_challenge_2dle {
	struct ec_mpi g1;
	struct ec_mpi g2;
	struct ec_mpi v;
	struct ec_mpi w;
	struct ec_mpi a;
	struct ec_mpi b;
};

struct zkp_challenge_0og {
	struct ec_mpi g;
	struct ec_mpi alpha;
	struct ec_mpi beta;
	struct ec_mpi a1;
	struct ec_mpi a2;
	struct ec_mpi b1;
	struct ec_mpi b2;
};


gcry_ctx_t       ec_ctx = NULL;
gcry_mpi_point_t ec_gen = NULL;
gcry_mpi_point_t ec_zero = NULL;
gcry_mpi_t       ec_n = NULL;


/**
 * brandt_crypto_init initializes the crypto system and must be called before
 * any other function from this file.
 *
 * @param[in] dlogctx Pointer to the prepared dlog context.
 */
void
brandt_crypto_init ()
{
	gcry_error_t rc;

	rc = gcry_mpi_ec_new (&ec_ctx, NULL, CURVE);
	ASSERT_GCRY ("gcry_mpi_ec_new", rc);

	ec_gen = gcry_mpi_ec_get_point ("g", ec_ctx, 0);
	brandt_assert (NULL != ec_gen);

	ec_zero = gcry_mpi_point_new (0);
	brandt_assert (NULL != ec_zero);
	gcry_mpi_ec_sub (ec_zero, ec_gen, ec_gen, ec_ctx);

	ec_n = gcry_mpi_ec_get_mpi ("n", ec_ctx, 1);
	brandt_assert (NULL != ec_n);
}


/* --- EC --- */

/**
 * ec_skey_create
 *
 * @param[out] skey where to store the generated secret key. This has to be an
 * already initialized mpi.
 */
void
ec_skey_create (gcry_mpi_t skey)
{
	gcry_mpi_t   ret;
	gcry_sexp_t  s_keyparam;
	gcry_sexp_t  priv_sexp;
	gcry_sexp_t  priv_key;
	gcry_sexp_t  priv_key2;
	gcry_error_t rc;

	rc = gcry_sexp_build (&s_keyparam, NULL, "(genkey(ecc(curve \"" CURVE "\")"
	                      "(flags)))");
	ASSERT_GCRY ("gcry_sexp_build", rc);

	rc = gcry_pk_genkey (&priv_sexp, s_keyparam);
	ASSERT_GCRY ("gcry_pk_genkey", rc);
	gcry_sexp_release (s_keyparam);

	priv_key = gcry_sexp_find_token (priv_sexp, "private-key", 11);
	brandt_assert (NULL != priv_key);
	gcry_sexp_release (priv_sexp);

	priv_key2 = gcry_sexp_find_token (priv_key, "d", 1);
	brandt_assert (NULL != priv_key2);
	gcry_sexp_release (priv_key);

	ret = gcry_sexp_nth_mpi (priv_key2, 1, GCRYMPI_FMT_USG);
	brandt_assert (NULL != ret);
	gcry_sexp_release (priv_key2);

	gcry_mpi_snatch (skey, ret);
}


/**
 * ec_keypair_create creates a new keypair by creating a random secret key first
 * and multipyling the base point with it to get the public key.
 *
 * @param[out] pkey where to store the generated public key
 * @param[out] skey where to store the generated secret key. May be NULL if
 * you're not interested in the secret key and just need a random point.
 */
void
ec_keypair_create (gcry_mpi_point_t pkey, gcry_mpi_t skey)
{
	gcry_mpi_t sk;

	if (NULL == pkey)
	{
		GNUNET_break (NULL != pkey);
		return;
	}
	sk = (NULL == skey) ? gcry_mpi_new (256) : skey;

	ec_skey_create (sk);
	gcry_mpi_ec_mul (pkey, sk, ec_gen, ec_ctx);

	if (NULL == skey)
		gcry_mpi_release (sk);
}


/**
 * ec_keypair_create_base
 *
 * @param[out] pkey where to store the generated public key
 * @param[out] skey where to store the generated secret key
 * @param[in] base which base point should be used to calculate the public key
 */
void
ec_keypair_create_base (gcry_mpi_point_t       pkey,
                        gcry_mpi_t             skey,
                        const gcry_mpi_point_t base)
{
	brandt_assert (NULL != pkey);
	brandt_assert (NULL != skey);
	brandt_assert (NULL != base);

	ec_skey_create (skey);
	gcry_mpi_ec_mul (pkey, skey, base, ec_ctx);
}


/**
 * ec_point_copy creates a copy of one curve point
 *
 * @param[out] dst where to store the copy
 * @param[in] src the input point to be copied
 */
void
ec_point_copy (gcry_mpi_point_t dst, const gcry_mpi_point_t src)
{
	gcry_mpi_t x = gcry_mpi_new (256);
	gcry_mpi_t y = gcry_mpi_new (256);
	gcry_mpi_t z = gcry_mpi_new (256);

	brandt_assert (dst && src);
	gcry_mpi_point_get (x, y, z, src);
	gcry_mpi_point_snatch_set (dst, x, y, z);
}


/**
 * ec_point_cmp compares two curve points
 *
 * @param[in] a the first point
 * @param[in] b the second point
 * @return 0 if @a a and @a b represent the same point on the curve, something
 * else otherwise
 */
int
ec_point_cmp (const gcry_mpi_point_t a, const gcry_mpi_point_t b)
{
	int        ret = 1;
	gcry_mpi_t ax = gcry_mpi_new (256);
	gcry_mpi_t bx = gcry_mpi_new (256);
	gcry_mpi_t ay = gcry_mpi_new (256);
	gcry_mpi_t by = gcry_mpi_new (256);

	brandt_assert (a && b);
	if (!ax || !bx || !ay || !by)
	{
		GNUNET_log_from (GNUNET_ERROR_TYPE_ERROR,
		                 "libbrandt",
		                 "could not init point in point_cmp\n");
		return 1;
	}

	if (!gcry_mpi_ec_get_affine (ax, ay, a, ec_ctx) &&
	    !gcry_mpi_ec_get_affine (bx, by, b, ec_ctx))
	{
		ret = gcry_mpi_cmp (ax, bx) || gcry_mpi_cmp (ay, by);
	}

	gcry_mpi_release (ax);
	gcry_mpi_release (bx);
	gcry_mpi_release (ay);
	gcry_mpi_release (by);
	return ret;
}


/**
 * mpi_serialize outputs the given MPI value to the given destination buffer in
 * network byte order. The MPI @a src may not be negative.
 *
 * @param[out] dst where to output to
 * @param[in] src value to write to @a dst
 */
void
mpi_serialize (struct ec_mpi *dst, gcry_mpi_t src)
{
	size_t rsize = 0;

	if (gcry_mpi_get_flag (src, GCRYMPI_FLAG_OPAQUE))
	{   /* Store opaque MPIs left aligned. Used by Ed25519 point compression */
		unsigned int nbits;
		const void   *vp = gcry_mpi_get_opaque (src, &nbits);

		brandt_assert (vp);
		rsize = (nbits + 7) / 8;
		if (rsize > sizeof (struct ec_mpi))
			rsize = sizeof (struct ec_mpi);
		memcpy (dst, vp, rsize);
		if (rsize < sizeof (struct ec_mpi))
			memset (((char *)dst) + rsize, 0, sizeof (struct ec_mpi) - rsize);
	}
	else
	{   /* Store regular MPIs as unsigned ints right aligned into the buffer. */
		char         *cp = (char *)dst;
		gcry_error_t rc;

		rc = gcry_mpi_print (GCRYMPI_FMT_USG, (void *)dst,
		                     sizeof (struct ec_mpi), &rsize, src);
		ASSERT_GCRY ("gcry_mpi_print", rc);

		/* Shift the output to the right, if shorter than available space */
		if (rsize && rsize < sizeof (struct ec_mpi))
		{
			memmove (&cp[sizeof (struct ec_mpi) - rsize], dst, rsize);
			memset (dst, 0, sizeof (struct ec_mpi) - rsize);
		}
	}
}


/**
 * mpi_parse converts src buffer into MPI value.
 * The buffer is interpreted as network byte order, unsigned integer.
 *
 * @param[out] dst where to store MPI value. Must be initialized.
 * @param[in] src raw data source (GCRYMPI_FMT_USG)
 */
void
mpi_parse (gcry_mpi_t dst, const struct ec_mpi *src)
{
	gcry_mpi_t   ret;
	gcry_error_t rc;

	rc = gcry_mpi_scan (&ret,
	                    GCRYMPI_FMT_USG,
	                    src,
	                    sizeof (struct ec_mpi),
	                    NULL);
	ASSERT_GCRY ("gcry_mpi_scan", rc);

	gcry_mpi_snatch (dst, ret);
}


/**
 * ec_point_serialize outputs the given curve point to the @a dst buffer.
 *
 * @param[out] dst where to write the raw data to
 * @param[in] src curve point to write to @a dst
 */
void
ec_point_serialize (struct ec_mpi *dst, const gcry_mpi_point_t src)
{
	gcry_sexp_t  s;
	gcry_ctx_t   ctx;
	gcry_error_t rc;
	gcry_mpi_t   q;

	brandt_assert (dst);

	rc = gcry_sexp_build (&s, NULL, "(public-key(ecc(curve " CURVE ")))");
	ASSERT_GCRY ("gcry_sexp_build", rc);
	brandt_assert (NULL != s);

	rc = gcry_mpi_ec_new (&ctx, s, NULL);
	ASSERT_GCRY ("gcry_mpi_ec_new", rc);
	gcry_sexp_release (s);

	rc = gcry_mpi_ec_set_point ("q", src, ctx);
	ASSERT_GCRY ("gcry_mpi_ec_set_point", rc);

	q = gcry_mpi_ec_get_mpi ("q@eddsa", ctx, 0);
	brandt_assert (NULL != q);
	gcry_ctx_release (ctx);

	mpi_serialize (dst, q);
	gcry_mpi_release (q);
}


/**
 * ec_point_parse parses a point on the Ed25519 curve from @a src into @a dst.
 *
 * @param[out] dst where to store the curve point. Must be initialized
 * @param[in] src raw data source
 */
void
ec_point_parse (gcry_mpi_point_t dst, const struct ec_mpi *src)
{
	gcry_sexp_t      s;
	gcry_ctx_t       ctx;
	gcry_mpi_point_t ret;
	gcry_error_t     rc;

	rc = gcry_sexp_build (&s, NULL, "(public-key(ecc(curve " CURVE ")(q %b)))",
	                      sizeof (struct ec_mpi), src);
	ASSERT_GCRY ("gcry_sexp_build", rc);

	rc = gcry_mpi_ec_new (&ctx, s, NULL);
	ASSERT_GCRY ("gcry_mpi_ec_new", rc);
	gcry_sexp_release (s);

	ret = gcry_mpi_ec_get_point ("q", ctx, 0);
	brandt_assert (ret);
	gcry_ctx_release (ctx);
	gcry_mpi_ec_mul (dst, GCRYMPI_CONST_ONE, ret, ec_ctx);
	gcry_mpi_point_release (ret);
}


/**
 * smc_free1 releases all points in @a dst and frees the memory
 *
 * @param[in,out] dst The 1 dimensional array to clean up
 * @param[in] size1 size of the first dimension
 */
void
smc_free1 (gcry_mpi_point_t *dst, uint16_t size1)
{
	if (NULL == dst)
		return;

	for (uint16_t i = 0; i < size1; i++)
		if (NULL != dst[i])
			gcry_mpi_point_release (dst[i]);
	free (dst);
}


/**
 * smc_init1 creates a 1 dimensional array of curve points. Make sure to
 * initialize the values before using them, they are not automatically set to
 * the zero point!
 *
 * @param[in] size1 size of the first dimension
 * @return a pointer to the array or NULL on error.
 * If not used anymore use smc_free2 to reclaim the memory.
 */
gcry_mpi_point_t *
smc_init1 (uint16_t size1)
{
	gcry_mpi_point_t *ret;

	ret = GNUNET_new_array (size1, gcry_mpi_point_t);

	for (uint16_t i = 0; i < size1; i++)
	{
		if (NULL == (ret[i] = gcry_mpi_point_new (0)))
		{
			GNUNET_log_from (GNUNET_ERROR_TYPE_ERROR,
			                 "libbrandt",
			                 "could not init point in 1 dimensional array. "
			                 "out of memory?\n");
			smc_free1 (ret, size1);
			return NULL;
		}
	}
	return ret;
}


/**
 * smc_free2 releases all points in @a dst and frees the memory
 *
 * @param[in,out] dst The 2 dimensional array to clean up
 * @param[in] size1 size of the first dimension
 * @param[in] size2 size of the second dimension
 */
void
smc_free2 (gcry_mpi_point_t **dst, uint16_t size1, uint16_t size2)
{
	if (NULL == dst)
		return;

	for (uint16_t i = 0; i < size1; i++)
		for (uint16_t j = 0; j < size2; j++)
			if (NULL != dst[i][j])
				gcry_mpi_point_release (dst[i][j]);
	free (dst);
}


/**
 * smc_init2 creates a 2 dimensional array of curve points. Make sure to
 * initialize the values before using them, they are not automatically set to
 * the zero point!
 *
 * @param[in] size1 size of the first dimension
 * @param[in] size2 size of the second dimension
 * @return a pointer to the array or NULL on error.
 * If not used anymore use smc_free2 to reclaim the memory.
 */
gcry_mpi_point_t **
smc_init2 (uint16_t size1, uint16_t size2)
{
	gcry_mpi_point_t **ret;

	ret = GNUNET_new_array_2d (size1, size2, gcry_mpi_point_t);

	for (uint16_t i = 0; i < size1; i++)
	{
		for (uint16_t j = 0; j < size2; j++)
		{
			if (NULL == (ret[i][j] = gcry_mpi_point_new (0)))
			{
				GNUNET_log_from (
				    GNUNET_ERROR_TYPE_ERROR,
				    "libbrandt",
				    "could not init point in 2 dimensional array. "
				    "out of memory?\n");
				smc_free2 (ret, size1, size2);
				GNUNET_assert (0);
			}
		}
	}
	return ret;
}


/**
 * smc_free3 releases all points in @a dst and frees the memory
 *
 * @param[in,out] dst The 3 dimensional array to clean up
 * @param[in] size1 size of the first dimension
 * @param[in] size2 size of the second dimension
 * @param[in] size3 size of the third dimension
 */
void
smc_free3 (gcry_mpi_point_t ***dst,
           uint16_t         size1,
           uint16_t         size2,
           uint16_t         size3)
{
	if (NULL == dst)
		return;

	for (uint16_t i = 0; i < size1; i++)
		for (uint16_t j = 0; j < size2; j++)
			for (uint16_t k = 0; k < size3; k++)
				if (NULL != dst[i][j][k])
					gcry_mpi_point_release (dst[i][j][k]);
	free (dst);
}


/**
 * smc_init3 creates a 3 dimensional array of curve points. Make sure to
 * initialize the values before using them, they are not automatically set to
 * the zero point!
 *
 * @param[in] size1 size of the first dimension
 * @param[in] size2 size of the second dimension
 * @param[in] size3 size of the third dimension
 * @return a pointer to the array or NULL on error.
 * If not used anymore use smc_free3 to reclaim the memory.
 */
gcry_mpi_point_t ***
smc_init3 (uint16_t size1, uint16_t size2, uint16_t size3)
{
	gcry_mpi_point_t ***ret;

	ret = GNUNET_new_array_3d (size1, size2, size3, gcry_mpi_point_t);

	for (uint16_t i = 0; i < size1; i++)
	{
		for (uint16_t j = 0; j < size2; j++)
		{
			for (uint16_t k = 0; k < size3; k++)
			{
				if (NULL == (ret[i][j][k] = gcry_mpi_point_new (0)))
				{
					GNUNET_log_from (
					    GNUNET_ERROR_TYPE_ERROR,
					    "libbrandt",
					    "could not init point in 2 dimensional array. "
					    "out of memory?\n");
					smc_free3 (ret, size1, size2, size3);
					GNUNET_assert (0);
				}
			}
		}
	}
	return ret;
}


/**
 * smc_sums_partial calculates sums up until and including the current index and
 * stores them in @a out. \f$\forall i \leq len: out_i=\sum_{h=1}^iin_h\f$
 *
 * @param[out] out Where to store the resulting sums. Points must already be
 * initialized beforehand.
 * @param[in] in Input points.
 * @param[in] len The length of @a out. @a in must be at least @a step times @a
 * len elements long.
 * @param[in] stepi The amount of items to advance in @a in each step. Can be
 * used to sum over multi-dimensional arrays.
 * @param[in] stepo The amount of items to advance in @a out each step. Can be
 * used to store the sum in multi-dimensional arrays.
 */
void
smc_sums_partial (gcry_mpi_point_t out[],
                  gcry_mpi_point_t in[],
                  uint16_t         len,
                  uint16_t         stepi,
                  uint16_t         stepo)
{
	brandt_assert (NULL != out);
	for (uint16_t i = 0, o = 0; o < len * stepo; i += stepi, o += stepo)
		gcry_mpi_ec_add (out[o], (o ? out[o - stepo] : ec_zero), in[i], ec_ctx);
}


/**
 * smc_sum calculates the sum of all input points.
 * \f$out=\sum_{i=1}^{len}in_i\f$
 *
 * @param[out] out Where to store the result
 * @param[in] in Input points.
 * @param[in] len The amount of summands to use from @a in. @a in must be at
 * least @a step times @a len elements long.
 * @param[in] step The amount of items to advance in @a in each step. Can be
 * used to sum over multi-dimensional arrays.
 */
void
smc_sum (gcry_mpi_point_t out,
         gcry_mpi_point_t in[],
         uint16_t         len,
         uint16_t         step)
{
	brandt_assert (NULL != out);
	ec_point_copy (out, ec_zero);
	for (uint16_t i = 0; i < len * step; i += step)
		gcry_mpi_ec_add (out, out, in[i], ec_ctx);
}


void
smc_prep_keyshare (struct BRANDT_Auction *ad)
{
	ad->y = smc_init1 (ad->n);
	brandt_assert (ad->y);
}


/**
 * smc_gen_keyshare creates the private keyshare and computes the
 * public key share
 *
 * @param[in] ad Pointer to the BRANDT_Auction struct to operate on
 * @param[out] buflen Size of the returned message buffer in byte
 * @return A buffer containing the public key share
 * which needs to be broadcast
 */
unsigned char *
smc_gen_keyshare (struct BRANDT_Auction *ad, size_t *buflen)
{
	unsigned char   *ret;
	struct msg_head *head;
	struct ec_mpi   *pubkey_share;
	struct proof_dl *proof1;

	brandt_assert (ad && buflen);
	*buflen = (sizeof (*head) +
	           sizeof (*pubkey_share) +
	           sizeof (*proof1));
	ret = GNUNET_new_array (*buflen, unsigned char);

	head = (struct msg_head *)ret;
	head->prot_version = htonl (0);
	head->msg_type = htonl (msg_init);

	proof1 = (struct proof_dl *)(ret + sizeof (*head) + sizeof (*pubkey_share));
	ad->x = gcry_mpi_new (256);
	ec_skey_create (ad->x);
	smc_zkp_dl (ad->y[ad->i], ad->x, proof1);

	pubkey_share = (struct ec_mpi *)(ret + sizeof (*head));
	ec_point_serialize (pubkey_share, ad->y[ad->i]);

	return ret;
}


int
smc_recv_keyshare (struct BRANDT_Auction *ad,
                   const unsigned char   *buf,
                   size_t                buflen,
                   uint16_t              sender)
{
	int              ret = 0;
	struct proof_dl  *proof1;
	gcry_mpi_point_t y = gcry_mpi_point_new (0);

	brandt_assert (ad && buf);

	if (buflen != (sizeof (struct ec_mpi) + sizeof (*proof1)))
	{
		GNUNET_log_from (GNUNET_ERROR_TYPE_WARNING,
		                 "libbrandt",
		                 "wrong size of received key share\n");
		goto quit;
	}

	proof1 = (struct proof_dl *)(buf + sizeof (struct ec_mpi));
	ec_point_parse (y, (struct ec_mpi *)buf);
	if (smc_zkp_dl_check (y, proof1))
	{
		GNUNET_log_from (GNUNET_ERROR_TYPE_WARNING,
		                 "libbrandt",
		                 "wrong zkp1 for public key share received\n");
		goto quit;
	}

	ec_point_copy (ad->y[sender], y);

	ret = 1;
quit:
	gcry_mpi_point_release (y);
	return ret;
}


void
smc_prep_bid (struct BRANDT_Auction *ad)
{
	ad->alpha = smc_init2 (ad->n, ad->k);
	brandt_assert (ad->alpha);

	ad->beta = smc_init2 (ad->n, ad->k);
	brandt_assert (ad->beta);

	ad->Y = gcry_mpi_point_new (0);
	brandt_assert (ad->Y);
	smc_sum (ad->Y, ad->y, ad->n, 1);
	brandt_assert (ad->Y);
}


/**
 * smc_encrypt_bid encrypts the own bid with the shared public key and packs it
 * into a message together with proofs of correctnes.
 *
 * @param[in] ad Pointer to the BRANDT_Auction struct to operate on
 * @param[out] buflen Size of the returned message buffer in byte
 * @return A buffer containing the encrypted bid
 * which needs to be broadcast
 */
unsigned char *
smc_encrypt_bid (struct BRANDT_Auction *ad, size_t *buflen)
{
	unsigned char    *ret;
	unsigned char    *cur;
	struct msg_head  *head;
	struct proof_0og *proof3;
	gcry_mpi_t       r_sum;
	gcry_mpi_t       r_sum2;
	gcry_mpi_t       r_part;

	brandt_assert (ad && buflen);
	*buflen = (sizeof (*head) +              /* msg header */
	           ad->k *                       /* k * (alpha, beta, proof3) */
	           (sizeof (struct ec_mpi) * 2 +
	            sizeof (*proof3)) +
	           sizeof (struct proof_2dle));  /* proof2 */
	if (0 < ad->m)
		*buflen += sizeof (struct proof_2dle);
	ret = GNUNET_new_array (*buflen, unsigned char);

	head = (struct msg_head *)ret;
	head->prot_version = htonl (0);
	head->msg_type = htonl (msg_bid);
	cur = ret + sizeof (*head);

	r_sum = gcry_mpi_new (256);
	r_sum2 = gcry_mpi_new (256);
	r_part = gcry_mpi_new (256);

	for (uint16_t j = 0; j < ad->k; j++)
	{
		proof3 = (struct proof_0og *)(cur + 2 * sizeof (struct ec_mpi));
		smc_zkp_0og (j == ad->b,
		             ad->Y,
		             r_part,
		             ad->alpha[ad->i][j],
		             ad->beta[ad->i][j],
		             proof3);
		ec_point_serialize ((struct ec_mpi *)cur, ad->alpha[ad->i][j]);
		ec_point_serialize (&((struct ec_mpi *)cur)[1], ad->beta[ad->i][j]);
		gcry_mpi_addm (r_sum, r_sum, r_part, ec_n);

		/* prepare sum for additional  M+1st price auction proof (see below) */
		if (0 < ad->m && 1 == (ad->k - j - ad->i) % ad->n)
			gcry_mpi_addm (r_sum2, r_sum2, r_part, ec_n);

		cur += 2 * sizeof (struct ec_mpi) + sizeof (struct proof_0og);
	}
	smc_zkp_2dle (NULL, NULL, ad->Y, ec_gen, r_sum, (struct proof_2dle *)cur);

	/* in M+1st price auctions we need to prove that our bid is from the valid
	 * subset of bids as well */
	if (0 < ad->m)
	{
		struct proof_2dle *proof2 = (struct proof_2dle *)(ret + *buflen) - 1;
		smc_zkp_2dle (NULL, NULL, ad->Y, ec_gen, r_sum2, proof2);
	}

	gcry_mpi_release (r_sum);
	gcry_mpi_release (r_sum2);
	gcry_mpi_release (r_part);

	return ret;
}


int
smc_recv_encrypted_bid (struct BRANDT_Auction *ad,
                        const unsigned char   *buf,
                        size_t                buflen,
                        uint16_t              sender)
{
	int                 ret = 0;
	const unsigned char *cur = buf;
	struct proof_0og    *proof3;
	gcry_mpi_point_t    **ct; /* ciphertexts */
	gcry_mpi_point_t    alpha_sum = gcry_mpi_point_new (0);
	gcry_mpi_point_t    beta_sum = gcry_mpi_point_new (0);
	gcry_mpi_point_t    alpha_sum2 = gcry_mpi_point_new (0);
	gcry_mpi_point_t    beta_sum2 = gcry_mpi_point_new (0);

	brandt_assert (ad && buf);

	if (buflen != (ad->k * (sizeof (struct ec_mpi) * 2 + sizeof (*proof3)) +
	               (0 < ad->m ? 2 : 1) * sizeof (struct proof_2dle)) ||
	    NULL == (ct = smc_init2 (2, ad->k)))
	{
		GNUNET_log_from (GNUNET_ERROR_TYPE_WARNING,
		                 "libbrandt",
		                 "wrong size of received encrypted bid\n");
		goto quit;
	}

	ec_point_copy (alpha_sum, ec_zero);
	ec_point_copy (beta_sum, ec_zero);
	ec_point_copy (alpha_sum2, ec_zero);
	ec_point_copy (beta_sum2, ec_zero);

	for (uint16_t j = 0; j < ad->k; j++)
	{
		ec_point_parse (ct[0][j], (struct ec_mpi *)cur);
		ec_point_parse (ct[1][j], &((struct ec_mpi *)cur)[1]);
		proof3 = (struct proof_0og *)(cur + 2 * sizeof (struct ec_mpi));
		if (smc_zkp_0og_check (ad->Y, ct[0][j], ct[1][j], proof3))
		{
			GNUNET_log_from (GNUNET_ERROR_TYPE_WARNING,
			                 "libbrandt",
			                 "wrong zkp3 for alpha, beta received\n");
			goto quit;
		}
		gcry_mpi_ec_add (alpha_sum, alpha_sum, ct[0][j], ec_ctx);
		gcry_mpi_ec_add (beta_sum, beta_sum, ct[1][j], ec_ctx);

		/* precalculate ciphertext sums for second 2dle proof needed in M+1st
		 * price auctions */
		if (0 < ad->m && 1 == (ad->k - j - sender) % ad->n)
		{
			gcry_mpi_ec_add (alpha_sum2, alpha_sum2, ct[0][j], ec_ctx);
			gcry_mpi_ec_add (beta_sum2, beta_sum2, ct[1][j], ec_ctx);
		}

		cur += 2 * sizeof (struct ec_mpi) + sizeof (struct proof_0og);
	}

	gcry_mpi_ec_sub (alpha_sum, alpha_sum, ec_gen, ec_ctx);
	if (smc_zkp_2dle_check (alpha_sum,
	                        beta_sum,
	                        ad->Y,
	                        ec_gen,
	                        (struct proof_2dle *)cur))
	{
		GNUNET_log_from (GNUNET_ERROR_TYPE_WARNING,
		                 "libbrandt",
		                 "wrong zkp2 for alpha, beta received\n");
		goto quit;
	}

	/* On M+1st price auctions check with the second 2dle proof if the bidder
	 * only bid on one of his allowed indizes */
	if (0 < ad->m)
	{
		cur += sizeof (struct proof_2dle);
		gcry_mpi_ec_sub (alpha_sum2, alpha_sum2, ec_gen, ec_ctx);
		if (smc_zkp_2dle_check (alpha_sum2,
		                        beta_sum2,
		                        ad->Y,
		                        ec_gen,
		                        (struct proof_2dle *)cur))
		{
			GNUNET_log_from (
			    GNUNET_ERROR_TYPE_WARNING,
			    "libbrandt",
			    "wrong second zkp2 for alpha, beta received. "
			    "bid not allowed for this user in M+1st price auctions.\n");
			goto quit;
		}
	}

	for (uint16_t j = 0; j < ad->k; j++)
	{
		ec_point_copy (ad->alpha[sender][j], ct[0][j]);
		ec_point_copy (ad->beta[sender][j], ct[1][j]);
	}
	smc_free2 (ct, 2, ad->k);

	ret = 1; /* finally success */
quit:
	gcry_mpi_point_release (alpha_sum);
	gcry_mpi_point_release (beta_sum);
	gcry_mpi_point_release (alpha_sum2);
	gcry_mpi_point_release (beta_sum2);
	return ret;
}


/**
 * smc_zkp_dl creates a proof of knowledge of @a x with \f$v = xg\f$ where
 * \f$g\f$ is the base point on Ed25519.
 *
 * @param[out] v output point. Must be known to the verifier.
 * @param[in] x private key. Knowledge of this number is certified in the proof
 * @param[out] proof pointer where to save the output proof structure. Must be
 * shared with the verifier.
 */
void
smc_zkp_dl (gcry_mpi_point_t v,
            const gcry_mpi_t x,
            struct proof_dl  *proof)
{
	struct zkp_challenge_dl challenge;
	gcry_mpi_point_t        a = gcry_mpi_point_new (0);
	gcry_mpi_t              r = gcry_mpi_new (256);
	gcry_mpi_t              c;
	gcry_mpi_t              z = gcry_mpi_new (256);

	/* v = xg */
	gcry_mpi_ec_mul (v, x, ec_gen, ec_ctx);

	/* a = zg */
	ec_keypair_create (a, z);

	/* compute challenge c */
	ec_point_serialize (&challenge.g, ec_gen);
	ec_point_serialize (&challenge.v, v);
	ec_point_serialize (&challenge.a, a);
	GNUNET_CRYPTO_kdf_mod_mpi (&c,
	                           ec_n,
	                           NULL,
	                           0,
	                           &challenge,
	                           sizeof (challenge),
	                           "libbrandt zkp dl");

	/* r = z + cx */
	gcry_mpi_mulm (r, c, x, ec_n);
	gcry_mpi_addm (r, r, z, ec_n);

	ec_point_serialize (&proof->a, a);
	mpi_serialize (&proof->r, r);

	gcry_mpi_point_release (a);
	gcry_mpi_release (r);
	gcry_mpi_release (c);
	gcry_mpi_release (z);
}


/**
 * smc_zkp_dl_check verifies a proof of knowledge of \f$x = ECDL_g(v)\f$ where
 * \f$g\f$ is the base point on Ed25519.
 *
 * @param[in] v input point. Received from the prover.
 * @param[in] proof pointer to the proof structure. Received from the prover.
 * @return 0 if the proof is correct, something else otherwise
 */
int
smc_zkp_dl_check (const gcry_mpi_point_t v,
                  const struct proof_dl  *proof)
{
	int                     ret;
	struct zkp_challenge_dl challenge;
	gcry_mpi_point_t        a = gcry_mpi_point_new (0);
	gcry_mpi_t              r = gcry_mpi_new (256);
	gcry_mpi_t              c;
	gcry_mpi_point_t        left = gcry_mpi_point_new (0);
	gcry_mpi_point_t        right = gcry_mpi_point_new (0);

	ec_point_parse (a, &proof->a);
	mpi_parse (r, &proof->r);

	/* compute challenge c */
	ec_point_serialize (&challenge.g, ec_gen);
	ec_point_serialize (&challenge.v, v);
	ec_point_serialize (&challenge.a, a);
	GNUNET_CRYPTO_kdf_mod_mpi (&c,
	                           ec_n,
	                           NULL,
	                           0,
	                           &challenge,
	                           sizeof (challenge),
	                           "libbrandt zkp dl");

	/* rg =? a + cv */
	gcry_mpi_ec_mul (left, r, ec_gen, ec_ctx);
	gcry_mpi_ec_mul (right, c, v, ec_ctx);
	gcry_mpi_ec_add (right, a, right, ec_ctx);
	ret = ec_point_cmp (left, right);

	gcry_mpi_point_release (a);
	gcry_mpi_release (r);
	gcry_mpi_release (c);
	gcry_mpi_point_release (left);
	gcry_mpi_point_release (right);

	return ret;
}


/**
 * smc_zkp_2dle creates a proof that two ECDLs are equal without revealing the
 * ECDL. \f$v=xg_1, w=xg_2\f$ are calculated as well and can be returned to the
 * caller if needed.
 *
 * @param[out] v first output point. May be NULL if not needed by the caller.
 * Must be known to the verifier.
 * @param[out] w second output point. May be NULL if not needed by the caller.
 * Must be known to the verifier.
 * @param[in] g1 first base point. Must be known to the verifier.
 * @param[in] g2 second base point. Must be known to the verifier.
 * @param[in] x private number to prove knowledge of. May be NULL if not used by
 * the caller.
 * @param[out] proof pointer where to save the output proof structure. Must be
 * shared with the verifier.
 */
void
smc_zkp_2dle (gcry_mpi_point_t       v,
              gcry_mpi_point_t       w,
              const gcry_mpi_point_t g1,
              const gcry_mpi_point_t g2,
              const gcry_mpi_t       x,
              struct proof_2dle      *proof)
{
	struct zkp_challenge_2dle challenge;
	gcry_mpi_point_t          rv;
	gcry_mpi_point_t          rw;
	gcry_mpi_t                rx;
	gcry_mpi_point_t          a = gcry_mpi_point_new (0);
	gcry_mpi_point_t          b = gcry_mpi_point_new (0);
	gcry_mpi_t                r = gcry_mpi_new (256);
	gcry_mpi_t                c;
	gcry_mpi_t                z = gcry_mpi_new (256);

	rv = (NULL == v) ? gcry_mpi_point_new (0) : v;
	rw = (NULL == w) ? gcry_mpi_point_new (0) : w;
	rx = (NULL == x) ? gcry_mpi_new (256) : x;

	if (NULL == x)
		ec_skey_create (rx);

	/* v = x*g1 */
	gcry_mpi_ec_mul (rv, rx, g1, ec_ctx);

	/* w = x*g2 */
	gcry_mpi_ec_mul (rw, rx, g2, ec_ctx);

	/* a = z*g1 */
	ec_keypair_create_base (a, z, g1);

	/* b = z*g2 */
	gcry_mpi_ec_mul (b, z, g2, ec_ctx);

	/* compute challenge c */
	ec_point_serialize (&challenge.g1, g1);
	ec_point_serialize (&challenge.g2, g2);
	ec_point_serialize (&challenge.v, rv);
	ec_point_serialize (&challenge.w, rw);
	ec_point_serialize (&challenge.a, a);
	ec_point_serialize (&challenge.b, b);
	GNUNET_CRYPTO_kdf_mod_mpi (&c,
	                           ec_n,
	                           NULL,
	                           0,
	                           &challenge,
	                           sizeof (challenge),
	                           "libbrandt zkp 2dle");

	/* r = z + cx */
	gcry_mpi_mulm (r, c, rx, ec_n);
	gcry_mpi_addm (r, r, z, ec_n);

	mpi_serialize (&proof->r, r);
	ec_point_serialize (&proof->a, a);
	ec_point_serialize (&proof->b, b);

	if (NULL == v)
		gcry_mpi_point_release (rv);
	if (NULL == w)
		gcry_mpi_point_release (rw);
	if (NULL == x)
		gcry_mpi_release (rx);
	gcry_mpi_point_release (a);
	gcry_mpi_point_release (b);
	gcry_mpi_release (r);
	gcry_mpi_release (c);
	gcry_mpi_release (z);
}


/**
 * smc_zkp_2dle_check verifies a proof of knowledge of \f$x\f$ with \f$v=xg_1\f$
 * and \f$w=xg_2\f$.
 *
 * @param[in] v first input point.
 * @param[in] w second input point.
 * @param[in] g1 first base point.
 * @param[in] g2 second base point.
 * @param[in] proof pointer to the proof structure. Received from the prover.
 * @return 0 if the proof is correct, something else otherwise
 */
int
smc_zkp_2dle_check (const gcry_mpi_point_t  v,
                    const gcry_mpi_point_t  w,
                    const gcry_mpi_point_t  g1,
                    const gcry_mpi_point_t  g2,
                    const struct proof_2dle *proof)
{
	int                       ret;
	struct zkp_challenge_2dle challenge;
	gcry_mpi_point_t          a = gcry_mpi_point_new (0);
	gcry_mpi_point_t          b = gcry_mpi_point_new (0);
	gcry_mpi_t                r = gcry_mpi_new (256);
	gcry_mpi_t                c;
	gcry_mpi_point_t          left = gcry_mpi_point_new (0);
	gcry_mpi_point_t          right = gcry_mpi_point_new (0);

	mpi_parse (r, &proof->r);
	ec_point_parse (a, &proof->a);
	ec_point_parse (b, &proof->b);

	/* compute challenge c */
	ec_point_serialize (&challenge.g1, g1);
	ec_point_serialize (&challenge.g2, g2);
	ec_point_serialize (&challenge.v, v);
	ec_point_serialize (&challenge.w, w);
	ec_point_serialize (&challenge.a, a);
	ec_point_serialize (&challenge.b, b);
	GNUNET_CRYPTO_kdf_mod_mpi (&c,
	                           ec_n,
	                           NULL,
	                           0,
	                           &challenge,
	                           sizeof (challenge),
	                           "libbrandt zkp 2dle");

	/* r*g1 =? a + cv */
	gcry_mpi_ec_mul (left, r, g1, ec_ctx);
	gcry_mpi_ec_mul (right, c, v, ec_ctx);
	gcry_mpi_ec_add (right, a, right, ec_ctx);
	ret = ec_point_cmp (left, right);

	/* r*g2 =? b + cw */
	gcry_mpi_ec_mul (left, r, g2, ec_ctx);
	gcry_mpi_ec_mul (right, c, w, ec_ctx);
	gcry_mpi_ec_add (right, b, right, ec_ctx);
	ret |= ec_point_cmp (left, right);

	gcry_mpi_point_release (a);
	gcry_mpi_point_release (b);
	gcry_mpi_release (r);
	gcry_mpi_release (c);
	gcry_mpi_point_release (left);
	gcry_mpi_point_release (right);

	return ret;
}


/**
 * smc_zkp_0og encrypts one of two values and creates a proof that the
 * ciphertext decrypts to either one of those two values without revealing which
 * one was encrypted. The two values are the zero point or the base point of the
 * Ed25519 curve. Encryption is done via ElGamal: \f$(\alpha,\beta)=(m+ry,rg)\f$
 * where \f$m\f$ is the value to encrypt, \f$y\f$ is the public key and \f$g\f$
 * is the base point. The nonce \f$r\f$ is generated as well and can be returned
 * to the caller if he needs it (e.g. for another proof).
 *
 * @param[in] m_is_gen if true, the base point is encrypted, else the zero point
 * is encrypted.
 * @param[in] y public key to use for encryption.
 * @param[out] r random number used for encryption. May be NULL if caller
 * doesn't need it.
 * @param[out] alpha first part of the ciphertext output
 * @param[out] beta second part of the ciphertext output
 * @param[out] proof pointer where to save the output proof structure. Must be
 * shared with the verifier.
 */
void
smc_zkp_0og (int                    m_is_gen,
             const gcry_mpi_point_t y,
             gcry_mpi_t             r,
             gcry_mpi_point_t       alpha,
             gcry_mpi_point_t       beta,
             struct proof_0og       *proof)
{
	struct zkp_challenge_0og challenge;
	gcry_mpi_point_t         a1 = gcry_mpi_point_new (0);
	gcry_mpi_point_t         a2 = gcry_mpi_point_new (0);
	gcry_mpi_point_t         b1 = gcry_mpi_point_new (0);
	gcry_mpi_point_t         b2 = gcry_mpi_point_new (0);
	gcry_mpi_t               d1 = gcry_mpi_new (256);
	gcry_mpi_t               d2 = gcry_mpi_new (256);
	gcry_mpi_t               r1 = gcry_mpi_new (256);
	gcry_mpi_t               r2 = gcry_mpi_new (256);
	gcry_mpi_t               c;
	gcry_mpi_t               rr;
	gcry_mpi_t               w = gcry_mpi_new (256);

	rr = (NULL == r) ? gcry_mpi_new (256) : r;

	/* beta = r*g */
	ec_keypair_create (beta, rr);
	gcry_mpi_mod (rr, rr, ec_n);

	/* alpha = m + r*y */
	gcry_mpi_ec_mul (alpha, rr, y, ec_ctx);
	gcry_mpi_ec_add (alpha, m_is_gen ? ec_gen : ec_zero, alpha, ec_ctx);

	if (!m_is_gen)
	{   /* m == 0 */
		ec_keypair_create_base (a1, d1, beta);
		gcry_mpi_mod (d1, d1, ec_n);
		ec_keypair_create_base (b1, r1, y);
		gcry_mpi_mod (r1, r1, ec_n);

		/* a1 = r1*g + d1*beta */
		gcry_mpi_ec_mul (a2, r1, ec_gen, ec_ctx);
		gcry_mpi_ec_add (a1, a2, a1, ec_ctx);

		/* b1 = r1*y + d1*(alpha-g) */
		gcry_mpi_ec_sub (b2, alpha, ec_gen, ec_ctx);
		gcry_mpi_ec_mul (a2, d1, b2, ec_ctx);
		gcry_mpi_ec_add (b1, b1, a2, ec_ctx);

		/* a2 = w * g */
		ec_keypair_create_base (a2, w, ec_gen);
		gcry_mpi_mod (w, w, ec_n);

		/* b2 = w * y */
		gcry_mpi_ec_mul (b2, w, y, ec_ctx);
	}
	else
	{   /* m == g */
		ec_keypair_create_base (a2, d2, beta);
		gcry_mpi_mod (d2, d2, ec_n);
		ec_keypair_create_base (b2, r2, y);
		gcry_mpi_mod (r2, r2, ec_n);

		/* a2 = r2*g + d2*beta */
		gcry_mpi_ec_mul (a1, r2, ec_gen, ec_ctx);
		gcry_mpi_ec_add (a2, a1, a2, ec_ctx);

		/* b2 = r2*y + d2*(alpha-0) */
		/* useless subtraction to have same amount of operations as in m == 0 */
		gcry_mpi_ec_sub (b1, alpha, ec_zero, ec_ctx);
		gcry_mpi_ec_mul (a1, d2, b1, ec_ctx);
		gcry_mpi_ec_add (b2, b2, a1, ec_ctx);

		/* a1 = w * g */
		ec_keypair_create_base (a1, w, ec_gen);
		gcry_mpi_mod (w, w, ec_n);

		/* b1 = w * y */
		gcry_mpi_ec_mul (b1, w, y, ec_ctx);
	}

	/* compute challenge c */
	ec_point_serialize (&challenge.g, ec_gen);
	ec_point_serialize (&challenge.alpha, alpha);
	ec_point_serialize (&challenge.beta, beta);
	ec_point_serialize (&challenge.a1, a1);
	ec_point_serialize (&challenge.a2, a2);
	ec_point_serialize (&challenge.b1, b1);
	ec_point_serialize (&challenge.b2, b2);
	GNUNET_CRYPTO_kdf_mod_mpi (&c,
	                           ec_n,
	                           NULL,
	                           0,
	                           &challenge,
	                           sizeof (challenge),
	                           "libbrandt zkp 0og");

	if (!m_is_gen)
	{   /* m == 0 */
		/* d2 = c - d1 */
		gcry_mpi_subm (d2, c, d1, ec_n);

		/* r2 = w - r*d2 */
		gcry_mpi_mulm (r2, rr, d2, ec_n);
		gcry_mpi_subm (r2, w, r2, ec_n);
	}
	else
	{   /* m == g */
		/* d1 = c - d2 */
		gcry_mpi_subm (d1, c, d2, ec_n);

		/* r1 = w - r*d1 */
		gcry_mpi_mulm (r1, rr, d1, ec_n);
		gcry_mpi_subm (r1, w, r1, ec_n);
	}

	ec_point_serialize (&proof->a1, a1);
	ec_point_serialize (&proof->a2, a2);
	ec_point_serialize (&proof->b1, b1);
	ec_point_serialize (&proof->b2, b2);
	mpi_serialize (&proof->d1, d1);
	mpi_serialize (&proof->d2, d2);
	mpi_serialize (&proof->r1, r1);
	mpi_serialize (&proof->r2, r2);

	gcry_mpi_point_release (a1);
	gcry_mpi_point_release (a2);
	gcry_mpi_point_release (b1);
	gcry_mpi_point_release (b2);
	gcry_mpi_release (d1);
	gcry_mpi_release (d2);
	gcry_mpi_release (r1);
	gcry_mpi_release (r2);
	gcry_mpi_release (c);
	if (NULL == r)
		gcry_mpi_release (rr);
	gcry_mpi_release (w);
}


/**
 * smc_zkp_0og_check verifies a proof that \f$(\alpha,\beta\f$ decrypts either
 * to the base point \f$g\f$ or the zero point.
 *
 * @param[in] y the public key used for encryption
 * @param[in] alpha first part of the ciphertext
 * @param[in] beta second part of the ciphertext
 * @param[in] proof pointer to the proof structure. Received from the prover.
 * @return 0 if the proof is correct, something else otherwise
 */
int
smc_zkp_0og_check (const gcry_mpi_point_t y,
                   const gcry_mpi_point_t alpha,
                   const gcry_mpi_point_t beta,
                   const struct proof_0og *proof)
{
	int                      ret;
	struct zkp_challenge_0og challenge;
	gcry_mpi_point_t         a1 = gcry_mpi_point_new (0);
	gcry_mpi_point_t         a2 = gcry_mpi_point_new (0);
	gcry_mpi_point_t         b1 = gcry_mpi_point_new (0);
	gcry_mpi_point_t         b2 = gcry_mpi_point_new (0);
	gcry_mpi_t               d1 = gcry_mpi_new (256);
	gcry_mpi_t               d2 = gcry_mpi_new (256);
	gcry_mpi_t               r1 = gcry_mpi_new (256);
	gcry_mpi_t               r2 = gcry_mpi_new (256);
	gcry_mpi_t               c;
	gcry_mpi_t               sum = gcry_mpi_new (256);
	gcry_mpi_point_t         right = gcry_mpi_point_new (0);
	gcry_mpi_point_t         tmp = gcry_mpi_point_new (0);

	ec_point_parse (a1, &proof->a1);
	ec_point_parse (a2, &proof->a2);
	ec_point_parse (b1, &proof->b1);
	ec_point_parse (b2, &proof->b2);
	mpi_parse (d1, &proof->d1);
	mpi_parse (d2, &proof->d2);
	mpi_parse (r1, &proof->r1);
	mpi_parse (r2, &proof->r2);

	/* compute challenge c */
	ec_point_serialize (&challenge.g, ec_gen);
	ec_point_serialize (&challenge.alpha, alpha);
	ec_point_serialize (&challenge.beta, beta);
	ec_point_serialize (&challenge.a1, a1);
	ec_point_serialize (&challenge.a2, a2);
	ec_point_serialize (&challenge.b1, b1);
	ec_point_serialize (&challenge.b2, b2);
	GNUNET_CRYPTO_kdf_mod_mpi (&c,
	                           ec_n,
	                           NULL,
	                           0,
	                           &challenge,
	                           sizeof (challenge),
	                           "libbrandt zkp 0og");

	/* c == d1 + d2 */
	gcry_mpi_addm (sum, d1, d2, ec_n);
	ret = gcry_mpi_cmp (c, sum);

	/* a1 == r1*g + d1*beta */
	gcry_mpi_ec_mul (tmp, r1, ec_gen, ec_ctx);
	gcry_mpi_ec_mul (right, d1, beta, ec_ctx);
	gcry_mpi_ec_add (right, tmp, right, ec_ctx);
	ret |= ec_point_cmp (a1, right) << 1;

	/* b1 == r1*y + d1*(alpha-g) */
	gcry_mpi_ec_sub (right, alpha, ec_gen, ec_ctx);
	gcry_mpi_ec_mul (tmp, d1, right, ec_ctx);
	gcry_mpi_ec_mul (right, r1, y, ec_ctx);
	gcry_mpi_ec_add (right, right, tmp, ec_ctx);
	ret |= ec_point_cmp (b1, right) << 2;

	/* a2 == r2*g + d2*beta */
	gcry_mpi_ec_mul (tmp, d2, beta, ec_ctx);
	gcry_mpi_ec_mul (right, r2, ec_gen, ec_ctx);
	gcry_mpi_ec_add (right, right, tmp, ec_ctx);
	ret |= ec_point_cmp (a2, right) << 3;

	/* b2 == r2*y + d2*alpha */
	gcry_mpi_ec_mul (tmp, d2, alpha, ec_ctx);
	gcry_mpi_ec_mul (right, r2, y, ec_ctx);
	gcry_mpi_ec_add (right, right, tmp, ec_ctx);
	ret |= ec_point_cmp (b2, right) << 4;

	gcry_mpi_point_release (a1);
	gcry_mpi_point_release (a2);
	gcry_mpi_point_release (b1);
	gcry_mpi_point_release (b2);
	gcry_mpi_release (d1);
	gcry_mpi_release (d2);
	gcry_mpi_release (r1);
	gcry_mpi_release (r2);
	gcry_mpi_release (c);
	gcry_mpi_release (sum);
	gcry_mpi_point_release (right);
	gcry_mpi_point_release (tmp);

	return ret;
}