/* * test-rsa.c * ---------- * Test harness for RSA using Cryptech ModExp core. * * Authors: Rob Austein * Copyright (c) 2015, NORDUnet A/S * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are * met: * - Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * * - Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * - Neither the name of the NORDUnet nor the names of its contributors may * be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS * IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED * TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #include #include #include #include #include #include #include "test-rsa.h" /* * Run one modexp test. */ static int test_modexp(hal_core_t *core, const char * const kind, const rsa_tc_t * const tc, const rsa_tc_bn_t * const msg, /* Input message */ const rsa_tc_bn_t * const exp, /* Exponent */ const rsa_tc_bn_t * const val) /* Expected result */ { uint8_t result[tc->n.len]; printf("%s test for %lu-bit RSA key\n", kind, (unsigned long) tc->size); if (hal_modexp(core, msg->val, msg->len, exp->val, exp->len, tc->n.val, tc->n.len, result, sizeof(result)) != HAL_OK) return printf("ModExp failed\n"), 0; if (memcmp(result, val->val, val->len)) return printf("MISMATCH\n"), 0; return 1; } /* * Run one RSA CRT test. */ static int test_decrypt(hal_core_t *core, const char * const kind, const rsa_tc_t * const tc) { printf("%s test for %lu-bit RSA key\n", kind, (unsigned long) tc->size); uint8_t keybuf[hal_rsa_key_t_size]; hal_rsa_key_t *key = NULL; hal_error_t err = HAL_OK; if ((err = hal_rsa_key_load_private(&key, keybuf, sizeof(keybuf), tc->n.val, tc->n.len, tc->e.val, tc->e.len, tc->d.val, tc->d.len, tc->p.val, tc->p.len, tc->q.val, tc->q.len, tc->u.val, tc->u.len, tc->dP.val, tc->dP.len, tc->dQ.val, tc->dQ.len)) != HAL_OK) return printf("RSA CRT key load failed: %s\n", hal_error_string(err)), 0; uint8_t result[tc->n.len]; if ((err = hal_rsa_decrypt(core, key, tc->m.val, tc->m.len, result, sizeof(result))) != HAL_OK) printf("RSA CRT failed: %s\n", hal_error_string(err)); const int mismatch = (err == HAL_OK && memcmp(result, tc->s.val, tc->s.len) != 0); if (mismatch) printf("MISMATCH\n"); hal_rsa_key_clear(key); return err == HAL_OK && !mismatch; } /* * Run one RSA key generation + CRT test. */ static int test_gen(hal_core_t *core, const char * const kind, const rsa_tc_t * const tc) { printf("%s test for %lu-bit RSA key\n", kind, (unsigned long) tc->size); char fn[sizeof("test-rsa-private-key-xxxxxx.der")]; uint8_t keybuf1[hal_rsa_key_t_size], keybuf2[hal_rsa_key_t_size]; hal_rsa_key_t *key1 = NULL, *key2 = NULL; hal_error_t err = HAL_OK; FILE *f; const uint8_t f4[] = { 0x01, 0x00, 0x01 }; if ((err = hal_rsa_key_gen(core, &key1, keybuf1, sizeof(keybuf1), bitsToBytes(tc->size), f4, sizeof(f4))) != HAL_OK) return printf("RSA key generation failed: %s\n", hal_error_string(err)), 0; size_t der_len = 0; if ((err = hal_rsa_private_key_to_der(key1, NULL, &der_len, 0)) != HAL_OK) return printf("Getting DER length of RSA key failed: %s\n", hal_error_string(err)), 0; uint8_t der[der_len]; err = hal_rsa_private_key_to_der(key1, der, &der_len, sizeof(der)); snprintf(fn, sizeof(fn), "test-rsa-private-key-%04lu.der", (unsigned long) tc->size); printf("Writing %s\n", fn); if ((f = fopen(fn, "wb")) == NULL) return printf("Couldn't open %s: %s\n", fn, strerror(errno)), 0; if (fwrite(der, der_len, 1, f) != 1) return printf("Length mismatch writing %s\n", fn), 0; if (fclose(f) == EOF) return printf("Couldn't close %s: %s\n", fn, strerror(errno)), 0; /* Deferred error from hal_rsa_private_key_to_der() */ if (err != HAL_OK) return printf("Converting RSA private key to DER failed: %s\n", hal_error_string(err)), 0; if ((err = hal_rsa_private_key_from_der(&key2, keybuf2, sizeof(keybuf2), der, sizeof(der))) != HAL_OK) return printf("Converting RSA key back from DER failed: %s\n", hal_error_string(err)), 0; if (memcmp(keybuf1, keybuf2, hal_rsa_key_t_size) != 0) return printf("RSA private key mismatch after conversion to and back from DER\n"), 0; uint8_t result[tc->n.len]; if ((err = hal_rsa_decrypt(core, key1, tc->m.val, tc->m.len, result, sizeof(result))) != HAL_OK) printf("RSA CRT failed: %s\n", hal_error_string(err)); snprintf(fn, sizeof(fn), "test-rsa-sig-%04lu.der", (unsigned long) tc->size); printf("Writing %s\n", fn); if ((f = fopen(fn, "wb")) == NULL) return printf("Couldn't open %s: %s\n", fn, strerror(errno)), 0; if (fwrite(result, sizeof(result), 1, f) != 1) return printf("Length mismatch writing %s\n", fn), 0; if (fclose(f) == EOF) return printf("Couldn't close %s: %s\n", fn, strerror(errno)), 0; if (err != HAL_OK) /* Deferred failure from hal_rsa_decrypt(), above */ return 0; if ((err = hal_rsa_encrypt(core, key1, result, sizeof(result), result, sizeof(result))) != HAL_OK) printf("First RSA signature check failed: %s\n", hal_error_string(err)); int mismatch = 0; if (err == HAL_OK && memcmp(result, tc->m.val, tc->m.len) != 0) mismatch = (printf("MISMATCH\n"), 1); hal_rsa_key_clear(key2); key2 = NULL; if ((f = fopen(fn, "rb")) == NULL) return printf("Couldn't open %s: %s\n", fn, strerror(errno)), 0; if (fread(result, sizeof(result), 1, f) != 1) return printf("Length mismatch reading %s\n", fn), 0; if (fclose(f) == EOF) return printf("Couldn't close %s: %s\n", fn, strerror(errno)), 0; err = hal_rsa_public_key_to_der(key1, der, &der_len, sizeof(der)); snprintf(fn, sizeof(fn), "test-rsa-public-key-%04lu.der", (unsigned long) tc->size); printf("Writing %s\n", fn); if ((f = fopen(fn, "wb")) == NULL) return printf("Couldn't open %s: %s\n", fn, strerror(errno)), 0; if (fwrite(der, der_len, 1, f) != 1) return printf("Length mismatch writing %s\n", fn), 0; if (fclose(f) == EOF) return printf("Couldn't close %s: %s\n", fn, strerror(errno)), 0; /* Deferred error from hal_rsa_public_key_to_der() */ if (err != HAL_OK) return printf("Converting RSA public key to DER failed: %s\n", hal_error_string(err)), 0; if ((err = hal_rsa_public_key_from_der(&key2, keybuf2, sizeof(keybuf2), der, der_len)) != HAL_OK) return printf("Converting RSA public key back from DER failed: %s\n", hal_error_string(err)), 0; /* * Can't directly compare private key with public key. We could * extract and compare the public key components, not much point if * the public key passes the signature verification test below. */ if ((err = hal_rsa_encrypt(core, key2, result, sizeof(result), result, sizeof(result))) != HAL_OK) return printf("Second RSA signature check failed: %s\n", hal_error_string(err)), 0; if (err == HAL_OK && memcmp(result, tc->m.val, tc->m.len) != 0) mismatch = (printf("MISMATCH\n"), 1); hal_rsa_key_clear(key1); hal_rsa_key_clear(key2); return err == HAL_OK && !mismatch; } /* * Time a test. */ static void _time_check(const struct timeval t0, const int ok) { struct timeval t; gettimeofday(&t, NULL); t.tv_sec -= t0.tv_sec; t.tv_usec = t0.tv_usec; if (t.tv_usec < 0) { t.tv_usec += 1000000; t.tv_sec -= 1; } printf("Elapsed time %lu.%06lu seconds, %s\n", (unsigned long) t.tv_sec, (unsigned long) t.tv_usec, ok ? "OK" : "FAILED"); } #define time_check(_expr_) \ do { \ struct timeval _t; \ gettimeofday(&_t, NULL); \ int _ok = (_expr_); \ _time_check(_t, _ok); \ ok &= _ok; \ } while (0) /* * Test signature and exponentiation for one RSA keypair using * precompiled test vectors, then generate a key of the same length * and try generating a signature with that. */ static int test_rsa(hal_core_t *core, const rsa_tc_t * const tc) { int ok = 1; /* RSA encryption */ time_check(test_modexp(core, "Verification", tc, &tc->s, &tc->e, &tc->m)); /* Brute force RSA decryption */ time_check(test_modexp(core, "Signature (ModExp)", tc, &tc->m, &tc->d, &tc->s)); /* RSA decyrption using CRT */ time_check(test_decrypt(core, "Signature (CRT)", tc)); /* Key generation and CRT -- not test vector, so writes key and sig to file */ time_check(test_gen(core, "Generation and CRT", tc)); return ok; } int main(int argc, char *argv[]) { hal_core_t *core = hal_core_find(MODEXPS6_NAME, NULL); if (core == NULL) core = hal_core_find(MODEXPA7_NAME, NULL); const hal_core_info_t *core_info = hal_core_info(core); if (core_info != NULL) printf("\"%8.8s\" \"%4.4s\"\n\n", core_info->name, core_info->version); /* * Run the test cases. */ hal_modexp_set_debug(1); /* Normal test */ for (int i = 0; i < (sizeof(rsa_tc)/sizeof(*rsa_tc)); i++) if (!test_rsa(core, &rsa_tc[i])) return 1; return 0; } /* * Local variables: * indent-tabs-mode: nil * End: */ n235' href='#n235'>235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 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/*
 * ecdsa.c
 * -------
 * Elliptic Curve Digital Signature Algorithm for NIST prime curves.
 *
 * At some point we may want to refactor this code to separate
 * functionality that applies to all elliptic curve cryptography into
 * a separate module from functions specific to ECDSA over the NIST
 * prime curves, but it's simplest to keep this all in one place
 * initially.
 *
 * Much of the code in this module is based, at least loosely, on Tom
 * St Denis's libtomcrypt code.  Algorithms for point addition and
 * point doubling courtesy of the hyperelliptic.org formula database.
 *
 * Authors: Rob Austein
 * Copyright (c) 2015, NORDUnet A/S
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 * - Redistributions of source code must retain the above copyright notice,
 *   this list of conditions and the following disclaimer.
 *
 * - Redistributions in binary form must reproduce the above copyright
 *   notice, this list of conditions and the following disclaimer in the
 *   documentation and/or other materials provided with the distribution.
 *
 * - Neither the name of the NORDUnet nor the names of its contributors may
 *   be used to endorse or promote products derived from this software
 *   without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
 * IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
 * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
 * TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

/*
 * We use "Tom's Fast Math" library for our bignum implementation.
 * This particular implementation has a couple of nice features:
 *
 * - The code is relatively readable, thus reviewable.
 *
 * - The bignum representation doesn't use dynamic memory, which
 *   simplifies things for us.
 *
 * The price tag for not using dynamic memory is that libtfm has to be
 * configured to know about the largest bignum one wants it to be able
 * to support at compile time.  This should not be a serious problem.
 *
 * We use a lot of one-element arrays (fp_int[1] instead of plain
 * fp_int) to avoid having to prefix every use of an fp_int with "&".
 * Perhaps we should encapsulate this idiom in a typedef.
 *
 * Unfortunately, libtfm is bad about const-ification, but we want to
 * hide that from our users, so our public API uses const as
 * appropriate and we use inline functions to remove const constraints
 * in a relatively type-safe manner before calling libtom.
 */

#include <stdint.h>
#include <assert.h>

#include "hal.h"
#include "hal_internal.h"
#include <tfm.h>
#include "asn1_internal.h"

/*
 * Whether we're using static test vectors instead of the random
 * number generator.  Do NOT enable this in production (doh).
 */

#ifndef HAL_ECDSA_DEBUG_ONLY_STATIC_TEST_VECTOR_RANDOM
#define HAL_ECDSA_DEBUG_ONLY_STATIC_TEST_VECTOR_RANDOM 0
#endif

#if defined(RPC_CLIENT) && RPC_CLIENT != RPC_CLIENT_LOCAL
#define hal_get_random(core, buffer, length) hal_rpc_get_random(buffer, length)
#endif

/*
 * Whether we want debug output.
 */

static int debug = 0;

void hal_ecdsa_set_debug(const int onoff)
{
  debug = onoff;
}

/*
 * ECDSA curve descriptor.  We only deal with named curves; at the
 * moment, we only deal with NIST prime curves where the elliptic
 * curve's "a" parameter is always -3 and its "h" value (order of
 * elliptic curve group divided by order of base point) is always 1.
 *
 * Since the Montgomery parameters we need for the point arithmetic
 * depend only on the underlying field prime, we precompute them when
 * we load the curve and store them in the field descriptor, even
 * though they aren't really curve parameters per se.
 *
 * For similar reasons, we also include the ASN.1 OBJECT IDENTIFIERs
 * used to name these curves.
 */

typedef struct {
  fp_int q[1];                          /* Modulus of underlying prime field */
  fp_int b[1];                          /* Curve's "b" parameter */
  fp_int Gx[1];                         /* x component of base point G */
  fp_int Gy[1];                         /* y component of base point G */
  fp_int n[1];                          /* Order of base point G */
  fp_int mu[1];                         /* Montgomery normalization factor */
  fp_digit rho;                         /* Montgomery reduction value */
  const uint8_t *oid;                   /* OBJECT IDENTIFIER */
  size_t oid_len;                       /* Length of OBJECT IDENTIFIER */
} ecdsa_curve_t;

/*
 * ECDSA key implementation.  This structure type is private to this
 * module, anything else that needs to touch one of these just gets a
 * typed opaque pointer.  We do, however, export the size, so that we
 * can make memory allocation the caller's problem.
 *
 * EC points are stored in Jacobian format such that (x, y, z) =>
 * (x/z**2, y/z**3, 1) when interpretted as affine coordinates.
 *
 * There are really three different representations in use here:
 *
 * 1) Plain affine representation (z == 1);
 * 2) Montgomery form affine representation (z == curve->mu); and
 * 3) Montgomery form Jacobian representation (whatever).
 *
 * Only form (1) is ever visible outside this module.  We perform
 * explicit conversions from form (1) to form (2) and from forms (2,3)
 * to form (1).  Form (3) only occurs as the result of compuation.
 *
 * In theory, we could shave some microscopic amount of time off of
 * signature verification by supporting an explicit conversion from
 * form (3) to form (2), but it's not worth the additional complexity.
 */

typedef struct {
  fp_int x[1], y[1], z[1];
} ec_point_t;

struct hal_ecdsa_key {
  hal_key_type_t type;                  /* Public or private */
  hal_curve_name_t curve;               /* Curve descriptor */
  ec_point_t Q[1];                      /* Public key */
  fp_int d[1];                          /* Private key */
};

const size_t hal_ecdsa_key_t_size = sizeof(struct hal_ecdsa_key);

/*
 * Initializers.  We want to be able to initialize automatic fp_int
 * and ec_point_t variables to a sane value (less error prone), but
 * picky compilers whine about the number of curly braces required.
 * So we define macros which isolate that madness in one place, and
 * use those macros everywhere.
 */

#define INIT_FP_INT	{{{0}}}
#define	INIT_EC_POINT_T	{{INIT_FP_INT}}

/*
 * Error handling.
 */

#define lose(_code_) do { err = _code_; goto fail; } while (0)

/*
 * We can't (usefully) initialize fp_int variables to non-zero values
 * at compile time, so instead we load all the curve parameters the
 * first time anything asks for any of them.
 */

static const ecdsa_curve_t * const get_curve(const hal_curve_name_t curve)
{
  static ecdsa_curve_t curve_p256, curve_p384, curve_p521;
  static int initialized = 0;

  if (!initialized) {

#include "ecdsa_curves.h"

    fp_read_unsigned_bin(curve_p256.q,  unconst_uint8_t(p256_q),  sizeof(p256_q));
    fp_read_unsigned_bin(curve_p256.b,  unconst_uint8_t(p256_b),  sizeof(p256_b));
    fp_read_unsigned_bin(curve_p256.Gx, unconst_uint8_t(p256_Gx), sizeof(p256_Gx));
    fp_read_unsigned_bin(curve_p256.Gy, unconst_uint8_t(p256_Gy), sizeof(p256_Gy));
    fp_read_unsigned_bin(curve_p256.n,  unconst_uint8_t(p256_n),  sizeof(p256_n));
    if (fp_montgomery_setup(curve_p256.q, &curve_p256.rho) != FP_OKAY)
      return NULL;
    fp_zero(curve_p256.mu);
    fp_montgomery_calc_normalization(curve_p256.mu, curve_p256.q);
    curve_p256.oid = p256_oid;
    curve_p256.oid_len = sizeof(p256_oid);

    fp_read_unsigned_bin(curve_p384.q,  unconst_uint8_t(p384_q),  sizeof(p384_q));
    fp_read_unsigned_bin(curve_p384.b,  unconst_uint8_t(p384_b),  sizeof(p384_b));
    fp_read_unsigned_bin(curve_p384.Gx, unconst_uint8_t(p384_Gx), sizeof(p384_Gx));
    fp_read_unsigned_bin(curve_p384.Gy, unconst_uint8_t(p384_Gy), sizeof(p384_Gy));
    fp_read_unsigned_bin(curve_p384.n,  unconst_uint8_t(p384_n),  sizeof(p384_n));
    if (fp_montgomery_setup(curve_p384.q, &curve_p384.rho) != FP_OKAY)
      return NULL;
    fp_zero(curve_p384.mu);
    fp_montgomery_calc_normalization(curve_p384.mu, curve_p384.q);
    curve_p384.oid = p384_oid;
    curve_p384.oid_len = sizeof(p384_oid);

    fp_read_unsigned_bin(curve_p521.q,  unconst_uint8_t(p521_q),  sizeof(p521_q));
    fp_read_unsigned_bin(curve_p521.b,  unconst_uint8_t(p521_b),  sizeof(p521_b));
    fp_read_unsigned_bin(curve_p521.Gx, unconst_uint8_t(p521_Gx), sizeof(p521_Gx));
    fp_read_unsigned_bin(curve_p521.Gy, unconst_uint8_t(p521_Gy), sizeof(p521_Gy));
    fp_read_unsigned_bin(curve_p521.n,  unconst_uint8_t(p521_n),  sizeof(p521_n));
    if (fp_montgomery_setup(curve_p521.q, &curve_p521.rho) != FP_OKAY)
      return NULL;
    fp_zero(curve_p521.mu);
    fp_montgomery_calc_normalization(curve_p521.mu, curve_p521.q);
    curve_p521.oid = p521_oid;
    curve_p521.oid_len = sizeof(p521_oid);

    initialized = 1;
  }

  switch (curve) {
  case HAL_CURVE_P256:  return &curve_p256;
  case HAL_CURVE_P384:  return &curve_p384;
  case HAL_CURVE_P521:  return &curve_p521;
  default:              return NULL;
  }
}

static inline const ecdsa_curve_t * oid_to_curve(hal_curve_name_t *curve_name,
                                                 const uint8_t * const oid,
                                                 const size_t oid_len)
{
  assert(curve_name != NULL && oid != NULL);

  const ecdsa_curve_t *curve = NULL;
  *curve_name = HAL_CURVE_NONE;

  while ((curve = get_curve(++*curve_name)) != NULL)
    if (oid_len == curve->oid_len && memcmp(oid, curve->oid, oid_len) == 0)
      return curve;

  return NULL;
}

/*
 * Finite field operations (hence "ff_").  These are basically just
 * the usual bignum operations, constrained by the field modulus.
 *
 * All of these are operations in the field underlying the specified
 * curve, and assume that operands are already in Montgomery form.
 *
 * The ff_add() and ff_sub() are written a bit oddly, in an attempt to
 * make them run in constant time.  An optimizing compiler may be
 * clever enough to defeat this.  In the long run, we probably want to
 * perform these field operations in Verilog anyway.
 *
 * We might be able to squeeze a bit more speed out of the point
 * arithmetic by making using fp_mul_2d() when multiplying by a power
 * of two.  Skipping for now as a premature optimization, but if we do
 * need this, it'd probably be simplest to add a ff_dbl() function
 * which handles overflow in the same way that ff_add() does.
 */

static inline void ff_add(const ecdsa_curve_t * const curve,
                          const fp_int * const a,
                          const fp_int * const b,
                          fp_int *c)
{
  fp_int t[2][1] = {INIT_FP_INT};

  fp_add(unconst_fp_int(a), unconst_fp_int(b), t[0]);
  fp_sub(t[0], unconst_fp_int(curve->q), t[1]);

  fp_copy(t[fp_cmp_d(t[1], 0) != FP_LT], c);

  memset(t, 0, sizeof(t));
}

static inline void ff_sub(const ecdsa_curve_t * const curve,
                          const fp_int * const a,
                          const fp_int * const b,
                          fp_int *c)
{
  fp_int t[2][1] = {INIT_FP_INT};

  fp_sub(unconst_fp_int(a), unconst_fp_int(b), t[0]);
  fp_add(t[0], unconst_fp_int(curve->q), t[1]);

  fp_copy(t[fp_cmp_d(t[0], 0) == FP_LT], c);

  memset(t, 0, sizeof(t));
}

static inline void ff_mul(const ecdsa_curve_t * const curve,
                          const fp_int * const a,
                          const fp_int * const b,
                          fp_int *c)
{
  fp_mul(unconst_fp_int(a), unconst_fp_int(b), c);
  fp_montgomery_reduce(c, unconst_fp_int(curve->q), curve->rho);
}

static inline void ff_sqr(const ecdsa_curve_t * const curve,
                          const fp_int * const a,
                          fp_int *b)
{
  fp_sqr(unconst_fp_int(a), b);
  fp_montgomery_reduce(b, unconst_fp_int(curve->q), curve->rho);
}

/*
 * Test whether a point is the point at infinity.
 *
 * In Jacobian projective coordinate, any point of the form
 *
 *   (j ** 2, j **3, 0) for j in [1..q-1]
 *
 * is on the line at infinity, but for practical purposes simply
 * checking the z coordinate is probably sufficient.
 */

static inline int point_is_infinite(const ec_point_t * const P)
{
  assert(P != NULL);
  return fp_iszero(P->z);
}

/*
 * Set a point to be the point at infinity.  For Jacobian projective
 * coordinates, it's customary to use (1 : 1 : 0) as the
 * representitive value.
 *
 * If a curve is supplied, we want the Montgomery form of the point at
 * infinity for that curve.
 */

static inline void point_set_infinite(ec_point_t *P, const ecdsa_curve_t * const curve)
{
  assert(P != NULL);

  if (curve != NULL) {
    fp_copy(unconst_fp_int(curve->mu), P->x);
    fp_copy(unconst_fp_int(curve->mu), P->y);
    fp_zero(P->z);
  }

  else {
    fp_set(P->x, 1);
    fp_set(P->y, 1);
    fp_zero(P->z);
  }
}

/*
 * Copy a point.
 */

static inline void point_copy(const ec_point_t * const P, ec_point_t *R)
{
  if (P != NULL && R != NULL && P != R)
    *R = *P;
}

/**
 * Convert a point into Montgomery form.
 * @param P        [in/out] The point to map
 * @param curve    The curve parameters structure
 */

static inline hal_error_t point_to_montgomery(ec_point_t *P,
                                              const ecdsa_curve_t * const curve)
{
  assert(P != NULL && curve != NULL);

  if (fp_cmp_d(unconst_fp_int(P->z), 1) != FP_EQ)
    return HAL_ERROR_BAD_ARGUMENTS;

  if (fp_mulmod(P->x, unconst_fp_int(curve->mu), unconst_fp_int(curve->q), P->x) != FP_OKAY ||
      fp_mulmod(P->y, unconst_fp_int(curve->mu), unconst_fp_int(curve->q), P->y) != FP_OKAY)
    return HAL_ERROR_IMPOSSIBLE;

  fp_copy(unconst_fp_int(curve->mu), P->z);
  return HAL_OK;
}

/**
 * Map a point in projective Jacbobian coordinates back to affine
 * space.  This also converts back from Montgomery to plain form.
 * @param P        [in/out] The point to map
 * @param curve    The curve parameters structure
 *
 * It's not possible to represent the point at infinity in plain
 * affine coordinates, and the calling function will have to handle
 * the point at infinity specially in any case, so we declare this to
 * be the calling function's problem.
 */

static inline hal_error_t point_to_affine(ec_point_t *P,
                                          const ecdsa_curve_t * const curve)
{
  assert(P != NULL && curve != NULL);

  if (point_is_infinite(P))
    return HAL_ERROR_IMPOSSIBLE;

  hal_error_t err = HAL_ERROR_IMPOSSIBLE;

  fp_int t1[1] = INIT_FP_INT;
  fp_int t2[1] = INIT_FP_INT;

  fp_int * const q = unconst_fp_int(curve->q);

  fp_montgomery_reduce(P->z, q, curve->rho);

  if (fp_invmod (P->z,   q, t1) != FP_OKAY ||    /* t1 = 1 / z    */
      fp_sqrmod (t1,     q, t2) != FP_OKAY ||    /* t2 = 1 / z**2 */
      fp_mulmod (t1, t2, q, t1) != FP_OKAY)      /* t1 = 1 / z**3 */
    goto fail;

  fp_mul (P->x,  t2,  P->x);                     /* x = x / z**2 */
  fp_mul (P->y,  t1,  P->y);                     /* y = y / z**3 */
  fp_set (P->z,  1);                             /* z = 1        */

  fp_montgomery_reduce(P->x, q, curve->rho);
  fp_montgomery_reduce(P->y, q, curve->rho);

  err = HAL_OK;

 fail:
  fp_zero(t1);
  fp_zero(t2);
  return err;
}

/**
 * Double an EC point.
 * @param P             The point to double
 * @param R             [out] The destination of the double
 * @param curve         The curve parameters structure
 *
 * Algorithm is dbl-2001-b from
 * http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html
 */

static inline void point_double(const ec_point_t * const P,
                                ec_point_t *R,
                                const ecdsa_curve_t * const curve)
{
  assert(P != NULL && R != NULL && curve != NULL);

  const int was_infinite = point_is_infinite(P);

  fp_int alpha[1] = INIT_FP_INT;
  fp_int beta[1]  = INIT_FP_INT;
  fp_int gamma[1] = INIT_FP_INT;
  fp_int delta[1] = INIT_FP_INT;
  fp_int t1[1]    = INIT_FP_INT;
  fp_int t2[1]    = INIT_FP_INT;

  ff_sqr  (curve,  P->z,          delta);       /* delta = Pz ** 2 */
  ff_sqr  (curve,  P->y,          gamma);       /* gamma = Py ** 2 */
  ff_mul  (curve,  P->x,  gamma,  beta);        /* beta  = Px * gamma */
  ff_sub  (curve,  P->x,  delta,  t1);          /* alpha = 3 * (Px - delta) * (Px + delta) */
  ff_add  (curve,  P->x,  delta,  t2);
  ff_mul  (curve,  t1,    t2,     t1);
  ff_add  (curve,  t1,    t1,     t2);
  ff_add  (curve,  t1,    t2,     alpha);

  ff_sqr  (curve,  alpha,         t1);          /* Rx = (alpha ** 2) - (8 * beta) */
  ff_add  (curve,  beta,  beta,   t2);
  ff_add  (curve,  t2,    t2,     t2);
  ff_add  (curve,  t2,    t2,     t2);
  ff_sub  (curve,  t1,    t2,     R->x);

  ff_add  (curve,  P->y,  P->z,   t1);          /* Rz = ((Py + Pz) ** 2) - gamma - delta */
  ff_sqr  (curve,  t1,            t1);
  ff_sub  (curve,  t1,    gamma,  t1);
  ff_sub  (curve,  t1,    delta,  R->z);

  ff_add  (curve,  beta,  beta,   t1);          /* Ry = (((4 * beta) - Rx) * alpha) - (8 * (gamma ** 2)) */
  ff_add  (curve,  t1,    t1,     t1);
  ff_sub  (curve,  t1,    R->x,   t1);
  ff_mul  (curve,  t1,    alpha,  t1);
  ff_sqr  (curve,  gamma,         t2);
  ff_add  (curve,  t2,    t2,     t2);
  ff_add  (curve,  t2,    t2,     t2);
  ff_add  (curve,  t2,    t2,     t2);
  ff_sub  (curve,  t1,    t2,     R->y);

  assert(was_infinite == point_is_infinite(P));

  fp_zero(alpha); fp_zero(beta); fp_zero(gamma); fp_zero(delta); fp_zero(t1); fp_zero(t2);
}

/**
 * Add two EC points
 * @param P             The point to add
 * @param Q             The point to add
 * @param R             [out] The destination of the double
 * @param curve         The curve parameters structure
 *
 * Algorithm is madd-2007-bl from
 * http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html
 *
 * The special cases are unfortunate, but are probably unavoidable for
 * this type of curve.  We do what we can to make this constant-time
 * in spite of the special cases.  The one we really can't do much
 * about is P == Q, because in that case we have to switch to the
 * point doubling algorithm.
 */

static inline void point_add(const ec_point_t * const P,
                             const ec_point_t * const Q,
                             ec_point_t *R,
                             const ecdsa_curve_t * const curve)
{
  assert(P != NULL && Q != NULL && R != NULL && curve != NULL);

  /*
   * Q must be affine in Montgomery form.
   */

  assert(fp_cmp(unconst_fp_int(Q->z), unconst_fp_int(curve->mu)) == FP_EQ);

#warning What happens here if P and Q are not equal but map to the same point in affine space?

  const int same_xz = (fp_cmp(unconst_fp_int(P->z), unconst_fp_int(Q->z)) == FP_EQ &&
                       fp_cmp(unconst_fp_int(P->x), unconst_fp_int(Q->x)) == FP_EQ);

  /*
   * If P == Q, we must use point doubling instead of point addition,
   * and there's nothing we can do to mask the timing differences.
   * So just do it, right away.
   */

  if (same_xz && fp_cmp(unconst_fp_int(P->y), unconst_fp_int(Q->y)) == FP_EQ)
    return point_double(P, R, curve);

  /*
   * Check now for the other special cases, but defer handling them
   * until the end, to mask timing differences.
   */

  const int P_was_infinite = point_is_infinite(P);

  fp_int Qy_neg[1] = INIT_FP_INT;
  fp_sub(unconst_fp_int(curve->q), unconst_fp_int(Q->y), Qy_neg);
  const int result_is_infinite = fp_cmp(unconst_fp_int(P->y), Qy_neg) == FP_EQ && same_xz;
  fp_zero(Qy_neg);

  /*
   * Main point addition algorithm.
   */

  fp_int Z1Z1[1] = INIT_FP_INT;
  fp_int H[1]    = INIT_FP_INT;
  fp_int HH[1]   = INIT_FP_INT;
  fp_int I[1]    = INIT_FP_INT;
  fp_int J[1]    = INIT_FP_INT;
  fp_int r[1]    = INIT_FP_INT;
  fp_int V[1]    = INIT_FP_INT;
  fp_int t[1]    = INIT_FP_INT;

  ff_sqr  (curve,  P->z,           Z1Z1);       /* Z1Z1 = Pz ** 2 */

  ff_mul  (curve,  Q->x,   Z1Z1,   H);          /* H = (Qx * Z1Z1) - Px */
  ff_sub  (curve,  H,      P->x,   H);

  ff_sqr  (curve,  H,              HH);         /* HH = H ** 2 */

  ff_add  (curve,  HH,     HH,     I);          /* I = 4 * HH */
  ff_add  (curve,  I,      I,      I);

  ff_mul  (curve,  H,      I,      J);          /* J = H * I */

  ff_mul  (curve,  P->z,   Z1Z1,   r);          /* r = 2 * ((Qy * Pz * Z1Z1) - Py) */
  ff_mul  (curve,  Q->y,   r,      r);
  ff_sub  (curve,  r,      P->y,   r);
  ff_add  (curve,  r,      r,      r);

  ff_mul  (curve,  P->x,   I,      V);          /* V = Px * I */

  ff_sqr  (curve,  r,              R->x);       /* Rx = (r ** 2) - J - (2 * V) */
  ff_sub  (curve,  R->x,   J,      R->x);
  ff_sub  (curve,  R->x,   V,      R->x);
  ff_sub  (curve,  R->x,   V,      R->x);

  ff_mul  (curve,  P->y,   J,      t);         /* Ry = (r * (V - Rx)) - (2 * Py * J) */
  ff_sub  (curve,  V,      R->x,   R->y);
  ff_mul  (curve,  r,      R->y,   R->y);
  ff_sub  (curve,  R->y,   t,      R->y);
  ff_sub  (curve,  R->y,   t,      R->y);

  ff_add  (curve,  P->z,   H,      R->z);       /* Rz = ((Pz + H) ** 2) - Z1Z1 - HH */
  ff_sqr  (curve,  R->z,           R->z);
  ff_sub  (curve,  R->z,   Z1Z1,   R->z);
  ff_sub  (curve,  R->z,   HH,     R->z);

  fp_zero(Z1Z1), fp_zero(H), fp_zero(HH), fp_zero(I), fp_zero(J), fp_zero(r), fp_zero(V), fp_zero(t);

  /*
   * Handle deferred special cases, then we're done.
   */

  if (P_was_infinite)
    point_copy(Q, R);

  else if (result_is_infinite)
    point_set_infinite(R, curve);
}

/**
 * Perform a point multiplication.
 * @param k             The scalar to multiply by
 * @param P             The base point
 * @param R             [out] Destination for kP
 * @param curve         Curve parameters
 * @return HAL_OK on success
 *
 * P must be in affine form.
 */

static hal_error_t point_scalar_multiply(const fp_int * const k,
                                         const ec_point_t * const P_,
                                         ec_point_t *R,
                                         const ecdsa_curve_t * const curve)
{
  assert(k != NULL && P_ != NULL && R != NULL &&  curve != NULL);

  if (fp_iszero(k) || fp_cmp_d(unconst_fp_int(P_->z), 1) != FP_EQ)
    return HAL_ERROR_BAD_ARGUMENTS;

  hal_error_t err;

  /*
   * Convert P to Montgomery form.
   */

  ec_point_t P[1];
  point_copy(P_, P);

  if ((err = point_to_montgomery(P, curve)) != HAL_OK) {
    memset(P, 0, sizeof(P));
    return err;
  }

  /*
   * Initialize table.
   * M[0] is a dummy for constant timing.
   * M[1] is where we accumulate the result.
   */

  ec_point_t M[2][1] = {INIT_EC_POINT_T};

  point_set_infinite(M[0], curve);
  point_set_infinite(M[1], curve);

  /*
   * Walk down bits of the scalar, performing dummy operations to mask
   * timing.
   *
   * Note that, in order for the timing protection to work, the
   * number of iterations in the loop has to depend on the order of
   * the base point rather than on the scalar.
   */

  for (int bit_index = fp_count_bits(unconst_fp_int(curve->n)) - 1; bit_index >= 0; bit_index--) {

    const int digit_index = bit_index / DIGIT_BIT;
    const fp_digit  digit = digit_index < k->used ? k->dp[digit_index] : 0;
    const fp_digit   mask = ((fp_digit) 1) << (bit_index % DIGIT_BIT);
    const int         bit = (digit & mask) != 0;

    point_double (M[1],        M[1],    curve);
    point_add    (M[bit],  P,  M[bit],  curve);

  }

  /*
   * Copy result, map back to affine, then done.
   */

  point_copy(M[1], R);

  err = point_to_affine(R, curve);

  memset(P, 0, sizeof(P));
  memset(M, 0, sizeof(M));

  return err;
}

/*
 * Testing only: ECDSA key generation and signature both have a
 * critical dependency on random numbers, but we can't use the random
 * number generator when testing against static test vectors. So add a
 * wrapper around the random number generator calls, with a hook to
 * let us override the generator for test purposes.  Do NOT use this
 * in production, kids.
 */

#if HAL_ECDSA_DEBUG_ONLY_STATIC_TEST_VECTOR_RANDOM

#warning hal_ecdsa random number generator overridden for test purposes
#warning DO NOT USE THIS IN PRODUCTION

typedef hal_error_t (*rng_override_test_function_t)(void *, const size_t);

static rng_override_test_function_t rng_test_override_function = 0;

rng_override_test_function_t hal_ecdsa_set_rng_override_test_function(rng_override_test_function_t new_func)
{
  rng_override_test_function_t old_func = rng_test_override_function;
  rng_test_override_function = new_func;
  return old_func;
}

static inline hal_error_t get_random(void *buffer, const size_t length)
{
  if (rng_test_override_function)
    return rng_test_override_function(buffer, length);
  else
    return hal_get_random(NULL, buffer, length);
}

#else /* HAL_ECDSA_DEBUG_ONLY_STATIC_TEST_VECTOR_RANDOM */

static inline hal_error_t get_random(void *buffer, const size_t length)
{
  return hal_get_random(NULL, buffer, length);
}

#endif /* HAL_ECDSA_DEBUG_ONLY_STATIC_TEST_VECTOR_RANDOM */

/*
 * Pick a random point on the curve, return random scalar and
 * resulting point.
 */

static hal_error_t point_pick_random(const ecdsa_curve_t * const curve,
                                     fp_int *k,
                                     ec_point_t *P)
{
  hal_error_t err;

  assert(curve != NULL && k != NULL && P != NULL);

  /*
   * Pick a random scalar corresponding to a point on the curve.  Per
   * the NSA (gulp) Suite B guidelines, we ask the CSPRNG for 64 more
   * bits than we need, which should be enough to mask any bias
   * induced by the modular reduction.
   *
   * We're picking a point out of the subgroup generated by the base
   * point on the elliptic curve, so the modulus for this calculation
   * is the order of the base point.
   *
   * Zero is an excluded value, but the chance of a non-broken CSPRNG
   * returning zero is so low that it would almost certainly indicate
   * an undiagnosed bug in the CSPRNG.
   */

  uint8_t k_buf[fp_unsigned_bin_size(unconst_fp_int(curve->n)) + 8];

  do {

    if ((err = get_random(k_buf, sizeof(k_buf))) != HAL_OK)
      return err;

    fp_read_unsigned_bin(k, k_buf, sizeof(k_buf));

    if (fp_iszero(k) || fp_mod(k, unconst_fp_int(curve->n), k) != FP_OKAY)
      return HAL_ERROR_IMPOSSIBLE;

  } while (fp_iszero(k));

  memset(k_buf, 0, sizeof(k_buf));

  /*
   * Calculate P = kG and return.
   */

  fp_copy(curve->Gx, P->x);
  fp_copy(curve->Gy, P->y);
  fp_set(P->z, 1);

  return point_scalar_multiply(k, P, P, curve);
}

/*
 * Test whether a point really is on a particular curve.  This is
 * called "validation" when applied to a public key, and is required
 * before verifying a signature.
 */

static int point_is_on_curve(const ec_point_t * const P,
                             const ecdsa_curve_t * const curve)
{
  assert(P != NULL && curve != NULL);

  fp_int t1[1] = INIT_FP_INT;
  fp_int t2[1] = INIT_FP_INT;

  /*
   * Compute y**2 - x**3 + 3*x.
   */

  fp_sqr(unconst_fp_int(P->y), t1);             /* t1 = y**2 */
  fp_sqr(unconst_fp_int(P->x), t2);             /* t2 = x**2 */
  if (fp_mod(t2, unconst_fp_int(curve->q), t2) != FP_OKAY)
    return 0;
  fp_mul(unconst_fp_int(P->x), t2, t2);         /* t2 = x**3 */
  fp_sub(t1, t2, t1);                           /* t1 = y**2 - x**3 */
  fp_add(t1, unconst_fp_int(P->x), t1);         /* t1 = y**2 - x**3 + 1*x */
  fp_add(t1, unconst_fp_int(P->x), t1);         /* t1 = y**2 - x**3 + 2*x */
  fp_add(t1, unconst_fp_int(P->x), t1);         /* t1 = y**2 - x**3 + 3*x */

  /*
   * Normalize and test whether computed value matches b.
   */

  if (fp_mod(t1, unconst_fp_int(curve->q), t1) != FP_OKAY)
    return 0;
  while (fp_cmp_d(t1, 0) == FP_LT)
    fp_add(t1, unconst_fp_int(curve->q), t1);
  while (fp_cmp(t1, unconst_fp_int(curve->q)) != FP_LT)
    fp_sub(t1, unconst_fp_int(curve->q), t1);

  return fp_cmp(t1, unconst_fp_int(curve->b)) == FP_EQ;
}

/*
 * Generate a new ECDSA key.
 */

hal_error_t hal_ecdsa_key_gen(const hal_core_t *core,
                              hal_ecdsa_key_t **key_,
                              void *keybuf, const size_t keybuf_len,
                              const hal_curve_name_t curve_)
{
  const ecdsa_curve_t * const curve = get_curve(curve_);
  hal_ecdsa_key_t *key = keybuf;
  hal_error_t err;

  if (key_ == NULL || key == NULL || keybuf_len < sizeof(*key) || curve == NULL)
    return HAL_ERROR_BAD_ARGUMENTS;

  memset(keybuf, 0, keybuf_len);

  key->type = HAL_KEY_TYPE_EC_PRIVATE;
  key->curve = curve_;

  if ((err = point_pick_random(curve, key->d, key->Q)) != HAL_OK)
    return err;

  assert(point_is_on_curve(key->Q, curve));

  *key_ = key;
  return HAL_OK;
}

/*
 * Extract key type (public or private).
 */

hal_error_t hal_ecdsa_key_get_type(const hal_ecdsa_key_t * const key,
                                   hal_key_type_t *key_type)
{
  if (key == NULL || key_type == NULL)
    return HAL_ERROR_BAD_ARGUMENTS;

  *key_type = key->type;
  return HAL_OK;
}

/*
 * Extract name of curve underlying a key.
 */

hal_error_t hal_ecdsa_key_get_curve(const hal_ecdsa_key_t * const key,
                                    hal_curve_name_t *curve)
{
  if (key == NULL || curve == NULL)
    return HAL_ERROR_BAD_ARGUMENTS;

  *curve = key->curve;
  return HAL_OK;
}

/*
 * Extract public key components.
 */

hal_error_t hal_ecdsa_key_get_public(const hal_ecdsa_key_t * const key,
                                     uint8_t *x, size_t *x_len, const size_t x_max,
                                     uint8_t *y, size_t *y_len, const size_t y_max)
{
  if (key == NULL || (x_len == NULL && x != NULL) || (y_len == NULL && y != NULL))
    return HAL_ERROR_BAD_ARGUMENTS;

  if (x_len != NULL)
    *x_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->x));

  if (y_len != NULL)
    *y_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->y));

  if ((x != NULL && *x_len > x_max) ||
      (y != NULL && *y_len > y_max))
    return HAL_ERROR_RESULT_TOO_LONG;

  if (x != NULL)
    fp_to_unsigned_bin(unconst_fp_int(key->Q->x), x);

  if (y != NULL)
    fp_to_unsigned_bin(unconst_fp_int(key->Q->y), y);

  return HAL_OK;
}

/*
 * Clear a key.
 */

void hal_ecdsa_key_clear(hal_ecdsa_key_t *key)
{
  if (key != NULL)
    memset(key, 0, sizeof(*key));
}

/*
 * Load a public key from components, and validate that the public key
 * really is on the named curve.
 */

hal_error_t hal_ecdsa_key_load_public(hal_ecdsa_key_t **key_,
                                      void *keybuf, const size_t keybuf_len,
                                      const hal_curve_name_t curve_,
                                      const uint8_t * const x, const size_t x_len,
                                      const uint8_t * const y, const size_t y_len)
{
  const ecdsa_curve_t * const curve = get_curve(curve_);
  hal_ecdsa_key_t *key = keybuf;

  if (key_ == NULL || key == NULL || keybuf_len < sizeof(*key) || curve == NULL || x == NULL || y == NULL)
    return HAL_ERROR_BAD_ARGUMENTS;

  memset(keybuf, 0, keybuf_len);

  key->type = HAL_KEY_TYPE_EC_PUBLIC;
  key->curve = curve_;

  fp_read_unsigned_bin(key->Q->x, unconst_uint8_t(x), x_len);
  fp_read_unsigned_bin(key->Q->y, unconst_uint8_t(y), y_len);
  fp_set(key->Q->z, 1);

  if (!point_is_on_curve(key->Q, curve))
    return HAL_ERROR_KEY_NOT_ON_CURVE;

  *key_ = key;

  return HAL_OK;
}

/*
 * Load a private key from components; does all the same things as
 * hal_ecdsa_key_load_public(), then loads the private key itself and
 * adjusts the key type.
 *
 * For extra paranoia, we could check Q == dG.
 */

hal_error_t hal_ecdsa_key_load_private(hal_ecdsa_key_t **key_,
                                       void *keybuf, const size_t keybuf_len,
                                       const hal_curve_name_t curve_,
                                       const uint8_t * const x, const size_t x_len,
                                       const uint8_t * const y, const size_t y_len,
                                       const uint8_t * const d, const size_t d_len)
{
  hal_ecdsa_key_t *key = keybuf;
  hal_error_t err;

  if (d == NULL)
    return HAL_ERROR_BAD_ARGUMENTS;

  if ((err = hal_ecdsa_key_load_public(key_, keybuf, keybuf_len, curve_, x, x_len, y, y_len)) != HAL_OK)
    return err;

  key->type = HAL_KEY_TYPE_EC_PRIVATE;
  fp_read_unsigned_bin(key->d, unconst_uint8_t(d), d_len);
  return HAL_OK;
}

/*
 * Write public key in X9.62 ECPoint format (ASN.1 OCTET STRING, first octet is compression flag).
 */

hal_error_t hal_ecdsa_key_to_ecpoint(const hal_ecdsa_key_t * const key,
                                     uint8_t *der, size_t *der_len, const size_t der_max)
{
  if (key == NULL)
    return HAL_ERROR_BAD_ARGUMENTS;

  const ecdsa_curve_t * const curve = get_curve(key->curve);
  if (curve == NULL)
    return HAL_ERROR_IMPOSSIBLE;

  const size_t q_len  = fp_unsigned_bin_size(unconst_fp_int(curve->q));
  const size_t Qx_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->x));
  const size_t Qy_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->y));
  assert(q_len >= Qx_len && q_len >= Qy_len);

  const size_t vlen = q_len * 2 + 1;
  size_t hlen;

  hal_error_t err = hal_asn1_encode_header(ASN1_OCTET_STRING, vlen, der, &hlen, der_max);

  if (der_len != NULL)
    *der_len = hlen + vlen;

  if (der == NULL || err != HAL_OK)
    return err;

  assert(hlen + vlen <= der_max);

  uint8_t *d = der + hlen;
  memset(d, 0, vlen);

  *d++ = 0x04;                  /* uncompressed */

  fp_to_unsigned_bin(unconst_fp_int(key->Q->x), d + q_len - Qx_len);
  d += q_len;

  fp_to_unsigned_bin(unconst_fp_int(key->Q->y), d + q_len - Qy_len);
  d += q_len;

  assert(d <= der + der_max);

  return HAL_OK;
}

/*
 * Convenience wrapper to return how many bytes a key would take if
 * encoded as an ECPoint.
 */

size_t hal_ecdsa_key_to_ecpoint_len(const hal_ecdsa_key_t * const key)
{
  size_t len;
  return hal_ecdsa_key_to_ecpoint(key, NULL, &len, 0) == HAL_OK ? len : 0;
}

/*
 * Read public key in X9.62 ECPoint format (ASN.1 OCTET STRING, first octet is compression flag).
 * ECPoint format doesn't include a curve identifier, so caller has to supply one.
 */

hal_error_t hal_ecdsa_key_from_ecpoint(hal_ecdsa_key_t **key_,
                                       void *keybuf, const size_t keybuf_len,
                                       const uint8_t * const der, const size_t der_len,
                                       const hal_curve_name_t curve)
{
  hal_ecdsa_key_t *key = keybuf;

  if (key_ == NULL || key == NULL || keybuf_len < sizeof(*key) || get_curve(curve) == NULL)
    return HAL_ERROR_BAD_ARGUMENTS;

  memset(keybuf, 0, keybuf_len);
  key->type = HAL_KEY_TYPE_EC_PUBLIC;
  key->curve = curve;

  size_t hlen, vlen;
  hal_error_t err;

  if ((err = hal_asn1_decode_header(ASN1_OCTET_STRING, der, der_len, &hlen, &vlen)) != HAL_OK)
    return err;

  const uint8_t * const der_end = der + hlen + vlen;
  const uint8_t *d = der + hlen;

  if (vlen < 3 || (vlen & 1) == 0 || *d++ != 0x04)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);

  vlen /= 2;

  fp_read_unsigned_bin(key->Q->x, unconst_uint8_t(d), vlen);
  d += vlen;

  fp_read_unsigned_bin(key->Q->y, unconst_uint8_t(d), vlen);
  d += vlen;

  fp_set(key->Q->z, 1);

  if (d != der_end)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);

  *key_ = key;
  return HAL_OK;

 fail:
  memset(keybuf, 0, keybuf_len);
  return err;
}

/*
 * Write private key in RFC 5915 ASN.1 DER format.
 *
 * This is hand-coded, and is approaching the limit where one should
 * probably be using an ASN.1 compiler like asn1c instead.
 */

hal_error_t hal_ecdsa_private_key_to_der(const hal_ecdsa_key_t * const key,
                                         uint8_t *der, size_t *der_len, const size_t der_max)
{
  if (key == NULL || key->type != HAL_KEY_TYPE_EC_PRIVATE)
    return HAL_ERROR_BAD_ARGUMENTS;

  const ecdsa_curve_t * const curve = get_curve(key->curve);
  if (curve == NULL)
    return HAL_ERROR_IMPOSSIBLE;

  const size_t q_len  = fp_unsigned_bin_size(unconst_fp_int(curve->q));
  const size_t d_len  = fp_unsigned_bin_size(unconst_fp_int(key->d));
  const size_t Qx_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->x));
  const size_t Qy_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->y));
  assert(q_len >= d_len && q_len >= Qx_len && q_len >= Qy_len);

  fp_int version[1] = INIT_FP_INT;
  fp_set(version, 1);

  hal_error_t err;

  size_t version_len, hlen, hlen_oct, hlen_oid, hlen_exp0, hlen_bit, hlen_exp1;

  if ((err = hal_asn1_encode_integer(version,                                    NULL, &version_len, 0)) != HAL_OK ||
      (err = hal_asn1_encode_header(ASN1_OCTET_STRING,          q_len,           NULL, &hlen_oct,    0)) != HAL_OK ||
      (err = hal_asn1_encode_header(ASN1_OBJECT_IDENTIFIER,     curve->oid_len,  NULL, &hlen_oid,    0)) != HAL_OK ||
      (err = hal_asn1_encode_header(ASN1_EXPLICIT_0, hlen_oid + curve->oid_len,  NULL, &hlen_exp0,   0)) != HAL_OK ||
      (err = hal_asn1_encode_header(ASN1_BIT_STRING,            (q_len + 1) * 2, NULL, &hlen_bit,    0)) != HAL_OK ||
      (err = hal_asn1_encode_header(ASN1_EXPLICIT_1, hlen_bit + (q_len + 1) * 2, NULL, &hlen_exp1,   0)) != HAL_OK)
    return err;

  const size_t vlen = (version_len   +
                       hlen_oct + q_len +
                       hlen_oid + hlen_exp0 + curve->oid_len +
                       hlen_bit + hlen_exp1 + (q_len + 1) * 2);

  err = hal_asn1_encode_header(ASN1_SEQUENCE, vlen, der, &hlen, der_max);

  if (der_len != NULL)
    *der_len = hlen + vlen;

  if (der == NULL || err != HAL_OK)
    return err;

  uint8_t *d = der + hlen;
  memset(d, 0, vlen);

  if ((err = hal_asn1_encode_integer(version, d, NULL, der + der_max - d)) != HAL_OK)
    return err;
  d += version_len;

  if ((err = hal_asn1_encode_header(ASN1_OCTET_STRING, q_len, d, &hlen, der + der_max - d)) != HAL_OK)
    return err;
  d += hlen;
  fp_to_unsigned_bin(unconst_fp_int(key->d), d + q_len - d_len);
  d += q_len;

  if ((err = hal_asn1_encode_header(ASN1_EXPLICIT_0, hlen_oid + curve->oid_len, d, &hlen, der + der_max - d)) != HAL_OK)
    return err;
  d += hlen;
  if ((err = hal_asn1_encode_header(ASN1_OBJECT_IDENTIFIER, curve->oid_len, d, &hlen, der + der_max - d)) != HAL_OK)
    return err;
  d += hlen;
  memcpy(d, curve->oid, curve->oid_len);
  d += curve->oid_len;

  if ((err = hal_asn1_encode_header(ASN1_EXPLICIT_1, hlen_bit + (q_len + 1) * 2, d, &hlen, der + der_max - d)) != HAL_OK)
    return err;
  d += hlen;
  if ((err = hal_asn1_encode_header(ASN1_BIT_STRING, (q_len + 1) * 2, d, &hlen, der + der_max - d)) != HAL_OK)
    return err;
  d += hlen;
  *d++ = 0x00;
  *d++ = 0x04;
  fp_to_unsigned_bin(unconst_fp_int(key->Q->x), d + q_len - Qx_len);
  d += q_len;
  fp_to_unsigned_bin(unconst_fp_int(key->Q->y), d + q_len - Qy_len);
  d += q_len;

  assert(d <= der + der_max);

  return HAL_OK;
}

/*
 * Convenience wrapper to return how many bytes a private key would
 * take if encoded as DER.
 */

size_t hal_ecdsa_private_key_to_der_len(const hal_ecdsa_key_t * const key)
{
  size_t len;
  return hal_ecdsa_private_key_to_der(key, NULL, &len, 0) == HAL_OK ? len : 0;
}

/*
 * Read private key in RFC 5915 ASN.1 DER format.
 *
 * This is hand-coded, and is approaching the limit where one should
 * probably be using an ASN.1 compiler like asn1c instead.
 */

hal_error_t hal_ecdsa_private_key_from_der(hal_ecdsa_key_t **key_,
                                           void *keybuf, const size_t keybuf_len,
                                           const uint8_t * const der, const size_t der_len)
{
  hal_ecdsa_key_t *key = keybuf;

  if (key_ == NULL || key == NULL || keybuf_len < sizeof(*key))
    return HAL_ERROR_BAD_ARGUMENTS;

  memset(keybuf, 0, keybuf_len);
  key->type = HAL_KEY_TYPE_EC_PRIVATE;

  size_t hlen, vlen;
  hal_error_t err;

  if ((err = hal_asn1_decode_header(ASN1_SEQUENCE, der, der_len, &hlen, &vlen)) != HAL_OK)
    return err;

  const uint8_t * const der_end = der + hlen + vlen;
  const uint8_t *d = der + hlen;
  const ecdsa_curve_t *curve = NULL;
  fp_int version[1] = INIT_FP_INT;

  if ((err = hal_asn1_decode_integer(version, d, &hlen, vlen)) != HAL_OK)
    goto fail;
  if (fp_cmp_d(version, 1) != FP_EQ)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);
  d += hlen;

  if ((err = hal_asn1_decode_header(ASN1_OCTET_STRING, d, der_end - d, &hlen, &vlen)) != HAL_OK)
    return err;
  d += hlen;
  fp_read_unsigned_bin(key->d, unconst_uint8_t(d), vlen);
  d += vlen;

  if ((err = hal_asn1_decode_header(ASN1_EXPLICIT_0, d, der_end - d, &hlen, &vlen)) != HAL_OK)
    return err;
  d += hlen;
  if (vlen > der_end - d)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);
  if ((err = hal_asn1_decode_header(ASN1_OBJECT_IDENTIFIER, d, vlen, &hlen, &vlen)) != HAL_OK)
    return err;
  d += hlen;
  if ((curve = oid_to_curve(&key->curve, d, vlen)) == NULL)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);
  d += vlen;

  if ((err = hal_asn1_decode_header(ASN1_EXPLICIT_1, d, der_end - d, &hlen, &vlen)) != HAL_OK)
    return err;
  d += hlen;
  if (vlen > der_end - d)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);
  if ((err = hal_asn1_decode_header(ASN1_BIT_STRING, d, vlen, &hlen, &vlen)) != HAL_OK)
    return err;
  d += hlen;
  if (vlen < 4 || (vlen & 1) != 0 || *d++ != 0x00 || *d++ != 0x04)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);
  vlen = vlen/2 - 1;
  fp_read_unsigned_bin(key->Q->x, unconst_uint8_t(d), vlen);
  d += vlen;
  fp_read_unsigned_bin(key->Q->y, unconst_uint8_t(d), vlen);
  d += vlen;
  fp_set(key->Q->z, 1);

  if (d != der_end)
    lose(HAL_ERROR_ASN1_PARSE_FAILED);

  *key_ = key;
  return HAL_OK;

 fail:
  memset(keybuf, 0, keybuf_len);
  return err;
}

/*
 * Write public key in SubjectPublicKeyInfo format, see RFCS 5280 and 5480.
 */

static const uint8_t oid_ecPublicKey[] = { 0x2A, 0x86, 0x48, 0xCE, 0x3D, 0x02, 0x01 };

hal_error_t hal_ecdsa_public_key_to_der(const hal_ecdsa_key_t * const key,
                                        uint8_t *der, size_t *der_len, const size_t der_max)
{
  if (key == NULL || (key->type != HAL_KEY_TYPE_EC_PRIVATE &&
                      key->type != HAL_KEY_TYPE_EC_PUBLIC))
    return HAL_ERROR_BAD_ARGUMENTS;

  const ecdsa_curve_t * const curve = get_curve(key->curve);
  if (curve == NULL)
    return HAL_ERROR_IMPOSSIBLE;

  const size_t q_len  = fp_unsigned_bin_size(unconst_fp_int(curve->q));
  const size_t Qx_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->x));
  const size_t Qy_len = fp_unsigned_bin_size(unconst_fp_int(key->Q->y));
  const size_t ecpoint_len = q_len * 2 + 1;
  assert(q_len >= Qx_len && q_len >= Qy_len);

  if (der != NULL && ecpoint_len < der_max) {
    memset(der, 0, ecpoint_len);

    uint8_t *d = der;
    *d++ = 0x04;                /* Uncompressed */

    fp_to_unsigned_bin(unconst_fp_int(key->Q->x), d + q_len - Qx_len);
    d += q_len;

    fp_to_unsigned_bin(unconst_fp_int(key->Q->y), d + q_len - Qy_len);
    d += q_len;

    assert(d < der + der_max);
  }

  return hal_asn1_encode_spki(oid_ecPublicKey, sizeof(oid_ecPublicKey),
                              curve->oid, curve->oid_len,
                              der, ecpoint_len,
                              der, der_len, der_max);
}

/*
 * Convenience wrapper to return how many bytes a public key would
 * take if encoded as DER.
 */

size_t hal_ecdsa_public_key_to_der_len(const hal_ecdsa_key_t * const key)
{
  size_t len;
  return hal_ecdsa_public_key_to_der(key, NULL, &len, 0) == HAL_OK ? len : 0;
}

/*
 * Read public key in SubjectPublicKeyInfo format, see RFCS 5280 and 5480.
 */

hal_error_t hal_ecdsa_public_key_from_der(hal_ecdsa_key_t **key_,
                                           void *keybuf, const size_t keybuf_len,
                                           const uint8_t * const der, const size_t der_len)
{
  hal_ecdsa_key_t *key = keybuf;

  if (key_ == NULL || key == NULL || keybuf_len < sizeof(*key))
    return HAL_ERROR_BAD_ARGUMENTS;

  memset(keybuf, 0, keybuf_len);
  key->type = HAL_KEY_TYPE_EC_PUBLIC;

  const uint8_t *alg_oid = NULL, *curve_oid = NULL, *pubkey = NULL;
  size_t         alg_oid_len,     curve_oid_len,     pubkey_len;
  const ecdsa_curve_t *curve;
  hal_error_t err;

  if ((err = hal_asn1_decode_spki(&alg_oid, &alg_oid_len, &curve_oid, &curve_oid_len, &pubkey, &pubkey_len,
                                  der, der_len)) != HAL_OK)
    return err;

  if (alg_oid == NULL || curve_oid == NULL || pubkey == NULL ||
      alg_oid_len != sizeof(oid_ecPublicKey) || memcmp(alg_oid, oid_ecPublicKey, alg_oid_len) != 0 ||
      (curve = oid_to_curve(&key->curve, curve_oid, curve_oid_len)) == NULL ||
      pubkey_len < 3 || (pubkey_len & 1) == 0 || pubkey[0] != 0x04 ||
      pubkey_len / 2 != fp_unsigned_bin_size(unconst_fp_int(curve->q)))
    return HAL_ERROR_ASN1_PARSE_FAILED;

  const uint8_t * const Qx = pubkey + 1;
  const uint8_t * const Qy = Qx + pubkey_len / 2;

  fp_read_unsigned_bin(key->Q->x, unconst_uint8_t(Qx), pubkey_len / 2);
  fp_read_unsigned_bin(key->Q->y, unconst_uint8_t(Qy), pubkey_len / 2);
  fp_set(key->Q->z, 1);

  *key_ = key;
  return HAL_OK;
}

/*
 * Encode a signature in PKCS #11 format: an octet string consisting
 * of concatenated values for r and s, each padded (if necessary) out
 * to the byte length of the order of the base point.
 */

static hal_error_t encode_signature_pkcs11(const ecdsa_curve_t * const curve,
                                           const fp_int * const r, const fp_int * const s,
                                           uint8_t *signature, size_t *signature_len, const size_t signature_max)
{
  assert(curve != NULL && r != NULL && s != NULL);

  const size_t n_len = fp_unsigned_bin_size(unconst_fp_int(curve->n));
  const size_t r_len = fp_unsigned_bin_size(unconst_fp_int(r));
  const size_t s_len = fp_unsigned_bin_size(unconst_fp_int(s));

  if (n_len < r_len || n_len < s_len)
    return HAL_ERROR_IMPOSSIBLE;

  if (signature_len != NULL)
    *signature_len = n_len * 2;

  if (signature == NULL)
    return HAL_OK;

  if (signature_max < n_len * 2)
    return HAL_ERROR_RESULT_TOO_LONG;

  memset(signature, 0, n_len * 2);
  fp_to_unsigned_bin(unconst_fp_int(r), signature + 1 * n_len - r_len);
  fp_to_unsigned_bin(unconst_fp_int(s), signature + 2 * n_len - s_len);

  return HAL_OK;
}

/*
 * Decode a signature from PKCS #11 format: an octet string consisting
 * of concatenated values for r and s, each of which occupies half of
 * the octet string (which must therefore be of even length).
 */

static hal_error_t decode_signature_pkcs11(const ecdsa_curve_t * const curve,
                                           fp_int *r, fp_int *s,
                                           const uint8_t * const signature, const size_t signature_len)
{
  assert(curve != NULL && r != NULL && s != NULL);

  if (signature == NULL || (signature_len & 1) != 0)
    return HAL_ERROR_BAD_ARGUMENTS;

  const size_t n_len = signature_len / 2;

  if (n_len > fp_unsigned_bin_size(unconst_fp_int(curve->n)))
    return HAL_ERROR_BAD_ARGUMENTS;

  fp_read_unsigned_bin(r, unconst_uint8_t(signature) + 0 * n_len, n_len);
  fp_read_unsigned_bin(s, unconst_uint8_t(signature) + 1 * n_len, n_len);

  return HAL_OK;
}

/*
 * Sign a caller-supplied hash.
 */

hal_error_t hal_ecdsa_sign(const hal_core_t *core,
                           const hal_ecdsa_key_t * const key,
                           const uint8_t * const hash, const size_t hash_len,
                           uint8_t *signature, size_t *signature_len, const size_t signature_max)
{
  if (key == NULL || hash == NULL || signature == NULL || signature_len == NULL || key->type != HAL_KEY_TYPE_EC_PRIVATE)
    return HAL_ERROR_BAD_ARGUMENTS;

  const ecdsa_curve_t * const curve = get_curve(key->curve);
  if (curve == NULL)
    return HAL_ERROR_IMPOSSIBLE;

  fp_int k[1] = INIT_FP_INT;
  fp_int r[1] = INIT_FP_INT;
  fp_int s[1] = INIT_FP_INT;
  fp_int e[1] = INIT_FP_INT;

  fp_int * const n = unconst_fp_int(curve->n);
  fp_int * const d = unconst_fp_int(key->d);

  ec_point_t R[1] = INIT_EC_POINT_T;

  hal_error_t err;

  fp_read_unsigned_bin(e, unconst_uint8_t(hash), hash_len);

  do {

    /*
     * Pick random curve point R, then calculate r = Rx % n.
     * If r == 0, we can't use this point, so go try again.
     */

    if ((err = point_pick_random(curve, k, R)) != HAL_OK)
      goto fail;

    assert(point_is_on_curve(R, curve));

    if (fp_mod(R->x, n, r) != FP_OKAY)
      lose(HAL_ERROR_IMPOSSIBLE);

    if (fp_iszero(r))
      continue;

    /*
     * Calculate s = ((e + dr)/k) % n.
     * If s == 0, we can't use this point, so go try again.
     */

    if (fp_mulmod (d, r, n, s) != FP_OKAY)
      lose(HAL_ERROR_IMPOSSIBLE);

    fp_add        (e, s, s);

    if (fp_mod    (s, n, s)    != FP_OKAY ||
        fp_invmod (k, n, k)    != FP_OKAY ||
        fp_mulmod (s, k, n, s) != FP_OKAY)
      lose(HAL_ERROR_IMPOSSIBLE);

  } while (fp_iszero(s));

  /*
   * Encode the signature, then we're done.
   */

  if ((err = encode_signature_pkcs11(curve, r, s, signature, signature_len, signature_max)) != HAL_OK)
    goto fail;

  err = HAL_OK;

 fail:
  fp_zero(k); fp_zero(r); fp_zero(s); fp_zero(e);
  memset(R, 0, sizeof(R));
  return err;
}

/*
 * Verify a signature using a caller-supplied hash.
 */

hal_error_t hal_ecdsa_verify(const hal_core_t *core,
                             const hal_ecdsa_key_t * const key,
                             const uint8_t * const hash, const size_t hash_len,
                             const uint8_t * const signature, const size_t signature_len)
{
  assert(key != NULL && hash != NULL && signature != NULL);

  const ecdsa_curve_t * const curve = get_curve(key->curve);

  if (curve == NULL)
    return HAL_ERROR_IMPOSSIBLE;

  if (!point_is_on_curve(key->Q, curve))
    return HAL_ERROR_KEY_NOT_ON_CURVE;

  fp_int * const n = unconst_fp_int(curve->n);

  hal_error_t err;

  fp_int r[1]  = INIT_FP_INT;
  fp_int s[1]  = INIT_FP_INT;
  fp_int e[1]  = INIT_FP_INT;
  fp_int w[1]  = INIT_FP_INT;
  fp_int u1[1] = INIT_FP_INT;
  fp_int u2[1] = INIT_FP_INT;
  fp_int v[1]  = INIT_FP_INT;

  ec_point_t u1G[1] = INIT_EC_POINT_T;
  ec_point_t u2Q[1] = INIT_EC_POINT_T;
  ec_point_t R[1]   = INIT_EC_POINT_T;

  /*
   * Start by decoding the signature.
   */

  if ((err = decode_signature_pkcs11(curve, r, s, signature, signature_len)) != HAL_OK)
    return err;

  /*
   * Check that r and s are in the allowed range, read the hash, then
   * compute:
   *
   * w  = 1 / s
   * u1 = e * w
   * u2 = r * w
   * R  = u1 * G + u2 * Q.
   */

  if (fp_cmp_d(r, 1) == FP_LT || fp_cmp(r, n) != FP_LT ||
      fp_cmp_d(s, 1) == FP_LT || fp_cmp(s, n) != FP_LT)
    return HAL_ERROR_INVALID_SIGNATURE;

  fp_read_unsigned_bin(e, unconst_uint8_t(hash), hash_len);

  if (fp_invmod(s, n, w)     != FP_OKAY ||
      fp_mulmod(e, w, n, u1) != FP_OKAY ||
      fp_mulmod(r, w, n, u2) != FP_OKAY)
    return HAL_ERROR_IMPOSSIBLE;

  fp_copy(unconst_fp_int(curve->Gx), u1G->x);
  fp_copy(unconst_fp_int(curve->Gy), u1G->y);
  fp_set(u1G->z, 1);

  if ((err = point_scalar_multiply(u1, u1G,    u1G, curve)) != HAL_OK ||
      (err = point_scalar_multiply(u2, key->Q, u2Q, curve)) != HAL_OK)
    return err;

  if (point_is_infinite(u1G))
    point_copy(u2Q, R);
  else if (point_is_infinite(u2Q))
    point_copy(u1G, R);
  else if ((err = point_to_montgomery(u1G, curve)) != HAL_OK ||
           (err = point_to_montgomery(u2Q, curve)) != HAL_OK)
    return err;
  else
    point_add(u1G, u2Q, R, curve);

  /*
   * Signature is OK if
   *   R is not the point at infinity, and
   *   Rx is congruent to r mod n.
   */

  if (point_is_infinite(R))
    return HAL_ERROR_INVALID_SIGNATURE;

  if ((err = point_to_affine(R, curve)) != HAL_OK)
    return err;

  if (fp_mod(R->x, n, v) != FP_OKAY)
    return HAL_ERROR_IMPOSSIBLE;

  return fp_cmp(v, r) == FP_EQ ? HAL_OK : HAL_ERROR_INVALID_SIGNATURE;
}

/*
 * Local variables:
 * indent-tabs-mode: nil
 * End:
 */
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