2 * The RSA public-key cryptosystem
4 * Based on XySSL: Copyright (C) 2006-2008 Christophe Devine
6 * Copyright (C) 2009 Paul Bakker <polarssl_maintainer at polarssl dot org>
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License along
19 * with this program; if not, write to the Free Software Foundation, Inc.,
20 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
23 * RSA was designed by Ron Rivest, Adi Shamir and Len Adleman.
25 * http://theory.lcs.mit.edu/~rivest/rsapaper.pdf
26 * http://www.cacr.math.uwaterloo.ca/hac/about/chap8.pdf
29 /* $Cambridge: exim/src/src/pdkim/rsa.c,v 1.2 2009/06/10 07:34:05 tom Exp $ */
40 * ASN.1 DER decoding routines
42 static int asn1_get_len( unsigned char **p,
46 if( ( end - *p ) < 1 )
47 return( POLARSSL_ERR_ASN1_OUT_OF_DATA );
49 if( ( **p & 0x80 ) == 0 )
56 if( ( end - *p ) < 2 )
57 return( POLARSSL_ERR_ASN1_OUT_OF_DATA );
64 if( ( end - *p ) < 3 )
65 return( POLARSSL_ERR_ASN1_OUT_OF_DATA );
67 *len = ( (*p)[1] << 8 ) | (*p)[2];
72 return( POLARSSL_ERR_ASN1_INVALID_LENGTH );
77 if( *len > (int) ( end - *p ) )
78 return( POLARSSL_ERR_ASN1_OUT_OF_DATA );
83 static int asn1_get_tag( unsigned char **p,
87 if( ( end - *p ) < 1 )
88 return( POLARSSL_ERR_ASN1_OUT_OF_DATA );
91 return( POLARSSL_ERR_ASN1_UNEXPECTED_TAG );
95 return( asn1_get_len( p, end, len ) );
98 static int asn1_get_int( unsigned char **p,
104 if( ( ret = asn1_get_tag( p, end, &len, ASN1_INTEGER ) ) != 0 )
107 if( len > (int) sizeof( int ) || ( **p & 0x80 ) != 0 )
108 return( POLARSSL_ERR_ASN1_INVALID_LENGTH );
114 *val = ( *val << 8 ) | **p;
121 static int asn1_get_mpi( unsigned char **p,
127 if( ( ret = asn1_get_tag( p, end, &len, ASN1_INTEGER ) ) != 0 )
130 ret = mpi_read_binary( X, *p, len );
139 * Initialize an RSA context
141 void rsa_init( rsa_context *ctx,
144 int (*f_rng)(void *),
147 memset( ctx, 0, sizeof( rsa_context ) );
149 ctx->padding = padding;
150 ctx->hash_id = hash_id;
158 * Check a public RSA key
160 int rsa_check_pubkey( rsa_context *ctx )
162 if( ( ctx->N.p[0] & 1 ) == 0 ||
163 ( ctx->E.p[0] & 1 ) == 0 )
164 return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED );
166 if( mpi_msb( &ctx->N ) < 128 ||
167 mpi_msb( &ctx->N ) > 4096 )
168 return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED );
170 if( mpi_msb( &ctx->E ) < 2 ||
171 mpi_msb( &ctx->E ) > 64 )
172 return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED );
178 * Check a private RSA key
180 int rsa_check_privkey( rsa_context *ctx )
183 mpi PQ, DE, P1, Q1, H, I, G;
185 if( ( ret = rsa_check_pubkey( ctx ) ) != 0 )
188 mpi_init( &PQ, &DE, &P1, &Q1, &H, &I, &G, NULL );
190 MPI_CHK( mpi_mul_mpi( &PQ, &ctx->P, &ctx->Q ) );
191 MPI_CHK( mpi_mul_mpi( &DE, &ctx->D, &ctx->E ) );
192 MPI_CHK( mpi_sub_int( &P1, &ctx->P, 1 ) );
193 MPI_CHK( mpi_sub_int( &Q1, &ctx->Q, 1 ) );
194 MPI_CHK( mpi_mul_mpi( &H, &P1, &Q1 ) );
195 MPI_CHK( mpi_mod_mpi( &I, &DE, &H ) );
196 MPI_CHK( mpi_gcd( &G, &ctx->E, &H ) );
198 if( mpi_cmp_mpi( &PQ, &ctx->N ) == 0 &&
199 mpi_cmp_int( &I, 1 ) == 0 &&
200 mpi_cmp_int( &G, 1 ) == 0 )
202 mpi_free( &G, &I, &H, &Q1, &P1, &DE, &PQ, NULL );
208 mpi_free( &G, &I, &H, &Q1, &P1, &DE, &PQ, NULL );
209 return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED | ret );
213 * Do an RSA public key operation
215 int rsa_public( rsa_context *ctx,
216 unsigned char *input,
217 unsigned char *output )
222 mpi_init( &T, NULL );
224 MPI_CHK( mpi_read_binary( &T, input, ctx->len ) );
226 if( mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
228 mpi_free( &T, NULL );
229 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
233 MPI_CHK( mpi_exp_mod( &T, &T, &ctx->E, &ctx->N, &ctx->RN ) );
234 MPI_CHK( mpi_write_binary( &T, output, olen ) );
238 mpi_free( &T, NULL );
241 return( POLARSSL_ERR_RSA_PUBLIC_FAILED | ret );
247 * Do an RSA private key operation
249 int rsa_private( rsa_context *ctx,
250 unsigned char *input,
251 unsigned char *output )
256 mpi_init( &T, &T1, &T2, NULL );
258 MPI_CHK( mpi_read_binary( &T, input, ctx->len ) );
260 if( mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
262 mpi_free( &T, NULL );
263 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
267 MPI_CHK( mpi_exp_mod( &T, &T, &ctx->D, &ctx->N, &ctx->RN ) );
270 * faster decryption using the CRT
272 * T1 = input ^ dP mod P
273 * T2 = input ^ dQ mod Q
275 MPI_CHK( mpi_exp_mod( &T1, &T, &ctx->DP, &ctx->P, &ctx->RP ) );
276 MPI_CHK( mpi_exp_mod( &T2, &T, &ctx->DQ, &ctx->Q, &ctx->RQ ) );
279 * T = (T1 - T2) * (Q^-1 mod P) mod P
281 MPI_CHK( mpi_sub_mpi( &T, &T1, &T2 ) );
282 MPI_CHK( mpi_mul_mpi( &T1, &T, &ctx->QP ) );
283 MPI_CHK( mpi_mod_mpi( &T, &T1, &ctx->P ) );
286 * output = T2 + T * Q
288 MPI_CHK( mpi_mul_mpi( &T1, &T, &ctx->Q ) );
289 MPI_CHK( mpi_add_mpi( &T, &T2, &T1 ) );
293 MPI_CHK( mpi_write_binary( &T, output, olen ) );
297 mpi_free( &T, &T1, &T2, NULL );
300 return( POLARSSL_ERR_RSA_PRIVATE_FAILED | ret );
306 * Add the message padding, then do an RSA operation
308 int rsa_pkcs1_encrypt( rsa_context *ctx,
310 unsigned char *input,
311 unsigned char *output )
314 unsigned char *p = output;
318 switch( ctx->padding )
322 if( ilen < 0 || olen < ilen + 11 )
323 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
325 nb_pad = olen - 3 - ilen;
330 while( nb_pad-- > 0 )
333 *p = (unsigned char) rand();
338 memcpy( p, input, ilen );
343 return( POLARSSL_ERR_RSA_INVALID_PADDING );
346 return( ( mode == RSA_PUBLIC )
347 ? rsa_public( ctx, output, output )
348 : rsa_private( ctx, output, output ) );
352 * Do an RSA operation, then remove the message padding
354 int rsa_pkcs1_decrypt( rsa_context *ctx,
356 unsigned char *input,
357 unsigned char *output,
362 unsigned char buf[512];
366 if( ilen < 16 || ilen > (int) sizeof( buf ) )
367 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
369 ret = ( mode == RSA_PUBLIC )
370 ? rsa_public( ctx, input, buf )
371 : rsa_private( ctx, input, buf );
378 switch( ctx->padding )
382 if( *p++ != 0 || *p++ != RSA_CRYPT )
383 return( POLARSSL_ERR_RSA_INVALID_PADDING );
387 if( p >= buf + ilen - 1 )
388 return( POLARSSL_ERR_RSA_INVALID_PADDING );
396 return( POLARSSL_ERR_RSA_INVALID_PADDING );
399 if (ilen - (int)(p - buf) > output_max_len)
400 return( POLARSSL_ERR_RSA_OUTPUT_TO_LARGE );
402 *olen = ilen - (int)(p - buf);
403 memcpy( output, p, *olen );
409 * Do an RSA operation to sign the message digest
411 int rsa_pkcs1_sign( rsa_context *ctx,
419 unsigned char *p = sig;
423 switch( ctx->padding )
430 nb_pad = olen - 3 - hashlen;
436 nb_pad = olen - 3 - 16 - 18;
440 nb_pad = olen - 3 - 20 - 15;
444 nb_pad = olen - 3 - 32 - 19;
448 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
452 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
456 memset( p, 0xFF, nb_pad );
463 return( POLARSSL_ERR_RSA_INVALID_PADDING );
469 memcpy( p, hash, hashlen );
473 memcpy( p, ASN1_HASH_MDX, 18 );
474 memcpy( p + 18, hash, 16 );
478 memcpy( p, ASN1_HASH_MDX, 18 );
479 memcpy( p + 18, hash, 16 );
483 memcpy( p, ASN1_HASH_MDX, 18 );
484 memcpy( p + 18, hash, 16 );
488 memcpy( p, ASN1_HASH_SHA1, 15 );
489 memcpy( p + 15, hash, 20 );
493 memcpy( p, ASN1_HASH_SHA256, 19 );
494 memcpy( p + 19, hash, 32 );
498 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
501 return( ( mode == RSA_PUBLIC )
502 ? rsa_public( ctx, sig, sig )
503 : rsa_private( ctx, sig, sig ) );
507 * Do an RSA operation and check the message digest
509 int rsa_pkcs1_verify( rsa_context *ctx,
516 int ret, len, siglen;
518 unsigned char buf[512];
522 if( siglen < 16 || siglen > (int) sizeof( buf ) )
523 return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
525 ret = ( mode == RSA_PUBLIC )
526 ? rsa_public( ctx, sig, buf )
527 : rsa_private( ctx, sig, buf );
534 switch( ctx->padding )
538 if( *p++ != 0 || *p++ != RSA_SIGN )
539 return( POLARSSL_ERR_RSA_INVALID_PADDING );
543 if( p >= buf + siglen - 1 || *p != 0xFF )
544 return( POLARSSL_ERR_RSA_INVALID_PADDING );
552 return( POLARSSL_ERR_RSA_INVALID_PADDING );
555 len = siglen - (int)( p - buf );
562 if( memcmp( p, ASN1_HASH_MDX, 18 ) != 0 )
563 return( POLARSSL_ERR_RSA_VERIFY_FAILED );
565 if( ( c == 2 && hash_id == RSA_MD2 ) ||
566 ( c == 4 && hash_id == RSA_MD4 ) ||
567 ( c == 5 && hash_id == RSA_MD5 ) )
569 if( memcmp( p + 18, hash, 16 ) == 0 )
572 return( POLARSSL_ERR_RSA_VERIFY_FAILED );
576 if( len == 35 && hash_id == RSA_SHA1 )
578 if( memcmp( p, ASN1_HASH_SHA1, 15 ) == 0 &&
579 memcmp( p + 15, hash, 20 ) == 0 )
582 return( POLARSSL_ERR_RSA_VERIFY_FAILED );
585 if( len == 51 && hash_id == RSA_SHA256 )
587 if( memcmp( p, ASN1_HASH_SHA256, 19 ) == 0 &&
588 memcmp( p + 19, hash, 32 ) == 0 )
591 return( POLARSSL_ERR_RSA_VERIFY_FAILED );
594 if( len == hashlen && hash_id == RSA_RAW )
596 if( memcmp( p, hash, hashlen ) == 0 )
599 return( POLARSSL_ERR_RSA_VERIFY_FAILED );
602 return( POLARSSL_ERR_RSA_INVALID_PADDING );
606 * Free the components of an RSA key
608 void rsa_free( rsa_context *ctx )
610 mpi_free( &ctx->RQ, &ctx->RP, &ctx->RN,
611 &ctx->QP, &ctx->DQ, &ctx->DP,
612 &ctx->Q, &ctx->P, &ctx->D,
613 &ctx->E, &ctx->N, NULL );
618 * Parse a public RSA key
620 OpenSSL RSA public key ASN1 container
621 0:d=0 hl=3 l= 159 cons: SEQUENCE
622 3:d=1 hl=2 l= 13 cons: SEQUENCE
623 5:d=2 hl=2 l= 9 prim: OBJECT:rsaEncryption
624 16:d=2 hl=2 l= 0 prim: NULL
625 18:d=1 hl=3 l= 141 prim: BIT STRING:RSAPublicKey (below)
627 RSAPublicKey ASN1 container
628 0:d=0 hl=3 l= 137 cons: SEQUENCE
629 3:d=1 hl=3 l= 129 prim: INTEGER:Public modulus
630 135:d=1 hl=2 l= 3 prim: INTEGER:Public exponent
633 int rsa_parse_public_key( rsa_context *rsa, unsigned char *buf, int buflen )
635 unsigned char *p, *end;
641 if( ( ret = asn1_get_tag( &p, end, &len,
642 ASN1_CONSTRUCTED | ASN1_SEQUENCE ) ) != 0 ) {
643 return( POLARSSL_ERR_X509_KEY_INVALID_FORMAT | ret );
646 if( ( ret = asn1_get_tag( &p, end, &len,
647 ASN1_CONSTRUCTED | ASN1_SEQUENCE ) ) == 0 ) {
648 /* Skip over embedded rsaEncryption Object */
651 /* The RSAPublicKey ASN1 container is wrapped in a BIT STRING */
652 if( ( ret = asn1_get_tag( &p, end, &len,
653 ASN1_BIT_STRING ) ) != 0 ) {
654 return( POLARSSL_ERR_X509_KEY_INVALID_FORMAT | ret );
657 /* Limit range to that BIT STRING */
661 if( ( ret = asn1_get_tag( &p, end, &len,
662 ASN1_CONSTRUCTED | ASN1_SEQUENCE ) ) != 0 ) {
663 return( POLARSSL_ERR_X509_KEY_INVALID_FORMAT | ret );
667 if ( ( ( ret = asn1_get_mpi( &p, end, &(rsa->N) ) ) == 0 ) &&
668 ( ( ret = asn1_get_mpi( &p, end, &(rsa->E) ) ) == 0 ) ) {
669 rsa->len = mpi_size( &rsa->N );
673 return( POLARSSL_ERR_X509_KEY_INVALID_FORMAT | ret );
677 * Parse a private RSA key
679 int rsa_parse_key( rsa_context *rsa, unsigned char *buf, int buflen,
680 unsigned char *pwd, int pwdlen )
683 unsigned char *s1, *s2;
684 unsigned char *p, *end;
686 s1 = (unsigned char *) strstr( (char *) buf,
687 "-----BEGIN RSA PRIVATE KEY-----" );
691 s2 = (unsigned char *) strstr( (char *) buf,
692 "-----END RSA PRIVATE KEY-----" );
694 if( s2 == NULL || s2 <= s1 )
695 return( POLARSSL_ERR_X509_KEY_INVALID_PEM );
698 if( *s1 == '\r' ) s1++;
699 if( *s1 == '\n' ) s1++;
700 else return( POLARSSL_ERR_X509_KEY_INVALID_PEM );
704 if( memcmp( s1, "Proc-Type: 4,ENCRYPTED", 22 ) == 0 )
706 return( POLARSSL_ERR_X509_FEATURE_UNAVAILABLE );
710 ret = base64_decode( NULL, &len, s1, s2 - s1 );
712 if( ret == POLARSSL_ERR_BASE64_INVALID_CHARACTER )
713 return( ret | POLARSSL_ERR_X509_KEY_INVALID_PEM );
715 if( ( buf = (unsigned char *) malloc( len ) ) == NULL )
718 if( ( ret = base64_decode( buf, &len, s1, s2 - s1 ) ) != 0 )
721 return( ret | POLARSSL_ERR_X509_KEY_INVALID_PEM );
728 return( POLARSSL_ERR_X509_FEATURE_UNAVAILABLE );
732 memset( rsa, 0, sizeof( rsa_context ) );
738 * RSAPrivateKey ::= SEQUENCE {
740 * modulus INTEGER, -- n
741 * publicExponent INTEGER, -- e
742 * privateExponent INTEGER, -- d
743 * prime1 INTEGER, -- p
744 * prime2 INTEGER, -- q
745 * exponent1 INTEGER, -- d mod (p-1)
746 * exponent2 INTEGER, -- d mod (q-1)
747 * coefficient INTEGER, -- (inverse of q) mod p
748 * otherPrimeInfos OtherPrimeInfos OPTIONAL
751 if( ( ret = asn1_get_tag( &p, end, &len,
752 ASN1_CONSTRUCTED | ASN1_SEQUENCE ) ) != 0 )
758 return( POLARSSL_ERR_X509_KEY_INVALID_FORMAT | ret );
763 if( ( ret = asn1_get_int( &p, end, &rsa->ver ) ) != 0 )
769 return( POLARSSL_ERR_X509_KEY_INVALID_FORMAT | ret );
778 return( ret | POLARSSL_ERR_X509_KEY_INVALID_VERSION );
781 if( ( ret = asn1_get_mpi( &p, end, &rsa->N ) ) != 0 ||
782 ( ret = asn1_get_mpi( &p, end, &rsa->E ) ) != 0 ||
783 ( ret = asn1_get_mpi( &p, end, &rsa->D ) ) != 0 ||
784 ( ret = asn1_get_mpi( &p, end, &rsa->P ) ) != 0 ||
785 ( ret = asn1_get_mpi( &p, end, &rsa->Q ) ) != 0 ||
786 ( ret = asn1_get_mpi( &p, end, &rsa->DP ) ) != 0 ||
787 ( ret = asn1_get_mpi( &p, end, &rsa->DQ ) ) != 0 ||
788 ( ret = asn1_get_mpi( &p, end, &rsa->QP ) ) != 0 )
794 return( ret | POLARSSL_ERR_X509_KEY_INVALID_FORMAT );
797 rsa->len = mpi_size( &rsa->N );
805 return( POLARSSL_ERR_X509_KEY_INVALID_FORMAT |
806 POLARSSL_ERR_ASN1_LENGTH_MISMATCH );
809 if( ( ret = rsa_check_privkey( rsa ) ) != 0 )