Nonce usage in ECDSA signing algorithm

Nonce usage in ECDSA signing algorithm

I'm trying to understand the signing function secp256k1_ecdsa_sig_sign(), and I'm curious about the nonce usage here.

static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
  unsigned char b[32];
  secp256k1_gej rp;
  secp256k1_ge r;
  secp256k1_scalar n;
  int overflow = 0;

  secp256k1_ecmult_gen(ctx, &rp, nonce);
  secp256k1_ge_set_gej(&r, &rp);
  secp256k1_fe_normalize(&r.x);
  secp256k1_fe_normalize(&r.y);
  secp256k1_fe_get_b32(b, &r.x);
  secp256k1_scalar_set_b32(sigr, b, &overflow);
  /* These two conditions should be checked before calling */
  VERIFY_CHECK(!secp256k1_scalar_is_zero(sigr));
  VERIFY_CHECK(overflow == 0);

  if (recid) {
    /* The overflow condition is cryptographically unreachable as hitting   it requires finding the discrete log
     * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria.
     */
     *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
  }
  secp256k1_scalar_mul(&n, sigr, seckey);
  secp256k1_scalar_add(&n, &n, message);
  secp256k1_scalar_inverse(sigs, nonce);
  secp256k1_scalar_mul(sigs, sigs, &n);
  secp256k1_scalar_clear(&n);
  secp256k1_gej_clear(&rp);
  secp256k1_ge_clear(&r);

  if (secp256k1_scalar_is_zero(sigs)) {
    return 0;
  }

  if (secp256k1_scalar_is_high(sigs)) {
    secp256k1_scalar_negate(sigs, sigs);

    if (recid) {
      *recid ^= 1;
    }

  }

  return 1;
}

I'm familiar with the standard ECDSA, but what exactly is being done with the nonce here and why?

Thanks!

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