2 * Copyright 2006-2016 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
11 #include "internal/cryptlib.h"
12 #include <openssl/asn1t.h>
13 #include <openssl/x509.h>
14 #include <openssl/rsa.h>
15 #include <openssl/bn.h>
16 #include <openssl/evp.h>
17 #include <openssl/x509v3.h>
18 #include <openssl/cms.h>
19 #include "internal/evp_int.h"
22 /* RSA pkey context structure */
25 /* Key gen parameters */
28 /* Keygen callback info */
30 /* RSA padding mode */
34 /* message digest for MGF1 */
38 /* Minimum salt length or -1 if no PSS parameter restriction */
43 unsigned char *oaep_label
;
47 /* True if PSS parameters are restricted */
48 #define rsa_pss_restricted(rctx) (rctx->min_saltlen != -1)
50 static int pkey_rsa_init(EVP_PKEY_CTX
*ctx
)
52 RSA_PKEY_CTX
*rctx
= OPENSSL_zalloc(sizeof(*rctx
));
56 if (pkey_ctx_is_pss(ctx
))
57 rctx
->pad_mode
= RSA_PKCS1_PSS_PADDING
;
59 rctx
->pad_mode
= RSA_PKCS1_PADDING
;
61 rctx
->min_saltlen
= -1;
63 ctx
->keygen_info
= rctx
->gentmp
;
64 ctx
->keygen_info_count
= 2;
69 static int pkey_rsa_copy(EVP_PKEY_CTX
*dst
, EVP_PKEY_CTX
*src
)
71 RSA_PKEY_CTX
*dctx
, *sctx
;
73 if (!pkey_rsa_init(dst
))
77 dctx
->nbits
= sctx
->nbits
;
79 dctx
->pub_exp
= BN_dup(sctx
->pub_exp
);
83 dctx
->pad_mode
= sctx
->pad_mode
;
85 dctx
->mgf1md
= sctx
->mgf1md
;
86 if (sctx
->oaep_label
) {
87 OPENSSL_free(dctx
->oaep_label
);
88 dctx
->oaep_label
= OPENSSL_memdup(sctx
->oaep_label
, sctx
->oaep_labellen
);
89 if (!dctx
->oaep_label
)
91 dctx
->oaep_labellen
= sctx
->oaep_labellen
;
96 static int setup_tbuf(RSA_PKEY_CTX
*ctx
, EVP_PKEY_CTX
*pk
)
98 if (ctx
->tbuf
!= NULL
)
100 ctx
->tbuf
= OPENSSL_malloc(EVP_PKEY_size(pk
->pkey
));
101 if (ctx
->tbuf
== NULL
)
106 static void pkey_rsa_cleanup(EVP_PKEY_CTX
*ctx
)
108 RSA_PKEY_CTX
*rctx
= ctx
->data
;
110 BN_free(rctx
->pub_exp
);
111 OPENSSL_free(rctx
->tbuf
);
112 OPENSSL_free(rctx
->oaep_label
);
117 static int pkey_rsa_sign(EVP_PKEY_CTX
*ctx
, unsigned char *sig
,
118 size_t *siglen
, const unsigned char *tbs
,
122 RSA_PKEY_CTX
*rctx
= ctx
->data
;
123 RSA
*rsa
= ctx
->pkey
->pkey
.rsa
;
126 if (tbslen
!= (size_t)EVP_MD_size(rctx
->md
)) {
127 RSAerr(RSA_F_PKEY_RSA_SIGN
, RSA_R_INVALID_DIGEST_LENGTH
);
131 if (EVP_MD_type(rctx
->md
) == NID_mdc2
) {
133 if (rctx
->pad_mode
!= RSA_PKCS1_PADDING
)
135 ret
= RSA_sign_ASN1_OCTET_STRING(0,
136 tbs
, tbslen
, sig
, &sltmp
, rsa
);
141 } else if (rctx
->pad_mode
== RSA_X931_PADDING
) {
142 if ((size_t)EVP_PKEY_size(ctx
->pkey
) < tbslen
+ 1) {
143 RSAerr(RSA_F_PKEY_RSA_SIGN
, RSA_R_KEY_SIZE_TOO_SMALL
);
146 if (!setup_tbuf(rctx
, ctx
)) {
147 RSAerr(RSA_F_PKEY_RSA_SIGN
, ERR_R_MALLOC_FAILURE
);
150 memcpy(rctx
->tbuf
, tbs
, tbslen
);
151 rctx
->tbuf
[tbslen
] = RSA_X931_hash_id(EVP_MD_type(rctx
->md
));
152 ret
= RSA_private_encrypt(tbslen
+ 1, rctx
->tbuf
,
153 sig
, rsa
, RSA_X931_PADDING
);
154 } else if (rctx
->pad_mode
== RSA_PKCS1_PADDING
) {
156 ret
= RSA_sign(EVP_MD_type(rctx
->md
),
157 tbs
, tbslen
, sig
, &sltmp
, rsa
);
161 } else if (rctx
->pad_mode
== RSA_PKCS1_PSS_PADDING
) {
162 if (!setup_tbuf(rctx
, ctx
))
164 if (!RSA_padding_add_PKCS1_PSS_mgf1(rsa
,
166 rctx
->md
, rctx
->mgf1md
,
169 ret
= RSA_private_encrypt(RSA_size(rsa
), rctx
->tbuf
,
170 sig
, rsa
, RSA_NO_PADDING
);
174 ret
= RSA_private_encrypt(tbslen
, tbs
, sig
, ctx
->pkey
->pkey
.rsa
,
182 static int pkey_rsa_verifyrecover(EVP_PKEY_CTX
*ctx
,
183 unsigned char *rout
, size_t *routlen
,
184 const unsigned char *sig
, size_t siglen
)
187 RSA_PKEY_CTX
*rctx
= ctx
->data
;
190 if (rctx
->pad_mode
== RSA_X931_PADDING
) {
191 if (!setup_tbuf(rctx
, ctx
))
193 ret
= RSA_public_decrypt(siglen
, sig
,
194 rctx
->tbuf
, ctx
->pkey
->pkey
.rsa
,
199 if (rctx
->tbuf
[ret
] != RSA_X931_hash_id(EVP_MD_type(rctx
->md
))) {
200 RSAerr(RSA_F_PKEY_RSA_VERIFYRECOVER
,
201 RSA_R_ALGORITHM_MISMATCH
);
204 if (ret
!= EVP_MD_size(rctx
->md
)) {
205 RSAerr(RSA_F_PKEY_RSA_VERIFYRECOVER
,
206 RSA_R_INVALID_DIGEST_LENGTH
);
210 memcpy(rout
, rctx
->tbuf
, ret
);
211 } else if (rctx
->pad_mode
== RSA_PKCS1_PADDING
) {
213 ret
= int_rsa_verify(EVP_MD_type(rctx
->md
),
214 NULL
, 0, rout
, &sltmp
,
215 sig
, siglen
, ctx
->pkey
->pkey
.rsa
);
222 ret
= RSA_public_decrypt(siglen
, sig
, rout
, ctx
->pkey
->pkey
.rsa
,
230 static int pkey_rsa_verify(EVP_PKEY_CTX
*ctx
,
231 const unsigned char *sig
, size_t siglen
,
232 const unsigned char *tbs
, size_t tbslen
)
234 RSA_PKEY_CTX
*rctx
= ctx
->data
;
235 RSA
*rsa
= ctx
->pkey
->pkey
.rsa
;
239 if (rctx
->pad_mode
== RSA_PKCS1_PADDING
)
240 return RSA_verify(EVP_MD_type(rctx
->md
), tbs
, tbslen
,
242 if (tbslen
!= (size_t)EVP_MD_size(rctx
->md
)) {
243 RSAerr(RSA_F_PKEY_RSA_VERIFY
, RSA_R_INVALID_DIGEST_LENGTH
);
246 if (rctx
->pad_mode
== RSA_X931_PADDING
) {
247 if (pkey_rsa_verifyrecover(ctx
, NULL
, &rslen
, sig
, siglen
) <= 0)
249 } else if (rctx
->pad_mode
== RSA_PKCS1_PSS_PADDING
) {
251 if (!setup_tbuf(rctx
, ctx
))
253 ret
= RSA_public_decrypt(siglen
, sig
, rctx
->tbuf
,
254 rsa
, RSA_NO_PADDING
);
257 ret
= RSA_verify_PKCS1_PSS_mgf1(rsa
, tbs
,
258 rctx
->md
, rctx
->mgf1md
,
259 rctx
->tbuf
, rctx
->saltlen
);
266 if (!setup_tbuf(rctx
, ctx
))
268 rslen
= RSA_public_decrypt(siglen
, sig
, rctx
->tbuf
,
269 rsa
, rctx
->pad_mode
);
274 if ((rslen
!= tbslen
) || memcmp(tbs
, rctx
->tbuf
, rslen
))
281 static int pkey_rsa_encrypt(EVP_PKEY_CTX
*ctx
,
282 unsigned char *out
, size_t *outlen
,
283 const unsigned char *in
, size_t inlen
)
286 RSA_PKEY_CTX
*rctx
= ctx
->data
;
288 if (rctx
->pad_mode
== RSA_PKCS1_OAEP_PADDING
) {
289 int klen
= RSA_size(ctx
->pkey
->pkey
.rsa
);
290 if (!setup_tbuf(rctx
, ctx
))
292 if (!RSA_padding_add_PKCS1_OAEP_mgf1(rctx
->tbuf
, klen
,
296 rctx
->md
, rctx
->mgf1md
))
298 ret
= RSA_public_encrypt(klen
, rctx
->tbuf
, out
,
299 ctx
->pkey
->pkey
.rsa
, RSA_NO_PADDING
);
301 ret
= RSA_public_encrypt(inlen
, in
, out
, ctx
->pkey
->pkey
.rsa
,
309 static int pkey_rsa_decrypt(EVP_PKEY_CTX
*ctx
,
310 unsigned char *out
, size_t *outlen
,
311 const unsigned char *in
, size_t inlen
)
314 RSA_PKEY_CTX
*rctx
= ctx
->data
;
316 if (rctx
->pad_mode
== RSA_PKCS1_OAEP_PADDING
) {
318 if (!setup_tbuf(rctx
, ctx
))
320 ret
= RSA_private_decrypt(inlen
, in
, rctx
->tbuf
,
321 ctx
->pkey
->pkey
.rsa
, RSA_NO_PADDING
);
324 for (i
= 0; i
< ret
; i
++) {
328 ret
= RSA_padding_check_PKCS1_OAEP_mgf1(out
, ret
, rctx
->tbuf
+ i
,
332 rctx
->md
, rctx
->mgf1md
);
334 ret
= RSA_private_decrypt(inlen
, in
, out
, ctx
->pkey
->pkey
.rsa
,
342 static int check_padding_md(const EVP_MD
*md
, int padding
)
349 mdnid
= EVP_MD_type(md
);
351 if (padding
== RSA_NO_PADDING
) {
352 RSAerr(RSA_F_CHECK_PADDING_MD
, RSA_R_INVALID_PADDING_MODE
);
356 if (padding
== RSA_X931_PADDING
) {
357 if (RSA_X931_hash_id(mdnid
) == -1) {
358 RSAerr(RSA_F_CHECK_PADDING_MD
, RSA_R_INVALID_X931_DIGEST
);
363 /* List of all supported RSA digests */
378 RSAerr(RSA_F_CHECK_PADDING_MD
, RSA_R_INVALID_DIGEST
);
387 static int pkey_rsa_ctrl(EVP_PKEY_CTX
*ctx
, int type
, int p1
, void *p2
)
389 RSA_PKEY_CTX
*rctx
= ctx
->data
;
392 case EVP_PKEY_CTRL_RSA_PADDING
:
393 if ((p1
>= RSA_PKCS1_PADDING
) && (p1
<= RSA_PKCS1_PSS_PADDING
)) {
394 if (!check_padding_md(rctx
->md
, p1
))
396 if (p1
== RSA_PKCS1_PSS_PADDING
) {
397 if (!(ctx
->operation
&
398 (EVP_PKEY_OP_SIGN
| EVP_PKEY_OP_VERIFY
)))
401 rctx
->md
= EVP_sha1();
402 } else if (pkey_ctx_is_pss(ctx
)) {
405 if (p1
== RSA_PKCS1_OAEP_PADDING
) {
406 if (!(ctx
->operation
& EVP_PKEY_OP_TYPE_CRYPT
))
409 rctx
->md
= EVP_sha1();
415 RSAerr(RSA_F_PKEY_RSA_CTRL
,
416 RSA_R_ILLEGAL_OR_UNSUPPORTED_PADDING_MODE
);
419 case EVP_PKEY_CTRL_GET_RSA_PADDING
:
420 *(int *)p2
= rctx
->pad_mode
;
423 case EVP_PKEY_CTRL_RSA_PSS_SALTLEN
:
424 case EVP_PKEY_CTRL_GET_RSA_PSS_SALTLEN
:
425 if (rctx
->pad_mode
!= RSA_PKCS1_PSS_PADDING
) {
426 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_INVALID_PSS_SALTLEN
);
429 if (type
== EVP_PKEY_CTRL_GET_RSA_PSS_SALTLEN
) {
430 *(int *)p2
= rctx
->saltlen
;
434 if (rsa_pss_restricted(rctx
) && p1
< rctx
->min_saltlen
) {
435 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_PSS_SALTLEN_TOO_SMALL
);
442 case EVP_PKEY_CTRL_RSA_KEYGEN_BITS
:
444 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_KEY_SIZE_TOO_SMALL
);
450 case EVP_PKEY_CTRL_RSA_KEYGEN_PUBEXP
:
451 if (p2
== NULL
|| !BN_is_odd((BIGNUM
*)p2
) || BN_is_one((BIGNUM
*)p2
)) {
452 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_BAD_E_VALUE
);
455 BN_free(rctx
->pub_exp
);
459 case EVP_PKEY_CTRL_RSA_OAEP_MD
:
460 case EVP_PKEY_CTRL_GET_RSA_OAEP_MD
:
461 if (rctx
->pad_mode
!= RSA_PKCS1_OAEP_PADDING
) {
462 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_INVALID_PADDING_MODE
);
465 if (type
== EVP_PKEY_CTRL_GET_RSA_OAEP_MD
)
466 *(const EVP_MD
**)p2
= rctx
->md
;
471 case EVP_PKEY_CTRL_MD
:
472 if (!check_padding_md(p2
, rctx
->pad_mode
))
474 if (rsa_pss_restricted(rctx
)) {
475 if (EVP_MD_type(rctx
->md
) == EVP_MD_type(p2
))
477 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_DIGEST_NOT_ALLOWED
);
483 case EVP_PKEY_CTRL_GET_MD
:
484 *(const EVP_MD
**)p2
= rctx
->md
;
487 case EVP_PKEY_CTRL_RSA_MGF1_MD
:
488 case EVP_PKEY_CTRL_GET_RSA_MGF1_MD
:
489 if (rctx
->pad_mode
!= RSA_PKCS1_PSS_PADDING
490 && rctx
->pad_mode
!= RSA_PKCS1_OAEP_PADDING
) {
491 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_INVALID_MGF1_MD
);
494 if (type
== EVP_PKEY_CTRL_GET_RSA_MGF1_MD
) {
496 *(const EVP_MD
**)p2
= rctx
->mgf1md
;
498 *(const EVP_MD
**)p2
= rctx
->md
;
500 if (rsa_pss_restricted(rctx
)) {
501 if (EVP_MD_type(rctx
->md
) == EVP_MD_type(p2
))
503 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_MGF1_DIGEST_NOT_ALLOWED
);
510 case EVP_PKEY_CTRL_RSA_OAEP_LABEL
:
511 if (rctx
->pad_mode
!= RSA_PKCS1_OAEP_PADDING
) {
512 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_INVALID_PADDING_MODE
);
515 OPENSSL_free(rctx
->oaep_label
);
517 rctx
->oaep_label
= p2
;
518 rctx
->oaep_labellen
= p1
;
520 rctx
->oaep_label
= NULL
;
521 rctx
->oaep_labellen
= 0;
525 case EVP_PKEY_CTRL_GET_RSA_OAEP_LABEL
:
526 if (rctx
->pad_mode
!= RSA_PKCS1_OAEP_PADDING
) {
527 RSAerr(RSA_F_PKEY_RSA_CTRL
, RSA_R_INVALID_PADDING_MODE
);
530 *(unsigned char **)p2
= rctx
->oaep_label
;
531 return rctx
->oaep_labellen
;
533 case EVP_PKEY_CTRL_DIGESTINIT
:
534 case EVP_PKEY_CTRL_PKCS7_SIGN
:
535 #ifndef OPENSSL_NO_CMS
536 case EVP_PKEY_CTRL_CMS_SIGN
:
540 case EVP_PKEY_CTRL_PKCS7_ENCRYPT
:
541 case EVP_PKEY_CTRL_PKCS7_DECRYPT
:
542 #ifndef OPENSSL_NO_CMS
543 case EVP_PKEY_CTRL_CMS_DECRYPT
:
544 case EVP_PKEY_CTRL_CMS_ENCRYPT
:
545 if (!pkey_ctx_is_pss(ctx
))
548 case EVP_PKEY_CTRL_PEER_KEY
:
549 RSAerr(RSA_F_PKEY_RSA_CTRL
,
550 RSA_R_OPERATION_NOT_SUPPORTED_FOR_THIS_KEYTYPE
);
559 static int pkey_rsa_ctrl_str(EVP_PKEY_CTX
*ctx
,
560 const char *type
, const char *value
)
563 RSAerr(RSA_F_PKEY_RSA_CTRL_STR
, RSA_R_VALUE_MISSING
);
566 if (strcmp(type
, "rsa_padding_mode") == 0) {
568 if (strcmp(value
, "pkcs1") == 0)
569 pm
= RSA_PKCS1_PADDING
;
570 else if (strcmp(value
, "sslv23") == 0)
571 pm
= RSA_SSLV23_PADDING
;
572 else if (strcmp(value
, "none") == 0)
574 else if (strcmp(value
, "oeap") == 0)
575 pm
= RSA_PKCS1_OAEP_PADDING
;
576 else if (strcmp(value
, "oaep") == 0)
577 pm
= RSA_PKCS1_OAEP_PADDING
;
578 else if (strcmp(value
, "x931") == 0)
579 pm
= RSA_X931_PADDING
;
580 else if (strcmp(value
, "pss") == 0)
581 pm
= RSA_PKCS1_PSS_PADDING
;
583 RSAerr(RSA_F_PKEY_RSA_CTRL_STR
, RSA_R_UNKNOWN_PADDING_TYPE
);
586 return EVP_PKEY_CTX_set_rsa_padding(ctx
, pm
);
589 if (strcmp(type
, "rsa_pss_saltlen") == 0) {
591 saltlen
= atoi(value
);
592 return EVP_PKEY_CTX_set_rsa_pss_saltlen(ctx
, saltlen
);
595 if (strcmp(type
, "rsa_keygen_bits") == 0) {
598 return EVP_PKEY_CTX_set_rsa_keygen_bits(ctx
, nbits
);
601 if (strcmp(type
, "rsa_keygen_pubexp") == 0) {
603 BIGNUM
*pubexp
= NULL
;
604 if (!BN_asc2bn(&pubexp
, value
))
606 ret
= EVP_PKEY_CTX_set_rsa_keygen_pubexp(ctx
, pubexp
);
612 if (strcmp(type
, "rsa_mgf1_md") == 0)
613 return EVP_PKEY_CTX_md(ctx
,
614 EVP_PKEY_OP_TYPE_SIG
| EVP_PKEY_OP_TYPE_CRYPT
,
615 EVP_PKEY_CTRL_RSA_MGF1_MD
, value
);
617 if (pkey_ctx_is_pss(ctx
)) {
619 if (strcmp(type
, "rsa_pss_keygen_mgf1_md") == 0)
620 return EVP_PKEY_CTX_md(ctx
, EVP_PKEY_OP_KEYGEN
,
621 EVP_PKEY_CTRL_RSA_MGF1_MD
, value
);
623 if (strcmp(type
, "rsa_pss_keygen_md") == 0)
624 return EVP_PKEY_CTX_md(ctx
, EVP_PKEY_OP_KEYGEN
,
625 EVP_PKEY_CTRL_MD
, value
);
627 if (strcmp(type
, "rsa_pss_keygen_saltlen") == 0) {
629 saltlen
= atoi(value
);
630 return EVP_PKEY_CTX_set_rsa_pss_keygen_saltlen(ctx
, saltlen
);
634 if (strcmp(type
, "rsa_oaep_md") == 0)
635 return EVP_PKEY_CTX_md(ctx
, EVP_PKEY_OP_TYPE_CRYPT
,
636 EVP_PKEY_CTRL_RSA_OAEP_MD
, value
);
638 if (strcmp(type
, "rsa_oaep_label") == 0) {
642 lab
= OPENSSL_hexstr2buf(value
, &lablen
);
645 ret
= EVP_PKEY_CTX_set0_rsa_oaep_label(ctx
, lab
, lablen
);
654 /* Set PSS parameters when generating a key, if necessary */
655 static int rsa_set_pss_param(RSA
*rsa
, EVP_PKEY_CTX
*ctx
)
657 RSA_PKEY_CTX
*rctx
= ctx
->data
;
659 if (!pkey_ctx_is_pss(ctx
))
661 /* If all parameters are default values don't set pss */
662 if (rctx
->md
== NULL
&& rctx
->mgf1md
== NULL
&& rctx
->saltlen
== -2)
664 rsa
->pss
= rsa_pss_params_create(rctx
->md
, rctx
->mgf1md
,
665 rctx
->saltlen
== -2 ? 0 : rctx
->saltlen
);
666 if (rsa
->pss
== NULL
)
671 static int pkey_rsa_keygen(EVP_PKEY_CTX
*ctx
, EVP_PKEY
*pkey
)
674 RSA_PKEY_CTX
*rctx
= ctx
->data
;
678 if (rctx
->pub_exp
== NULL
) {
679 rctx
->pub_exp
= BN_new();
680 if (rctx
->pub_exp
== NULL
|| !BN_set_word(rctx
->pub_exp
, RSA_F4
))
686 if (ctx
->pkey_gencb
) {
687 pcb
= BN_GENCB_new();
692 evp_pkey_set_cb_translate(pcb
, ctx
);
695 ret
= RSA_generate_key_ex(rsa
, rctx
->nbits
, rctx
->pub_exp
, pcb
);
697 if (ret
> 0 && !rsa_set_pss_param(rsa
, ctx
)) {
702 EVP_PKEY_assign(pkey
, ctx
->pmeth
->pkey_id
, rsa
);
708 const EVP_PKEY_METHOD rsa_pkey_meth
= {
710 EVP_PKEY_FLAG_AUTOARGLEN
,
727 pkey_rsa_verifyrecover
,
744 * Called for PSS sign or verify initialisation: checks PSS parameter
745 * sanity and sets any restrictions on key usage.
748 static int pkey_pss_init(EVP_PKEY_CTX
*ctx
)
751 RSA_PKEY_CTX
*rctx
= ctx
->data
;
753 const EVP_MD
*mgf1md
;
756 /* Should never happen */
757 if (!pkey_ctx_is_pss(ctx
))
759 rsa
= ctx
->pkey
->pkey
.rsa
;
760 /* If no restrictions just return */
761 if (rsa
->pss
== NULL
)
763 /* Get and check parameters */
764 if (!rsa_pss_get_param(rsa
->pss
, &md
, &mgf1md
, &min_saltlen
))
767 rctx
->min_saltlen
= min_saltlen
;
770 * Set PSS restrictions as defaults: we can then block any attempt to
771 * use invalid values in pkey_rsa_ctrl
775 rctx
->mgf1md
= mgf1md
;
776 rctx
->saltlen
= min_saltlen
;
781 const EVP_PKEY_METHOD rsa_pss_pkey_meth
= {
783 EVP_PKEY_FLAG_AUTOARGLEN
,
799 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,