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.
 */


#include <arpa/inet.h>
#include <gcrypt.h>

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

#define CURVE "Ed25519"


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;
};


static gcry_ctx_t       ec_ctx;
static gcry_mpi_point_t ec_gen;
static gcry_mpi_point_t ec_zero;
static gcry_mpi_t       ec_n;


/**
 * brandt_crypto_init initializes the crypto system and must be called before
 * any other function from this file.
 */
void
brandt_crypto_init ()
{
	gcry_error_t rc;

	rc = gcry_mpi_ec_new (&ec_ctx, NULL, CURVE);
	brandt_assert_gpgerr (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);
}


/* --- RANDOM --- */

void
brandt_rand_poll ()
{
	static unsigned char rand_amount = 255;

	if (!(rand_amount--))
		gcry_fast_random_poll ();
}


/* --- HASHING --- */

/**
 * Hash block of given size.
 *
 * @param block the data to #brandt_hash, length is given as a second argument
 * @param size the length of the data to #brandt_hash in @a block
 * @param ret pointer to where to write the hashcode
 */
void
brandt_hash (const void *block, size_t size, struct brandt_hash_code *ret)
{
	gcry_md_hash_buffer (GCRY_MD_SHA512, ret, block, size);
}


/* --- 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)))");
	brandt_assert_gpgerr (rc);

	rc = gcry_pk_genkey (&priv_sexp, s_keyparam);
	brandt_assert_gpgerr (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
 *
 * @param[out] pkey where to store the generated public key
 * @param[out] skey where to store the generated secret key
 */
void
ec_keypair_create (gcry_mpi_point_t pkey, gcry_mpi_t skey)
{
	brandt_assert (NULL != pkey);
	brandt_assert (NULL != skey);

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


/**
 * 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_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 (0);
	gcry_mpi_t bx = gcry_mpi_new (0);
	gcry_mpi_t ay = gcry_mpi_new (0);
	gcry_mpi_t by = gcry_mpi_new (0);

	brandt_assert (a && b);
	if (!ax || !bx || !ay || !by)
	{
		weprintf ("could not init point in point_cmp");
		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;
	unsigned int nbits;
	const void   *p;
	gcry_error_t rc;

	if (gcry_mpi_get_flag (src, GCRYMPI_FLAG_OPAQUE))
	{
		/* Store opaque MPIs left aligned into the buffer. Used by Ed25519 point
		 * compression */
		p = gcry_mpi_get_opaque (src, &nbits);
		brandt_assert (p);
		rsize = (nbits + 7) / 8;
		if (rsize > sizeof (struct ec_mpi))
			rsize = sizeof (struct ec_mpi);
		memcpy (dst, p, 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. */
		rc = gcry_mpi_print (GCRYMPI_FMT_USG, (void *)dst,
		                     sizeof (struct ec_mpi), &rsize, src);
		brandt_assert_gpgerr (rc);

		/* Shift the output to the right, if shorter than available space */
		if (rsize && rsize < sizeof (struct ec_mpi))
		{
			memmove (&dst[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);
	brandt_assert_gpgerr (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 ")))");
	brandt_assert_gpgerr (rc);
	brandt_assert (NULL != s);

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

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

	rc = gcry_mpi_ec_new (&ctx, s, NULL);
	brandt_assert_gpgerr (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);
}


/**
 * smc_init2 creates a 2 dimensional array of curve points
 *
 * @param[in] size1 size of the first dimension
 * @param[in] size2 size of the second dimension
 * @return a pointer to the array. If not used anymore use smc_free2 to reclaim
 * the memory.
 */
static gcry_mpi_point_t **
smc_init2 (uint16_t size1, uint16_t size2)
{
	uint16_t         i, j;
	gcry_mpi_point_t **ret;
	gcry_mpi_point_t *data;

	ret = calloc (size1, sizeof (*ret) + size2 * sizeof (**ret));
	brandt_assert (NULL != ret);

	data = (gcry_mpi_point_t *)&ret[size1];
	for (i = 0; i < size1; i++)
	{
		ret[i] = &data[i * size2];
		for (j = 0; j < size2; j++)
			ret[i][j] = gcry_mpi_point_new (0);
	}
	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
 */
static void
smc_free2 (gcry_mpi_point_t **dst, uint16_t size1, uint16_t size2)
{
	uint16_t i, j;

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


/**
 * smc_init3 creates a 3 dimensional array of curve points
 *
 * @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. If not used anymore use smc_free3 to reclaim
 * the memory.
 */
static gcry_mpi_point_t ***
smc_init3 (uint16_t size1, uint16_t size2, uint16_t size3)
{
	uint16_t         i, j, k;
	gcry_mpi_point_t ***ret;
	gcry_mpi_point_t **layer1;
	gcry_mpi_point_t *layer2;

	ret = calloc (size1, sizeof (*ret) +
	              size2 * sizeof (**ret) +
	              size2 * size3 * sizeof (***ret));
	brandt_assert (NULL != ret);

	layer1 = (gcry_mpi_point_t **)&ret[size1];
	layer2 = (gcry_mpi_point_t *)&layer1[size1 * size2];
	for (i = 0; i < size1; i++)
	{
		ret[i] = &layer1[i * size2];
		for (j = 0; j < size2; j++)
		{
			layer1[i * size2 + j] = &layer2[(i * size2 + j) * size3];
			for (k = 0; k < size3; k++)
				ret[i][j][k] = gcry_mpi_point_new (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
 */
static void
smc_free3 (gcry_mpi_point_t ***dst,
           uint16_t         size1,
           uint16_t         size2,
           uint16_t         size3)
{
	uint16_t i, j, k;

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


/**
 * smc_sums_partial calculates sums up until 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 may be given
 * uninitialized, but the appropriate amount of memory has to be allocated
 * beforehand.
 * @param[in] in Input points.
 * @param[in] len The length of both @a out and @a in.
 */
static void
smc_sums_partial (gcry_mpi_point_t out[], gcry_mpi_point_t in[], uint16_t len)
{
	uint16_t i;

	for (i = 0; i < len; i++)
	{
		out[i] = gcry_mpi_point_new (0);
		gcry_mpi_ec_add (out[i], in[i], (i ? out[i - 1] : ec_zero), ec_ctx);
		brandt_assert (NULL != out[i]);
	}
}


/**
 * 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 length of @a in.
 */
static void
smc_sum (gcry_mpi_point_t out, gcry_mpi_point_t in[], uint16_t len)
{
	uint16_t i;

	brandt_assert (NULL != out);
	/**\todo: how to copy a point more efficiently? */
	gcry_mpi_ec_add (out, ec_zero, ec_zero, ec_ctx);
	for (i = 0; i < len; i++)
		gcry_mpi_ec_add (out, out, in[i], ec_ctx);
}


/**
 * smc_compute_pkey calculates the shared public key
 *
 * @param[in,out] ad The struct AuctionData used
 */
void
smc_compute_pkey (struct AuctionData *ad)
{
	ad->Y = gcry_mpi_point_new (0);
	smc_sum (ad->Y, ad->y, ad->n);
}


/**
 * smc_gen_keyshare creates the private additive keyshare and computes the
 * public multiplicative key share
 *
 * @param[in,out] ad Pointer to the AuctionData struct to operate on
 */
void
smc_gen_keyshare (struct AuctionData *ad)
{
	uint16_t i;

	ad->y = calloc (ad->n, sizeof (*ad->y));
	for (i = 0; i < ad->n; i++)
		ad->y[0] = gcry_mpi_point_new (0);

	ad->x = gcry_mpi_new (0);
	ec_keypair_create (ad->y[ad->i], ad->x);
}


/**
 * smc_encrypt_bid \todo
 *
 * @param ad TODO
 * @param j TODO
 * @param a1 TODO
 * @param a2 TODO
 * @param b1 TODO
 * @param b2 TODO
 * @param d1 TODO
 * @param d2 TODO
 * @param r1 TODO
 * @param r2 TODO
 */
void
smc_encrypt_bid (struct AuctionData *ad,
                 uint16_t           j,
                 gcry_mpi_point_t   a1,
                 gcry_mpi_point_t   a2,
                 gcry_mpi_point_t   b1,
                 gcry_mpi_point_t   b2,
                 gcry_mpi_t         d1,
                 gcry_mpi_t         d2,
                 gcry_mpi_t         r1,
                 gcry_mpi_t         r2)
{
	smc_zkp_0og (ad->alpha[ad->i][j], (j == ad->b ? ec_gen : ec_zero), ad->Y,
	             ad->beta[ad->i][j], a1, a2, b1, b2, d1, d2, r1, r2);
}


/**
 * smc_compute_outcome \todo
 *
 * @param ad TODO
 */
void
smc_compute_outcome (struct AuctionData *ad)
{
	uint16_t i, j;

	// create temporary table with partial sums


	for (i = 0; i < ad->n; i++)
	{

	}
	/*\todo ZKP*/
}


/**
 * smc_zkp_dl
 *
 * @param v \todo
 * @param g \todo
 * @param x \todo
 * @param a \todo
 * @param r \todo
 */
void
smc_zkp_dl (const gcry_mpi_point_t v,
            const gcry_mpi_point_t g,
            const gcry_mpi_t       x,
            const gcry_mpi_point_t a,
            gcry_mpi_t             r)
{
	struct zkp_challenge_dl challenge;
	struct brandt_hash_code challhash;
	gcry_mpi_t              c = gcry_mpi_new (0);
	gcry_mpi_t              z = gcry_mpi_new (0);

	ec_keypair_create_base (a, z, g);

	/* compute challenge c */
	ec_point_serialize (&challenge.g, ec_gen);
	ec_point_serialize (&challenge.v, v);
	ec_point_serialize (&challenge.a, a);
	brandt_hash (&challenge, sizeof (struct zkp_challenge_dl), &challhash);
	mpi_parse (c, (struct ec_mpi *)&challhash);
	gcry_mpi_mod (c, c, ec_n);

	gcry_mpi_mulm (r, c, x, ec_n);
	gcry_mpi_addm (r, r, z, ec_n);

	gcry_mpi_release (c);
	gcry_mpi_release (z);
}


/**
 * smc_zkp_dl_check
 *
 * @param v \todo
 * @param g \todo
 * @param a \todo
 * @param r \todo
 * @return 0 if the proof is correct, something else otherwise
 */
int
smc_zkp_dl_check (const gcry_mpi_point_t v,
                  const gcry_mpi_point_t g,
                  const gcry_mpi_point_t a,
                  const gcry_mpi_t       r)
{
	int                     ret;
	struct zkp_challenge_dl challenge;
	struct brandt_hash_code challhash;
	gcry_mpi_t              c = gcry_mpi_new (0);
	gcry_mpi_point_t        left = gcry_mpi_point_new (0);
	gcry_mpi_point_t        right = gcry_mpi_point_new (0);

	/* compute challenge c */
	ec_point_serialize (&challenge.g, ec_gen);
	ec_point_serialize (&challenge.v, v);
	ec_point_serialize (&challenge.a, a);
	brandt_hash (&challenge, sizeof (struct zkp_challenge_dl), &challhash);
	mpi_parse (c, (struct ec_mpi *)&challhash);
	gcry_mpi_mod (c, c, ec_n);

	gcry_mpi_ec_mul (left, r, g, 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_release (c);
	gcry_mpi_point_release (left);
	gcry_mpi_point_release (right);

	return ret;
}


/**
 * smc_zkp_2dle \todo
 *
 * @param v TODO
 * @param w TODO
 * @param g1 TODO
 * @param g2 TODO
 * @param x TODO
 * @param a TODO
 * @param b TODO
 * @param r TODO
 */
void
smc_zkp_2dle (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 gcry_mpi_t       x,
              gcry_mpi_point_t       a,
              gcry_mpi_point_t       b,
              gcry_mpi_t             r)
{
	struct zkp_challenge_2dle challenge;
	struct brandt_hash_code   challhash;
	gcry_mpi_t                c = gcry_mpi_new (0);
	gcry_mpi_t                z = gcry_mpi_new (0);

	ec_keypair_create_base (a, z, g1);
	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, v);
	ec_point_serialize (&challenge.w, w);
	ec_point_serialize (&challenge.a, a);
	ec_point_serialize (&challenge.b, b);
	brandt_hash (&challenge, sizeof (struct zkp_challenge_dl), &challhash);
	mpi_parse (c, (struct ec_mpi *)&challhash);
	gcry_mpi_mod (c, c, ec_n);

	gcry_mpi_mulm (r, c, x, ec_n);
	gcry_mpi_addm (r, r, z, ec_n);

	gcry_mpi_release (c);
	gcry_mpi_release (z);
}


/**
 * smc_zkp_2dle_check \todo
 *
 * @param v TODO
 * @param w TODO
 * @param g1 TODO
 * @param g2 TODO
 * @param a TODO
 * @param b TODO
 * @param r TODO
 * @return TODO
 */
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 gcry_mpi_point_t a,
                    const gcry_mpi_point_t b,
                    const gcry_mpi_t       r)
{
	int                       ret;
	struct zkp_challenge_2dle challenge;
	struct brandt_hash_code   challhash;
	gcry_mpi_t                c = gcry_mpi_new (0);
	gcry_mpi_point_t          left = gcry_mpi_point_new (0);
	gcry_mpi_point_t          right = gcry_mpi_point_new (0);

	/* 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);
	brandt_hash (&challenge, sizeof (struct zkp_challenge_dl), &challhash);
	mpi_parse (c, (struct ec_mpi *)&challhash);
	gcry_mpi_mod (c, c, ec_n);

	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);

	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_release (c);
	gcry_mpi_point_release (left);
	gcry_mpi_point_release (right);

	return ret;
}


/**
 * smc_zkp_0og \todo
 *
 * @param alpha TODO
 * @param m TODO
 * @param y TODO
 * @param beta TODO
 * @param a1 TODO
 * @param a2 TODO
 * @param b1 TODO
 * @param b2 TODO
 * @param d1 TODO
 * @param d2 TODO
 * @param r1 TODO
 * @param r2 TODO
 */
void
smc_zkp_0og (gcry_mpi_point_t       alpha,
             const gcry_mpi_point_t m,
             const gcry_mpi_point_t y,
             gcry_mpi_point_t       beta,
             gcry_mpi_point_t       a1,
             gcry_mpi_point_t       a2,
             gcry_mpi_point_t       b1,
             gcry_mpi_point_t       b2,
             gcry_mpi_t             d1,
             gcry_mpi_t             d2,
             gcry_mpi_t             r1,
             gcry_mpi_t             r2)
{
	struct zkp_challenge_0og challenge;
	struct brandt_hash_code  challhash;
	gcry_mpi_t               c = gcry_mpi_new (0);
	gcry_mpi_t               r = gcry_mpi_new (0);
	gcry_mpi_t               w = gcry_mpi_new (0);
	int                      eq0 = !ec_point_cmp (m, ec_zero);
	int                      eqg = !ec_point_cmp (m, ec_gen);

	if (!(eq0 ^ eqg))
		eprintf ("zero knowledge proof: m is neither 0 nor g");

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

	/* alpha = m + r*y */
	gcry_mpi_ec_mul (alpha, r, y, ec_ctx);
	gcry_mpi_ec_add (alpha, m, alpha, ec_ctx);

	if (eq0)
	{   /* 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);
	brandt_hash (&challenge, sizeof (struct zkp_challenge_dl), &challhash);
	mpi_parse (c, (struct ec_mpi *)&challhash);
	gcry_mpi_mod (c, c, ec_n);

	if (eq0)
	{   /* m == 0 */
		/* d2 = c - d1 */
		gcry_mpi_subm (d2, c, d1, ec_n);

		/* r2 = w - r*d2 */
		gcry_mpi_mulm (r2, r, 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, r, d1, ec_n);
		gcry_mpi_subm (r1, w, r1, ec_n);
	}

	gcry_mpi_release (c);
	gcry_mpi_release (r);
	gcry_mpi_release (w);
}


/**
 * smc_zkp_0og_check \todo
 *
 * @param alpha TODO
 * @param y TODO
 * @param beta TODO
 * @param a1 TODO
 * @param a2 TODO
 * @param b1 TODO
 * @param b2 TODO
 * @param d1 TODO
 * @param d2 TODO
 * @param r1 TODO
 * @param r2 TODO
 * @return TODO
 */
int
smc_zkp_0og_check (const gcry_mpi_point_t alpha,
                   const gcry_mpi_point_t y,
                   const gcry_mpi_point_t beta,
                   const gcry_mpi_point_t a1,
                   const gcry_mpi_point_t a2,
                   const gcry_mpi_point_t b1,
                   const gcry_mpi_point_t b2,
                   const gcry_mpi_t       d1,
                   const gcry_mpi_t       d2,
                   const gcry_mpi_t       r1,
                   const gcry_mpi_t       r2)
{
	int                      ret;
	struct zkp_challenge_0og challenge;
	struct brandt_hash_code  challhash;
	gcry_mpi_t               c = gcry_mpi_new (0);
	gcry_mpi_t               sum = gcry_mpi_new (0);
	gcry_mpi_point_t         right = gcry_mpi_point_new (0);
	gcry_mpi_point_t         tmp = gcry_mpi_point_new (0);

	/* 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);
	brandt_hash (&challenge, sizeof (struct zkp_challenge_dl), &challhash);
	mpi_parse (c, (struct ec_mpi *)&challhash);
	gcry_mpi_mod (c, c, ec_n);

	/* 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_release (c);
	gcry_mpi_release (sum);
	gcry_mpi_point_release (right);
	gcry_mpi_point_release (tmp);

	if (ret)
		weprintf ("ret: 0x%x", ret);
	return ret;
}


/* --- unused stuff, might become useful later --- */

///**
// * Clear memory that was used to store a private key.
// *
// * @param skey the key
// */
//void
//brandt_ec_key_clear (gcry_mpi_t skey)
//{
//	gcry_mpi_randomize (skey, 256, GCRY_WEAK_RANDOM);
//	gcry_mpi_release (skey);
//}


///**
// * Generate a random value mod n.
// *
// * @param edc ECC context
// * @return random value mod n.
// */
//gcry_mpi_t
//GNUNET_CRYPTO_ecc_random_mod_n (struct GNUNET_CRYPTO_EccDlogContext *edc)
//{
//  gcry_mpi_t n;
//  unsigned int highbit;
//  gcry_mpi_t r;
//
//  n = gcry_mpi_ec_get_mpi ("n", edc->ctx, 1);
//
//  /* check public key for number of bits, bail out if key is all zeros */
//  highbit = 256; /* Curve25519 */
//  while ( (! gcry_mpi_test_bit (n, highbit)) &&
//          (0 != highbit) )
//    highbit--;
//  GNUNET_assert (0 != highbit);
//  /* generate fact < n (without bias) */
//  GNUNET_assert (NULL != (r = gcry_mpi_new (0)));
//  do {
//    gcry_mpi_randomize (r,
//			highbit + 1,
//			GCRY_STRONG_RANDOM);
//  }
//  while (gcry_mpi_cmp (r, n) >= 0);
//  gcry_mpi_release (n);
//  return r;
//}