int compute_password_element (pwd_session_t *session, uint16_t grp_num,
			      char const *password, int password_len,
			      char const *id_server, int id_server_len,
			      char const *id_peer, int id_peer_len,
			      uint32_t *token)
{
	BIGNUM *x_candidate = NULL, *rnd = NULL, *cofactor = NULL;
	HMAC_CTX *ctx = NULL;
	uint8_t pwe_digest[SHA256_DIGEST_LENGTH], *prfbuf = NULL, ctr;
	int nid, is_odd, primebitlen, primebytelen, ret = 0;

	ctx = HMAC_CTX_new();
	if (ctx == NULL) {
		DEBUG("failed allocating HMAC context");
		goto fail;
	}

	switch (grp_num) { /* from IANA registry for IKE D-H groups */
	case 19:
		nid = NID_X9_62_prime256v1;
		break;

	case 20:
		nid = NID_secp384r1;
		break;

	case 21:
		nid = NID_secp521r1;
		break;

	case 25:
		nid = NID_X9_62_prime192v1;
		break;

	case 26:
		nid = NID_secp224r1;
		break;

	default:
		DEBUG("unknown group %d", grp_num);
		goto fail;
	}

	session->pwe = NULL;
	session->order = NULL;
	session->prime = NULL;

	if ((session->group = EC_GROUP_new_by_curve_name(nid)) == NULL) {
		DEBUG("unable to create EC_GROUP");
		goto fail;
	}

	if (((rnd = BN_new()) == NULL) ||
	    ((cofactor = BN_new()) == NULL) ||
	    ((session->pwe = EC_POINT_new(session->group)) == NULL) ||
	    ((session->order = BN_new()) == NULL) ||
	    ((session->prime = BN_new()) == NULL) ||
	    ((x_candidate = BN_new()) == NULL)) {
		DEBUG("unable to create bignums");
		goto fail;
	}

	if (!EC_GROUP_get_curve_GFp(session->group, session->prime, NULL, NULL, NULL)) {
		DEBUG("unable to get prime for GFp curve");
		goto fail;
	}

	if (!EC_GROUP_get_order(session->group, session->order, NULL)) {
		DEBUG("unable to get order for curve");
		goto fail;
	}

	if (!EC_GROUP_get_cofactor(session->group, cofactor, NULL)) {
		DEBUG("unable to get cofactor for curve");
		goto fail;
	}

	primebitlen = BN_num_bits(session->prime);
	primebytelen = BN_num_bytes(session->prime);
	if ((prfbuf = talloc_zero_array(session, uint8_t, primebytelen)) == NULL) {
		DEBUG("unable to alloc space for prf buffer");
		goto fail;
	}
	ctr = 0;
	while (1) {
		if (ctr > 100) {
			DEBUG("unable to find random point on curve for group %d, something's fishy", grp_num);
			goto fail;
		}
		ctr++;

		/*
		 * compute counter-mode password value and stretch to prime
		 *    pwd-seed = H(token | peer-id | server-id | password |
		 *		   counter)
		 */
		H_Init(ctx);
		H_Update(ctx, (uint8_t *)token, sizeof(*token));
		H_Update(ctx, (uint8_t const *)id_peer, id_peer_len);
		H_Update(ctx, (uint8_t const *)id_server, id_server_len);
		H_Update(ctx, (uint8_t const *)password, password_len);
		H_Update(ctx, (uint8_t *)&ctr, sizeof(ctr));
		H_Final(ctx, pwe_digest);

		BN_bin2bn(pwe_digest, SHA256_DIGEST_LENGTH, rnd);
		if (eap_pwd_kdf(pwe_digest, SHA256_DIGEST_LENGTH, "EAP-pwd Hunting And Pecking",
			        strlen("EAP-pwd Hunting And Pecking"), prfbuf, primebitlen) != 0) {
			DEBUG("key derivation function failed");
			goto fail;
		}

		BN_bin2bn(prfbuf, primebytelen, x_candidate);
		/*
		 * eap_pwd_kdf() returns a string of bits 0..primebitlen but
		 * BN_bin2bn will treat that string of bits as a big endian
		 * number. If the primebitlen is not an even multiple of 8
		 * then excessive bits-- those _after_ primebitlen-- so now
		 * we have to shift right the amount we masked off.
		 */
		if (primebitlen % 8) BN_rshift(x_candidate, x_candidate, (8 - (primebitlen % 8)));
		if (BN_ucmp(x_candidate, session->prime) >= 0) continue;

		/*
		 * need to unambiguously identify the solution, if there is
		 * one...
		 */
		is_odd = BN_is_odd(rnd) ? 1 : 0;

		/*
		 * solve the quadratic equation, if it's not solvable then we
		 * don't have a point
		 */
		if (!EC_POINT_set_compressed_coordinates_GFp(session->group, session->pwe, x_candidate, is_odd, NULL)) {
			continue;
		}

		/*
		 * If there's a solution to the equation then the point must be
		 * on the curve so why check again explicitly? OpenSSL code
		 * says this is required by X9.62. We're not X9.62 but it can't
		 * hurt just to be sure.
		 */
		if (!EC_POINT_is_on_curve(session->group, session->pwe, NULL)) {
			DEBUG("EAP-pwd: point is not on curve");
			continue;
		}

		if (BN_cmp(cofactor, BN_value_one())) {
			/* make sure the point is not in a small sub-group */
			if (!EC_POINT_mul(session->group, session->pwe, NULL, session->pwe,
				cofactor, NULL)) {
				DEBUG("EAP-pwd: cannot multiply generator by order");
				continue;
			}

			if (EC_POINT_is_at_infinity(session->group, session->pwe)) {
				DEBUG("EAP-pwd: point is at infinity");
				continue;
			}
		}
		/* if we got here then we have a new generator. */
		break;
	}

	session->group_num = grp_num;
	if (0) {
		fail:		/* DON'T free session, it's in handler->opaque */
		ret = -1;
	}

	/* cleanliness and order.... */
	BN_clear_free(cofactor);
	BN_clear_free(x_candidate);
	BN_clear_free(rnd);
	talloc_free(prfbuf);
	HMAC_CTX_free(ctx);

	return ret;
}