text: /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
   * All rights reserved.
   *
   * This package is an SSL implementation written
   * by Eric Young (eay@cryptsoft.com).
   * The implementation was written so as to conform with Netscapes SSL.
   *
   * This library is free for commercial and non-commercial use as long as
   * the following conditions are aheared to.  The following conditions
   * apply to all code found in this distribution, be it the RC4, RSA,
   * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
   * included with this distribution is covered by the same copyright terms
   * except that the holder is Tim Hudson (tjh@cryptsoft.com).
   *
   * Copyright remains Eric Young's, and as such any Copyright notices in
   * the code are not to be removed.
   * If this package is used in a product, Eric Young should be given attribution
   * as the author of the parts of the library used.
   * This can be in the form of a textual message at program startup or
   * in documentation (online or textual) provided with the package.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   * 1. Redistributions of source code must retain the copyright
   *    notice, this list of conditions and the following disclaimer.
   * 2. 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.
   * 3. All advertising materials mentioning features or use of this software
   *    must display the following acknowledgement:
   *    "This product includes cryptographic software written by
   *     Eric Young (eay@cryptsoft.com)"
   *    The word 'cryptographic' can be left out if the rouines from the library
   *    being used are not cryptographic related :-).
   * 4. If you include any Windows specific code (or a derivative thereof) from
   *    the apps directory (application code) you must include an acknowledgement:
   *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
   *
   * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``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 AUTHOR 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.
   *
   * The licence and distribution terms for any publically available version or
   * derivative of this code cannot be changed.  i.e. this code cannot simply be
   * copied and put under another distribution licence
   * [including the GNU Public Licence.]
   *
   * The DSS routines are based on patches supplied by
   * Steven Schoch <schoch@sheba.arc.nasa.gov>. */
  
  #include <CCryptoBoringSSL_dsa.h>
  
  #include <string.h>
  
  #include <CCryptoBoringSSL_bn.h>
  #include <CCryptoBoringSSL_dh.h>
  #include <CCryptoBoringSSL_digest.h>
  #include <CCryptoBoringSSL_engine.h>
  #include <CCryptoBoringSSL_err.h>
  #include <CCryptoBoringSSL_ex_data.h>
  #include <CCryptoBoringSSL_mem.h>
  #include <CCryptoBoringSSL_rand.h>
  #include <CCryptoBoringSSL_sha.h>
  #include <CCryptoBoringSSL_thread.h>
  
  #include "../fipsmodule/bn/internal.h"
  #include "../internal.h"
  
  
  #define OPENSSL_DSA_MAX_MODULUS_BITS 10000
  
  // Primality test according to FIPS PUB 186[-1], Appendix 2.1: 50 rounds of
  // Miller-Rabin.
  #define DSS_prime_checks 50
  
  static int dsa_sign_setup(const DSA *dsa, BN_CTX *ctx_in, BIGNUM **out_kinv,
                            BIGNUM **out_r);
  
  static CRYPTO_EX_DATA_CLASS g_ex_data_class = CRYPTO_EX_DATA_CLASS_INIT;
  
  DSA *DSA_new(void) {
    DSA *dsa = OPENSSL_malloc(sizeof(DSA));
    if (dsa == NULL) {
      OPENSSL_PUT_ERROR(DSA, ERR_R_MALLOC_FAILURE);
      return NULL;
    }
  
    OPENSSL_memset(dsa, 0, sizeof(DSA));
  
    dsa->references = 1;
  
    CRYPTO_MUTEX_init(&dsa->method_mont_lock);
    CRYPTO_new_ex_data(&dsa->ex_data);
  
    return dsa;
  }
  
  void DSA_free(DSA *dsa) {
    if (dsa == NULL) {
      return;
    }
  
    if (!CRYPTO_refcount_dec_and_test_zero(&dsa->references)) {
      return;
    }
  
    CRYPTO_free_ex_data(&g_ex_data_class, dsa, &dsa->ex_data);
  
    BN_clear_free(dsa->p);
    BN_clear_free(dsa->q);
    BN_clear_free(dsa->g);
    BN_clear_free(dsa->pub_key);
    BN_clear_free(dsa->priv_key);
    BN_MONT_CTX_free(dsa->method_mont_p);
    BN_MONT_CTX_free(dsa->method_mont_q);
    CRYPTO_MUTEX_cleanup(&dsa->method_mont_lock);
    OPENSSL_free(dsa);
  }
  
  int DSA_up_ref(DSA *dsa) {
    CRYPTO_refcount_inc(&dsa->references);
    return 1;
  }
  
  void DSA_get0_key(const DSA *dsa, const BIGNUM **out_pub_key,
                    const BIGNUM **out_priv_key) {
    if (out_pub_key != NULL) {
      *out_pub_key = dsa->pub_key;
    }
    if (out_priv_key != NULL) {
      *out_priv_key = dsa->priv_key;
    }
  }
  
  void DSA_get0_pqg(const DSA *dsa, const BIGNUM **out_p, const BIGNUM **out_q,
                    const BIGNUM **out_g) {
    if (out_p != NULL) {
      *out_p = dsa->p;
    }
    if (out_q != NULL) {
      *out_q = dsa->q;
    }
    if (out_g != NULL) {
      *out_g = dsa->g;
    }
  }
  
  int DSA_set0_key(DSA *dsa, BIGNUM *pub_key, BIGNUM *priv_key) {
    if (dsa->pub_key == NULL && pub_key == NULL) {
      return 0;
    }
  
    if (pub_key != NULL) {
      BN_free(dsa->pub_key);
      dsa->pub_key = pub_key;
    }
    if (priv_key != NULL) {
      BN_free(dsa->priv_key);
      dsa->priv_key = priv_key;
    }
  
    return 1;
  }
  
  int DSA_set0_pqg(DSA *dsa, BIGNUM *p, BIGNUM *q, BIGNUM *g) {
    if ((dsa->p == NULL && p == NULL) ||
        (dsa->q == NULL && q == NULL) ||
        (dsa->g == NULL && g == NULL)) {
      return 0;
    }
  
    if (p != NULL) {
      BN_free(dsa->p);
      dsa->p = p;
    }
    if (q != NULL) {
      BN_free(dsa->q);
      dsa->q = q;
    }
    if (g != NULL) {
      BN_free(dsa->g);
      dsa->g = g;
    }
  
    return 1;
  }
  
  int DSA_generate_parameters_ex(DSA *dsa, unsigned bits, const uint8_t *seed_in,
                                 size_t seed_len, int *out_counter,
                                 unsigned long *out_h, BN_GENCB *cb) {
    int ok = 0;
    unsigned char seed[SHA256_DIGEST_LENGTH];
    unsigned char md[SHA256_DIGEST_LENGTH];
    unsigned char buf[SHA256_DIGEST_LENGTH], buf2[SHA256_DIGEST_LENGTH];
    BIGNUM *r0, *W, *X, *c, *test;
    BIGNUM *g = NULL, *q = NULL, *p = NULL;
    BN_MONT_CTX *mont = NULL;
    int k, n = 0, m = 0;
    unsigned i;
    int counter = 0;
    int r = 0;
    BN_CTX *ctx = NULL;
    unsigned int h = 2;
    unsigned qsize;
    const EVP_MD *evpmd;
  
    evpmd = (bits >= 2048) ? EVP_sha256() : EVP_sha1();
    qsize = EVP_MD_size(evpmd);
  
    if (bits < 512) {
      bits = 512;
    }
  
    bits = (bits + 63) / 64 * 64;
  
    if (seed_in != NULL) {
      if (seed_len < (size_t)qsize) {
        return 0;
      }
      if (seed_len > (size_t)qsize) {
        // Only consume as much seed as is expected.
        seed_len = qsize;
      }
      OPENSSL_memcpy(seed, seed_in, seed_len);
    }
  
    ctx = BN_CTX_new();
    if (ctx == NULL) {
      goto err;
    }
    BN_CTX_start(ctx);
  
    r0 = BN_CTX_get(ctx);
    g = BN_CTX_get(ctx);
    W = BN_CTX_get(ctx);
    q = BN_CTX_get(ctx);
    X = BN_CTX_get(ctx);
    c = BN_CTX_get(ctx);
    p = BN_CTX_get(ctx);
    test = BN_CTX_get(ctx);
  
    if (test == NULL || !BN_lshift(test, BN_value_one(), bits - 1)) {
      goto err;
    }
  
    for (;;) {
      // Find q.
      for (;;) {
        // step 1
        if (!BN_GENCB_call(cb, BN_GENCB_GENERATED, m++)) {
          goto err;
        }
  
        int use_random_seed = (seed_in == NULL);
        if (use_random_seed) {
          if (!RAND_bytes(seed, qsize)) {
            goto err;
          }
        } else {
          // If we come back through, use random seed next time.
          seed_in = NULL;
        }
        OPENSSL_memcpy(buf, seed, qsize);
        OPENSSL_memcpy(buf2, seed, qsize);
        // precompute "SEED + 1" for step 7:
        for (i = qsize - 1; i < qsize; i--) {
          buf[i]++;
          if (buf[i] != 0) {
            break;
          }
        }
  
        // step 2
        if (!EVP_Digest(seed, qsize, md, NULL, evpmd, NULL) ||
            !EVP_Digest(buf, qsize, buf2, NULL, evpmd, NULL)) {
          goto err;
        }
        for (i = 0; i < qsize; i++) {
          md[i] ^= buf2[i];
        }
  
        // step 3
        md[0] |= 0x80;
        md[qsize - 1] |= 0x01;
        if (!BN_bin2bn(md, qsize, q)) {
          goto err;
        }
  
        // step 4
        r = BN_is_prime_fasttest_ex(q, DSS_prime_checks, ctx, use_random_seed, cb);
        if (r > 0) {
          break;
        }
        if (r != 0) {
          goto err;
        }
  
        // do a callback call
        // step 5
      }
  
      if (!BN_GENCB_call(cb, 2, 0) || !BN_GENCB_call(cb, 3, 0)) {
        goto err;
      }
  
      // step 6
      counter = 0;
      // "offset = 2"
  
      n = (bits - 1) / 160;
  
      for (;;) {
        if ((counter != 0) && !BN_GENCB_call(cb, BN_GENCB_GENERATED, counter)) {
          goto err;
        }
  
        // step 7
        BN_zero(W);
        // now 'buf' contains "SEED + offset - 1"
        for (k = 0; k <= n; k++) {
          // obtain "SEED + offset + k" by incrementing:
          for (i = qsize - 1; i < qsize; i--) {
            buf[i]++;
            if (buf[i] != 0) {
              break;
            }
          }
  
          if (!EVP_Digest(buf, qsize, md, NULL, evpmd, NULL)) {
            goto err;
          }
  
          // step 8
          if (!BN_bin2bn(md, qsize, r0) ||
              !BN_lshift(r0, r0, (qsize << 3) * k) ||
              !BN_add(W, W, r0)) {
            goto err;
          }
        }
  
        // more of step 8
        if (!BN_mask_bits(W, bits - 1) ||
            !BN_copy(X, W) ||
            !BN_add(X, X, test)) {
          goto err;
        }
  
        // step 9
        if (!BN_lshift1(r0, q) ||
            !BN_mod(c, X, r0, ctx) ||
            !BN_sub(r0, c, BN_value_one()) ||
            !BN_sub(p, X, r0)) {
          goto err;
        }
  
        // step 10
        if (BN_cmp(p, test) >= 0) {
          // step 11
          r = BN_is_prime_fasttest_ex(p, DSS_prime_checks, ctx, 1, cb);
          if (r > 0) {
            goto end;  // found it
          }
          if (r != 0) {
            goto err;
          }
        }
  
        // step 13
        counter++;
        // "offset = offset + n + 1"
  
        // step 14
        if (counter >= 4096) {
          break;
        }
      }
    }
  end:
    if (!BN_GENCB_call(cb, 2, 1)) {
      goto err;
    }
  
    // We now need to generate g
    // Set r0=(p-1)/q
    if (!BN_sub(test, p, BN_value_one()) ||
        !BN_div(r0, NULL, test, q, ctx)) {
      goto err;
    }
  
    mont = BN_MONT_CTX_new_for_modulus(p, ctx);
    if (mont == NULL ||
        !BN_set_word(test, h)) {
      goto err;
    }
  
    for (;;) {
      // g=test^r0%p
      if (!BN_mod_exp_mont(g, test, r0, p, ctx, mont)) {
        goto err;
      }
      if (!BN_is_one(g)) {
        break;
      }
      if (!BN_add(test, test, BN_value_one())) {
        goto err;
      }
      h++;
    }
  
    if (!BN_GENCB_call(cb, 3, 1)) {
      goto err;
    }
  
    ok = 1;
  
  err:
    if (ok) {
      BN_free(dsa->p);
      BN_free(dsa->q);
      BN_free(dsa->g);
      dsa->p = BN_dup(p);
      dsa->q = BN_dup(q);
      dsa->g = BN_dup(g);
      if (dsa->p == NULL || dsa->q == NULL || dsa->g == NULL) {
        ok = 0;
        goto err;
      }
      if (out_counter != NULL) {
        *out_counter = counter;
      }
      if (out_h != NULL) {
        *out_h = h;
      }
    }
  
    if (ctx) {
      BN_CTX_end(ctx);
      BN_CTX_free(ctx);
    }
  
    BN_MONT_CTX_free(mont);
  
    return ok;
  }
  
  DSA *DSAparams_dup(const DSA *dsa) {
    DSA *ret = DSA_new();
    if (ret == NULL) {
      return NULL;
    }
    ret->p = BN_dup(dsa->p);
    ret->q = BN_dup(dsa->q);
    ret->g = BN_dup(dsa->g);
    if (ret->p == NULL || ret->q == NULL || ret->g == NULL) {
      DSA_free(ret);
      return NULL;
    }
    return ret;
  }
  
  int DSA_generate_key(DSA *dsa) {
    int ok = 0;
    BN_CTX *ctx = NULL;
    BIGNUM *pub_key = NULL, *priv_key = NULL;
  
    ctx = BN_CTX_new();
    if (ctx == NULL) {
      goto err;
    }
  
    priv_key = dsa->priv_key;
    if (priv_key == NULL) {
      priv_key = BN_new();
      if (priv_key == NULL) {
        goto err;
      }
    }
  
    if (!BN_rand_range_ex(priv_key, 1, dsa->q)) {
      goto err;
    }
  
    pub_key = dsa->pub_key;
    if (pub_key == NULL) {
      pub_key = BN_new();
      if (pub_key == NULL) {
        goto err;
      }
    }
  
    if (!BN_MONT_CTX_set_locked(&dsa->method_mont_p, &dsa->method_mont_lock,
                                dsa->p, ctx) ||
        !BN_mod_exp_mont_consttime(pub_key, dsa->g, priv_key, dsa->p, ctx,
                                   dsa->method_mont_p)) {
      goto err;
    }
  
    dsa->priv_key = priv_key;
    dsa->pub_key = pub_key;
    ok = 1;
  
  err:
    if (dsa->pub_key == NULL) {
      BN_free(pub_key);
    }
    if (dsa->priv_key == NULL) {
      BN_free(priv_key);
    }
    BN_CTX_free(ctx);
  
    return ok;
  }
  
  DSA_SIG *DSA_SIG_new(void) {
    DSA_SIG *sig;
    sig = OPENSSL_malloc(sizeof(DSA_SIG));
    if (!sig) {
      return NULL;
    }
    sig->r = NULL;
    sig->s = NULL;
    return sig;
  }
  
  void DSA_SIG_free(DSA_SIG *sig) {
    if (!sig) {
      return;
    }
  
    BN_free(sig->r);
    BN_free(sig->s);
    OPENSSL_free(sig);
  }
  
  // mod_mul_consttime sets |r| to |a| * |b| modulo |mont->N|, treating |a| and
  // |b| as secret. This function internally uses Montgomery reduction, but
  // neither inputs nor outputs are in Montgomery form.
  static int mod_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                               const BN_MONT_CTX *mont, BN_CTX *ctx) {
    BN_CTX_start(ctx);
    BIGNUM *tmp = BN_CTX_get(ctx);
    // |BN_mod_mul_montgomery| removes a factor of R, so we cancel it with a
    // single |BN_to_montgomery| which adds one factor of R.
    int ok = tmp != NULL &&
             BN_to_montgomery(tmp, a, mont, ctx) &&
             BN_mod_mul_montgomery(r, tmp, b, mont, ctx);
    BN_CTX_end(ctx);
    return ok;
  }
  
  DSA_SIG *DSA_do_sign(const uint8_t *digest, size_t digest_len, const DSA *dsa) {
    if (!dsa->p || !dsa->q || !dsa->g) {
      OPENSSL_PUT_ERROR(DSA, DSA_R_MISSING_PARAMETERS);
      return NULL;
    }
  
    // Reject invalid parameters. In particular, the algorithm will infinite loop
    // if |g| is zero.
    if (BN_is_zero(dsa->p) || BN_is_zero(dsa->q) || BN_is_zero(dsa->g)) {
      OPENSSL_PUT_ERROR(DSA, DSA_R_INVALID_PARAMETERS);
      return NULL;
    }
  
    // We only support DSA keys that are a multiple of 8 bits. (This is a weaker
    // check than the one in |DSA_do_check_signature|, which only allows 160-,
    // 224-, and 256-bit keys.
    if (BN_num_bits(dsa->q) % 8 != 0) {
      OPENSSL_PUT_ERROR(DSA, DSA_R_BAD_Q_VALUE);
      return NULL;
    }
  
    BIGNUM *kinv = NULL, *r = NULL, *s = NULL;
    BIGNUM m;
    BIGNUM xr;
    BN_CTX *ctx = NULL;
    DSA_SIG *ret = NULL;
  
    BN_init(&m);
    BN_init(&xr);
    s = BN_new();
    if (s == NULL) {
      goto err;
    }
    ctx = BN_CTX_new();
    if (ctx == NULL) {
      goto err;
    }
  
  redo:
    if (!dsa_sign_setup(dsa, ctx, &kinv, &r)) {
      goto err;
    }
  
    if (digest_len > BN_num_bytes(dsa->q)) {
      // If the digest length is greater than the size of |dsa->q| use the
      // BN_num_bits(dsa->q) leftmost bits of the digest, see FIPS 186-3, 4.2.
      // Note the above check that |dsa->q| is a multiple of 8 bits.
      digest_len = BN_num_bytes(dsa->q);
    }
  
    if (BN_bin2bn(digest, digest_len, &m) == NULL) {
      goto err;
    }
  
    // |m| is bounded by 2^(num_bits(q)), which is slightly looser than q. This
    // violates |bn_mod_add_consttime| and |mod_mul_consttime|'s preconditions.
    // (The underlying algorithms could accept looser bounds, but we reduce for
    // simplicity.)
    size_t q_width = bn_minimal_width(dsa->q);
    if (!bn_resize_words(&m, q_width) ||
        !bn_resize_words(&xr, q_width)) {
      goto err;
    }
    bn_reduce_once_in_place(m.d, 0 /* no carry word */, dsa->q->d,
                            xr.d /* scratch space */, q_width);
  
    // Compute s = inv(k) (m + xr) mod q. Note |dsa->method_mont_q| is
    // initialized by |dsa_sign_setup|.
    if (!mod_mul_consttime(&xr, dsa->priv_key, r, dsa->method_mont_q, ctx) ||
        !bn_mod_add_consttime(s, &xr, &m, dsa->q, ctx) ||
        !mod_mul_consttime(s, s, kinv, dsa->method_mont_q, ctx)) {
      goto err;
    }
  
    // Redo if r or s is zero as required by FIPS 186-3: this is
    // very unlikely.
    if (BN_is_zero(r) || BN_is_zero(s)) {
      goto redo;
    }
    ret = DSA_SIG_new();
    if (ret == NULL) {
      goto err;
    }
    ret->r = r;
    ret->s = s;
  
  err:
    if (ret == NULL) {
      OPENSSL_PUT_ERROR(DSA, ERR_R_BN_LIB);
      BN_free(r);
      BN_free(s);
    }
    BN_CTX_free(ctx);
    BN_clear_free(&m);
    BN_clear_free(&xr);
    BN_clear_free(kinv);
  
    return ret;
  }
  
  int DSA_do_verify(const uint8_t *digest, size_t digest_len, DSA_SIG *sig,
                    const DSA *dsa) {
    int valid;
    if (!DSA_do_check_signature(&valid, digest, digest_len, sig, dsa)) {
      return -1;
    }
    return valid;
  }
  
  int DSA_do_check_signature(int *out_valid, const uint8_t *digest,
                             size_t digest_len, DSA_SIG *sig, const DSA *dsa) {
    BN_CTX *ctx;
    BIGNUM u1, u2, t1;
    int ret = 0;
    unsigned i;
  
    *out_valid = 0;
  
    if (!dsa->p || !dsa->q || !dsa->g) {
      OPENSSL_PUT_ERROR(DSA, DSA_R_MISSING_PARAMETERS);
      return 0;
    }
  
    i = BN_num_bits(dsa->q);
    // FIPS 186-3 allows only different sizes for q.
    if (i != 160 && i != 224 && i != 256) {
      OPENSSL_PUT_ERROR(DSA, DSA_R_BAD_Q_VALUE);
      return 0;
    }
  
    if (BN_num_bits(dsa->p) > OPENSSL_DSA_MAX_MODULUS_BITS) {
      OPENSSL_PUT_ERROR(DSA, DSA_R_MODULUS_TOO_LARGE);
      return 0;
    }
  
    BN_init(&u1);
    BN_init(&u2);
    BN_init(&t1);
  
    ctx = BN_CTX_new();
    if (ctx == NULL) {
      goto err;
    }
  
    if (BN_is_zero(sig->r) || BN_is_negative(sig->r) ||
        BN_ucmp(sig->r, dsa->q) >= 0) {
      ret = 1;
      goto err;
    }
    if (BN_is_zero(sig->s) || BN_is_negative(sig->s) ||
        BN_ucmp(sig->s, dsa->q) >= 0) {
      ret = 1;
      goto err;
    }
  
    // Calculate W = inv(S) mod Q
    // save W in u2
    if (BN_mod_inverse(&u2, sig->s, dsa->q, ctx) == NULL) {
      goto err;
    }
  
    // save M in u1
    if (digest_len > (i >> 3)) {
      // if the digest length is greater than the size of q use the
      // BN_num_bits(dsa->q) leftmost bits of the digest, see
      // fips 186-3, 4.2
      digest_len = (i >> 3);
    }
  
    if (BN_bin2bn(digest, digest_len, &u1) == NULL) {
      goto err;
    }
  
    // u1 = M * w mod q
    if (!BN_mod_mul(&u1, &u1, &u2, dsa->q, ctx)) {
      goto err;
    }
  
    // u2 = r * w mod q
    if (!BN_mod_mul(&u2, sig->r, &u2, dsa->q, ctx)) {
      goto err;
    }
  
    if (!BN_MONT_CTX_set_locked((BN_MONT_CTX **)&dsa->method_mont_p,
                                (CRYPTO_MUTEX *)&dsa->method_mont_lock, dsa->p,
                                ctx)) {
      goto err;
    }
  
    if (!BN_mod_exp2_mont(&t1, dsa->g, &u1, dsa->pub_key, &u2, dsa->p, ctx,
                          dsa->method_mont_p)) {
      goto err;
    }
  
    // BN_copy(&u1,&t1);
    // let u1 = u1 mod q
    if (!BN_mod(&u1, &t1, dsa->q, ctx)) {
      goto err;
    }
  
    // V is now in u1.  If the signature is correct, it will be
    // equal to R.
    *out_valid = BN_ucmp(&u1, sig->r) == 0;
    ret = 1;
  
  err:
    if (ret != 1) {
      OPENSSL_PUT_ERROR(DSA, ERR_R_BN_LIB);
    }
    BN_CTX_free(ctx);
    BN_free(&u1);
    BN_free(&u2);
    BN_free(&t1);
  
    return ret;
  }
  
  int DSA_sign(int type, const uint8_t *digest, size_t digest_len,
               uint8_t *out_sig, unsigned int *out_siglen, const DSA *dsa) {
    DSA_SIG *s;
  
    s = DSA_do_sign(digest, digest_len, dsa);
    if (s == NULL) {
      *out_siglen = 0;
      return 0;
    }
  
    *out_siglen = i2d_DSA_SIG(s, &out_sig);
    DSA_SIG_free(s);
    return 1;
  }
  
  int DSA_verify(int type, const uint8_t *digest, size_t digest_len,
                 const uint8_t *sig, size_t sig_len, const DSA *dsa) {
    int valid;
    if (!DSA_check_signature(&valid, digest, digest_len, sig, sig_len, dsa)) {
      return -1;
    }
    return valid;
  }
  
  int DSA_check_signature(int *out_valid, const uint8_t *digest,
                          size_t digest_len, const uint8_t *sig, size_t sig_len,
                          const DSA *dsa) {
    DSA_SIG *s = NULL;
    int ret = 0;
    uint8_t *der = NULL;
  
    s = DSA_SIG_new();
    if (s == NULL) {
      goto err;
    }
  
    const uint8_t *sigp = sig;
    if (d2i_DSA_SIG(&s, &sigp, sig_len) == NULL || sigp != sig + sig_len) {
      goto err;
    }
  
    // Ensure that the signature uses DER and doesn't have trailing garbage.
    int der_len = i2d_DSA_SIG(s, &der);
    if (der_len < 0 || (size_t)der_len != sig_len ||
        OPENSSL_memcmp(sig, der, sig_len)) {
      goto err;
    }
  
    ret = DSA_do_check_signature(out_valid, digest, digest_len, s, dsa);
  
  err:
    OPENSSL_free(der);
    DSA_SIG_free(s);
    return ret;
  }
  
  // der_len_len returns the number of bytes needed to represent a length of |len|
  // in DER.
  static size_t der_len_len(size_t len) {
    if (len < 0x80) {
      return 1;
    }
    size_t ret = 1;
    while (len > 0) {
      ret++;
      len >>= 8;
    }
    return ret;
  }
  
  int DSA_size(const DSA *dsa) {
    size_t order_len = BN_num_bytes(dsa->q);
    // Compute the maximum length of an |order_len| byte integer. Defensively
    // assume that the leading 0x00 is included.
    size_t integer_len = 1 /* tag */ + der_len_len(order_len + 1) + 1 + order_len;
    if (integer_len < order_len) {
      return 0;
    }
    // A DSA signature is two INTEGERs.
    size_t value_len = 2 * integer_len;
    if (value_len < integer_len) {
      return 0;
    }
    // Add the header.
    size_t ret = 1 /* tag */ + der_len_len(value_len) + value_len;
    if (ret < value_len) {
      return 0;
    }
    return ret;
  }
  
  static int dsa_sign_setup(const DSA *dsa, BN_CTX *ctx, BIGNUM **out_kinv,
                            BIGNUM **out_r) {
    if (!dsa->p || !dsa->q || !dsa->g) {
      OPENSSL_PUT_ERROR(DSA, DSA_R_MISSING_PARAMETERS);
      return 0;
    }
  
    int ret = 0;
    BIGNUM k;
    BN_init(&k);
    BIGNUM *r = BN_new();
    BIGNUM *kinv = BN_new();
    if (r == NULL || kinv == NULL ||
        // Get random k
        !BN_rand_range_ex(&k, 1, dsa->q) ||
        !BN_MONT_CTX_set_locked((BN_MONT_CTX **)&dsa->method_mont_p,
                                (CRYPTO_MUTEX *)&dsa->method_mont_lock, dsa->p,
                                ctx) ||
        !BN_MONT_CTX_set_locked((BN_MONT_CTX **)&dsa->method_mont_q,
                                (CRYPTO_MUTEX *)&dsa->method_mont_lock, dsa->q,
                                ctx) ||
        // Compute r = (g^k mod p) mod q
        !BN_mod_exp_mont_consttime(r, dsa->g, &k, dsa->p, ctx,
                                   dsa->method_mont_p) ||
        // Note |BN_mod| below is not constant-time and may leak information about
        // |r|. |dsa->p| may be significantly larger than |dsa->q|, so this is not
        // easily performed in constant-time with Montgomery reduction.
        //
        // However, |r| at this point is g^k (mod p). It is almost the value of
        // |r| revealed in the signature anyway (g^k (mod p) (mod q)), going from
        // it to |k| would require computing a discrete log.
        !BN_mod(r, r, dsa->q, ctx) ||
        // Compute part of 's = inv(k) (m + xr) mod q' using Fermat's Little
        // Theorem.
        !bn_mod_inverse_prime(kinv, &k, dsa->q, ctx, dsa->method_mont_q)) {
      OPENSSL_PUT_ERROR(DSA, ERR_R_BN_LIB);
      goto err;
    }
  
    BN_clear_free(*out_kinv);
    *out_kinv = kinv;
    kinv = NULL;
  
    BN_clear_free(*out_r);
    *out_r = r;
    r = NULL;
  
    ret = 1;
  
  err:
    BN_clear_free(&k);
    BN_clear_free(r);
    BN_clear_free(kinv);
    return ret;
  }
  
  int DSA_get_ex_new_index(long argl, void *argp, CRYPTO_EX_unused *unused,
                           CRYPTO_EX_dup *dup_unused, CRYPTO_EX_free *free_func) {
    int index;
    if (!CRYPTO_get_ex_new_index(&g_ex_data_class, &index, argl, argp,
                                 free_func)) {
      return -1;
    }
    return index;
  }
  
  int DSA_set_ex_data(DSA *dsa, int idx, void *arg) {
    return CRYPTO_set_ex_data(&dsa->ex_data, idx, arg);
  }
  
  void *DSA_get_ex_data(const DSA *dsa, int idx) {
    return CRYPTO_get_ex_data(&dsa->ex_data, idx);
  }
  
  DH *DSA_dup_DH(const DSA *dsa) {
    if (dsa == NULL) {
      return NULL;
    }
  
    DH *ret = DH_new();
    if (ret == NULL) {
      goto err;
    }
    if (dsa->q != NULL) {
      ret->priv_length = BN_num_bits(dsa->q);
      if ((ret->q = BN_dup(dsa->q)) == NULL) {
        goto err;
      }
    }
    if ((dsa->p != NULL && (ret->p = BN_dup(dsa->p)) == NULL) ||
        (dsa->g != NULL && (ret->g = BN_dup(dsa->g)) == NULL) ||
        (dsa->pub_key != NULL && (ret->pub_key = BN_dup(dsa->pub_key)) == NULL) ||
        (dsa->priv_key != NULL &&
         (ret->priv_key = BN_dup(dsa->priv_key)) == NULL)) {
      goto err;
    }
  
    return ret;
  
  err:
    DH_free(ret);
    return NULL;
  }
  