2 * RSA implementation for PuTTY.
13 int makekey(unsigned char *data
, int len
, struct RSAKey
*result
,
14 unsigned char **keystr
, int order
)
16 unsigned char *p
= data
;
24 for (i
= 0; i
< 4; i
++)
25 result
->bits
= (result
->bits
<< 8) + *p
++;
32 * order=0 means exponent then modulus (the keys sent by the
33 * server). order=1 means modulus then exponent (the keys
34 * stored in a keyfile).
38 n
= ssh1_read_bignum(p
, len
, result ?
&result
->exponent
: NULL
);
44 n
= ssh1_read_bignum(p
, len
, result ?
&result
->modulus
: NULL
);
45 if (n
< 0 || (result
&& bignum_bitcount(result
->modulus
) == 0)) return -1;
47 result
->bytes
= n
- 2;
54 n
= ssh1_read_bignum(p
, len
, result ?
&result
->exponent
: NULL
);
62 int makeprivate(unsigned char *data
, int len
, struct RSAKey
*result
)
64 return ssh1_read_bignum(data
, len
, &result
->private_exponent
);
67 int rsaencrypt(unsigned char *data
, int length
, struct RSAKey
*key
)
73 if (key
->bytes
< length
+ 4)
74 return 0; /* RSA key too short! */
76 memmove(data
+ key
->bytes
- length
, data
, length
);
80 for (i
= 2; i
< key
->bytes
- length
- 1; i
++) {
82 data
[i
] = random_byte();
83 } while (data
[i
] == 0);
85 data
[key
->bytes
- length
- 1] = 0;
87 b1
= bignum_from_bytes(data
, key
->bytes
);
89 b2
= modpow(b1
, key
->exponent
, key
->modulus
);
92 for (i
= key
->bytes
; i
--;) {
93 *p
++ = bignum_byte(b2
, i
);
102 static void sha512_mpint(SHA512_State
* s
, Bignum b
)
104 unsigned char lenbuf
[4];
106 len
= (bignum_bitcount(b
) + 8) / 8;
107 PUT_32BIT(lenbuf
, len
);
108 SHA512_Bytes(s
, lenbuf
, 4);
110 lenbuf
[0] = bignum_byte(b
, len
);
111 SHA512_Bytes(s
, lenbuf
, 1);
113 memset(lenbuf
, 0, sizeof(lenbuf
));
117 * This function is a wrapper on modpow(). It has the same effect
118 * as modpow(), but employs RSA blinding to protect against timing
121 static Bignum
rsa_privkey_op(Bignum input
, struct RSAKey
*key
)
123 Bignum random
, random_encrypted
, random_inverse
;
124 Bignum input_blinded
, ret_blinded
;
128 unsigned char digest512
[64];
129 int digestused
= lenof(digest512
);
133 * Start by inventing a random number chosen uniformly from the
134 * range 2..modulus-1. (We do this by preparing a random number
135 * of the right length and retrying if it's greater than the
136 * modulus, to prevent any potential Bleichenbacher-like
137 * attacks making use of the uneven distribution within the
138 * range that would arise from just reducing our number mod n.
139 * There are timing implications to the potential retries, of
140 * course, but all they tell you is the modulus, which you
143 * To preserve determinism and avoid Pageant needing to share
144 * the random number pool, we actually generate this `random'
145 * number by hashing stuff with the private key.
148 int bits
, byte
, bitsleft
, v
;
149 random
= copybn(key
->modulus
);
151 * Find the topmost set bit. (This function will return its
152 * index plus one.) Then we'll set all bits from that one
153 * downwards randomly.
155 bits
= bignum_bitcount(random
);
162 * Conceptually the following few lines are equivalent to
163 * byte = random_byte();
165 if (digestused
>= lenof(digest512
)) {
166 unsigned char seqbuf
[4];
167 PUT_32BIT(seqbuf
, hashseq
);
169 SHA512_Bytes(&ss
, "RSA deterministic blinding", 26);
170 SHA512_Bytes(&ss
, seqbuf
, sizeof(seqbuf
));
171 sha512_mpint(&ss
, key
->private_exponent
);
172 SHA512_Final(&ss
, digest512
);
176 * Now hash that digest plus the signature
180 SHA512_Bytes(&ss
, digest512
, sizeof(digest512
));
181 sha512_mpint(&ss
, input
);
182 SHA512_Final(&ss
, digest512
);
186 byte
= digest512
[digestused
++];
191 bignum_set_bit(random
, bits
, v
);
195 * Now check that this number is strictly greater than
196 * zero, and strictly less than modulus.
198 if (bignum_cmp(random
, Zero
) <= 0 ||
199 bignum_cmp(random
, key
->modulus
) >= 0) {
208 * RSA blinding relies on the fact that (xy)^d mod n is equal
209 * to (x^d mod n) * (y^d mod n) mod n. We invent a random pair
210 * y and y^d; then we multiply x by y, raise to the power d mod
211 * n as usual, and divide by y^d to recover x^d. Thus an
212 * attacker can't correlate the timing of the modpow with the
213 * input, because they don't know anything about the number
214 * that was input to the actual modpow.
216 * The clever bit is that we don't have to do a huge modpow to
217 * get y and y^d; we will use the number we just invented as
218 * _y^d_, and use the _public_ exponent to compute (y^d)^e = y
219 * from it, which is much faster to do.
221 random_encrypted
= modpow(random
, key
->exponent
, key
->modulus
);
222 random_inverse
= modinv(random
, key
->modulus
);
223 input_blinded
= modmul(input
, random_encrypted
, key
->modulus
);
224 ret_blinded
= modpow(input_blinded
, key
->private_exponent
, key
->modulus
);
225 ret
= modmul(ret_blinded
, random_inverse
, key
->modulus
);
228 freebn(input_blinded
);
229 freebn(random_inverse
);
230 freebn(random_encrypted
);
236 Bignum
rsadecrypt(Bignum input
, struct RSAKey
*key
)
238 return rsa_privkey_op(input
, key
);
241 int rsastr_len(struct RSAKey
*key
)
248 mdlen
= (bignum_bitcount(md
) + 15) / 16;
249 exlen
= (bignum_bitcount(ex
) + 15) / 16;
250 return 4 * (mdlen
+ exlen
) + 20;
253 void rsastr_fmt(char *str
, struct RSAKey
*key
)
256 int len
= 0, i
, nibbles
;
257 static const char hex
[] = "0123456789abcdef";
262 len
+= sprintf(str
+ len
, "0x");
264 nibbles
= (3 + bignum_bitcount(ex
)) / 4;
267 for (i
= nibbles
; i
--;)
268 str
[len
++] = hex
[(bignum_byte(ex
, i
/ 2) >> (4 * (i
% 2))) & 0xF];
270 len
+= sprintf(str
+ len
, ",0x");
272 nibbles
= (3 + bignum_bitcount(md
)) / 4;
275 for (i
= nibbles
; i
--;)
276 str
[len
++] = hex
[(bignum_byte(md
, i
/ 2) >> (4 * (i
% 2))) & 0xF];
282 * Generate a fingerprint string for the key. Compatible with the
283 * OpenSSH fingerprint code.
285 void rsa_fingerprint(char *str
, int len
, struct RSAKey
*key
)
287 struct MD5Context md5c
;
288 unsigned char digest
[16];
289 char buffer
[16 * 3 + 40];
293 numlen
= ssh1_bignum_length(key
->modulus
) - 2;
294 for (i
= numlen
; i
--;) {
295 unsigned char c
= bignum_byte(key
->modulus
, i
);
296 MD5Update(&md5c
, &c
, 1);
298 numlen
= ssh1_bignum_length(key
->exponent
) - 2;
299 for (i
= numlen
; i
--;) {
300 unsigned char c
= bignum_byte(key
->exponent
, i
);
301 MD5Update(&md5c
, &c
, 1);
303 MD5Final(digest
, &md5c
);
305 sprintf(buffer
, "%d ", bignum_bitcount(key
->modulus
));
306 for (i
= 0; i
< 16; i
++)
307 sprintf(buffer
+ strlen(buffer
), "%s%02x", i ?
":" : "",
309 strncpy(str
, buffer
, len
);
312 if (key
->comment
&& slen
< len
- 1) {
314 strncpy(str
+ slen
+ 1, key
->comment
, len
- slen
- 1);
320 * Verify that the public data in an RSA key matches the private
321 * data. We also check the private data itself: we ensure that p >
322 * q and that iqmp really is the inverse of q mod p.
324 int rsa_verify(struct RSAKey
*key
)
326 Bignum n
, ed
, pm1
, qm1
;
329 /* n must equal pq. */
330 n
= bigmul(key
->p
, key
->q
);
331 cmp
= bignum_cmp(n
, key
->modulus
);
336 /* e * d must be congruent to 1, modulo (p-1) and modulo (q-1). */
337 pm1
= copybn(key
->p
);
339 ed
= modmul(key
->exponent
, key
->private_exponent
, pm1
);
340 cmp
= bignum_cmp(ed
, One
);
345 qm1
= copybn(key
->q
);
347 ed
= modmul(key
->exponent
, key
->private_exponent
, qm1
);
348 cmp
= bignum_cmp(ed
, One
);
356 if (bignum_cmp(key
->p
, key
->q
) <= 0)
360 * Ensure iqmp * q is congruent to 1, modulo p.
362 n
= modmul(key
->iqmp
, key
->q
, key
->p
);
363 cmp
= bignum_cmp(n
, One
);
371 /* Public key blob as used by Pageant: exponent before modulus. */
372 unsigned char *rsa_public_blob(struct RSAKey
*key
, int *len
)
377 length
= (ssh1_bignum_length(key
->modulus
) +
378 ssh1_bignum_length(key
->exponent
) + 4);
379 ret
= snewn(length
, unsigned char);
381 PUT_32BIT(ret
, bignum_bitcount(key
->modulus
));
383 pos
+= ssh1_write_bignum(ret
+ pos
, key
->exponent
);
384 pos
+= ssh1_write_bignum(ret
+ pos
, key
->modulus
);
390 /* Given a public blob, determine its length. */
391 int rsa_public_blob_len(void *data
, int maxlen
)
393 unsigned char *p
= (unsigned char *)data
;
398 p
+= 4; /* length word */
401 n
= ssh1_read_bignum(p
, maxlen
, NULL
); /* exponent */
406 n
= ssh1_read_bignum(p
, maxlen
, NULL
); /* modulus */
411 return p
- (unsigned char *)data
;
414 void freersakey(struct RSAKey
*key
)
417 freebn(key
->modulus
);
419 freebn(key
->exponent
);
420 if (key
->private_exponent
)
421 freebn(key
->private_exponent
);
426 /* ----------------------------------------------------------------------
427 * Implementation of the ssh-rsa signing key type.
430 static void getstring(char **data
, int *datalen
, char **p
, int *length
)
435 *length
= GET_32BIT(*data
);
438 if (*datalen
< *length
)
444 static Bignum
getmp(char **data
, int *datalen
)
450 getstring(data
, datalen
, &p
, &length
);
453 b
= bignum_from_bytes((unsigned char *)p
, length
);
457 static void *rsa2_newkey(char *data
, int len
)
463 rsa
= snew(struct RSAKey
);
466 getstring(&data
, &len
, &p
, &slen
);
468 if (!p
|| slen
!= 7 || memcmp(p
, "ssh-rsa", 7)) {
472 rsa
->exponent
= getmp(&data
, &len
);
473 rsa
->modulus
= getmp(&data
, &len
);
474 rsa
->private_exponent
= NULL
;
480 static void rsa2_freekey(void *key
)
482 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
487 static char *rsa2_fmtkey(void *key
)
489 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
493 len
= rsastr_len(rsa
);
494 p
= snewn(len
, char);
499 static unsigned char *rsa2_public_blob(void *key
, int *len
)
501 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
502 int elen
, mlen
, bloblen
;
504 unsigned char *blob
, *p
;
506 elen
= (bignum_bitcount(rsa
->exponent
) + 8) / 8;
507 mlen
= (bignum_bitcount(rsa
->modulus
) + 8) / 8;
510 * string "ssh-rsa", mpint exp, mpint mod. Total 19+elen+mlen.
511 * (three length fields, 12+7=19).
513 bloblen
= 19 + elen
+ mlen
;
514 blob
= snewn(bloblen
, unsigned char);
518 memcpy(p
, "ssh-rsa", 7);
523 *p
++ = bignum_byte(rsa
->exponent
, i
);
527 *p
++ = bignum_byte(rsa
->modulus
, i
);
528 assert(p
== blob
+ bloblen
);
533 static unsigned char *rsa2_private_blob(void *key
, int *len
)
535 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
536 int dlen
, plen
, qlen
, ulen
, bloblen
;
538 unsigned char *blob
, *p
;
540 dlen
= (bignum_bitcount(rsa
->private_exponent
) + 8) / 8;
541 plen
= (bignum_bitcount(rsa
->p
) + 8) / 8;
542 qlen
= (bignum_bitcount(rsa
->q
) + 8) / 8;
543 ulen
= (bignum_bitcount(rsa
->iqmp
) + 8) / 8;
546 * mpint private_exp, mpint p, mpint q, mpint iqmp. Total 16 +
549 bloblen
= 16 + dlen
+ plen
+ qlen
+ ulen
;
550 blob
= snewn(bloblen
, unsigned char);
555 *p
++ = bignum_byte(rsa
->private_exponent
, i
);
559 *p
++ = bignum_byte(rsa
->p
, i
);
563 *p
++ = bignum_byte(rsa
->q
, i
);
567 *p
++ = bignum_byte(rsa
->iqmp
, i
);
568 assert(p
== blob
+ bloblen
);
573 static void *rsa2_createkey(unsigned char *pub_blob
, int pub_len
,
574 unsigned char *priv_blob
, int priv_len
)
577 char *pb
= (char *) priv_blob
;
579 rsa
= rsa2_newkey((char *) pub_blob
, pub_len
);
580 rsa
->private_exponent
= getmp(&pb
, &priv_len
);
581 rsa
->p
= getmp(&pb
, &priv_len
);
582 rsa
->q
= getmp(&pb
, &priv_len
);
583 rsa
->iqmp
= getmp(&pb
, &priv_len
);
585 if (!rsa_verify(rsa
)) {
593 static void *rsa2_openssh_createkey(unsigned char **blob
, int *len
)
595 char **b
= (char **) blob
;
598 rsa
= snew(struct RSAKey
);
603 rsa
->modulus
= getmp(b
, len
);
604 rsa
->exponent
= getmp(b
, len
);
605 rsa
->private_exponent
= getmp(b
, len
);
606 rsa
->iqmp
= getmp(b
, len
);
607 rsa
->p
= getmp(b
, len
);
608 rsa
->q
= getmp(b
, len
);
610 if (!rsa
->modulus
|| !rsa
->exponent
|| !rsa
->private_exponent
||
611 !rsa
->iqmp
|| !rsa
->p
|| !rsa
->q
) {
613 sfree(rsa
->exponent
);
614 sfree(rsa
->private_exponent
);
625 static int rsa2_openssh_fmtkey(void *key
, unsigned char *blob
, int len
)
627 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
631 ssh2_bignum_length(rsa
->modulus
) +
632 ssh2_bignum_length(rsa
->exponent
) +
633 ssh2_bignum_length(rsa
->private_exponent
) +
634 ssh2_bignum_length(rsa
->iqmp
) +
635 ssh2_bignum_length(rsa
->p
) + ssh2_bignum_length(rsa
->q
);
642 PUT_32BIT(blob+bloblen, ssh2_bignum_length((x))-4); bloblen += 4; \
643 for (i = ssh2_bignum_length((x))-4; i-- ;) blob[bloblen++]=bignum_byte((x),i);
646 ENC(rsa
->private_exponent
);
654 static int rsa2_pubkey_bits(void *blob
, int len
)
659 rsa
= rsa2_newkey((char *) blob
, len
);
660 ret
= bignum_bitcount(rsa
->modulus
);
666 static char *rsa2_fingerprint(void *key
)
668 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
669 struct MD5Context md5c
;
670 unsigned char digest
[16], lenbuf
[4];
671 char buffer
[16 * 3 + 40];
676 MD5Update(&md5c
, (unsigned char *)"\0\0\0\7ssh-rsa", 11);
678 #define ADD_BIGNUM(bignum) \
679 numlen = (bignum_bitcount(bignum)+8)/8; \
680 PUT_32BIT(lenbuf, numlen); MD5Update(&md5c, lenbuf, 4); \
681 for (i = numlen; i-- ;) { \
682 unsigned char c = bignum_byte(bignum, i); \
683 MD5Update(&md5c, &c, 1); \
685 ADD_BIGNUM(rsa
->exponent
);
686 ADD_BIGNUM(rsa
->modulus
);
689 MD5Final(digest
, &md5c
);
691 sprintf(buffer
, "ssh-rsa %d ", bignum_bitcount(rsa
->modulus
));
692 for (i
= 0; i
< 16; i
++)
693 sprintf(buffer
+ strlen(buffer
), "%s%02x", i ?
":" : "",
695 ret
= snewn(strlen(buffer
) + 1, char);
702 * This is the magic ASN.1/DER prefix that goes in the decoded
703 * signature, between the string of FFs and the actual SHA hash
704 * value. The meaning of it is:
706 * 00 -- this marks the end of the FFs; not part of the ASN.1 bit itself
708 * 30 21 -- a constructed SEQUENCE of length 0x21
709 * 30 09 -- a constructed sub-SEQUENCE of length 9
710 * 06 05 -- an object identifier, length 5
711 * 2B 0E 03 02 1A -- object id { 1 3 14 3 2 26 }
712 * (the 1,3 comes from 0x2B = 43 = 40*1+3)
714 * 04 14 -- a primitive OCTET STRING of length 0x14
715 * [0x14 bytes of hash data follows]
717 * The object id in the middle there is listed as `id-sha1' in
718 * ftp://ftp.rsasecurity.com/pub/pkcs/pkcs-1/pkcs-1v2-1d2.asn (the
719 * ASN module for PKCS #1) and its expanded form is as follows:
721 * id-sha1 OBJECT IDENTIFIER ::= {
722 * iso(1) identified-organization(3) oiw(14) secsig(3)
725 static const unsigned char asn1_weird_stuff
[] = {
726 0x00, 0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2B,
727 0x0E, 0x03, 0x02, 0x1A, 0x05, 0x00, 0x04, 0x14,
730 #define ASN1_LEN ( (int) sizeof(asn1_weird_stuff) )
732 static int rsa2_verifysig(void *key
, char *sig
, int siglen
,
733 char *data
, int datalen
)
735 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
739 int bytes
, i
, j
, ret
;
740 unsigned char hash
[20];
742 getstring(&sig
, &siglen
, &p
, &slen
);
743 if (!p
|| slen
!= 7 || memcmp(p
, "ssh-rsa", 7)) {
746 in
= getmp(&sig
, &siglen
);
747 out
= modpow(in
, rsa
->exponent
, rsa
->modulus
);
752 bytes
= (bignum_bitcount(rsa
->modulus
)+7) / 8;
753 /* Top (partial) byte should be zero. */
754 if (bignum_byte(out
, bytes
- 1) != 0)
756 /* First whole byte should be 1. */
757 if (bignum_byte(out
, bytes
- 2) != 1)
759 /* Most of the rest should be FF. */
760 for (i
= bytes
- 3; i
>= 20 + ASN1_LEN
; i
--) {
761 if (bignum_byte(out
, i
) != 0xFF)
764 /* Then we expect to see the asn1_weird_stuff. */
765 for (i
= 20 + ASN1_LEN
- 1, j
= 0; i
>= 20; i
--, j
++) {
766 if (bignum_byte(out
, i
) != asn1_weird_stuff
[j
])
769 /* Finally, we expect to see the SHA-1 hash of the signed data. */
770 SHA_Simple(data
, datalen
, hash
);
771 for (i
= 19, j
= 0; i
>= 0; i
--, j
++) {
772 if (bignum_byte(out
, i
) != hash
[j
])
780 static unsigned char *rsa2_sign(void *key
, char *data
, int datalen
,
783 struct RSAKey
*rsa
= (struct RSAKey
*) key
;
784 unsigned char *bytes
;
786 unsigned char hash
[20];
790 SHA_Simple(data
, datalen
, hash
);
792 nbytes
= (bignum_bitcount(rsa
->modulus
) - 1) / 8;
793 assert(1 <= nbytes
- 20 - ASN1_LEN
);
794 bytes
= snewn(nbytes
, unsigned char);
797 for (i
= 1; i
< nbytes
- 20 - ASN1_LEN
; i
++)
799 for (i
= nbytes
- 20 - ASN1_LEN
, j
= 0; i
< nbytes
- 20; i
++, j
++)
800 bytes
[i
] = asn1_weird_stuff
[j
];
801 for (i
= nbytes
- 20, j
= 0; i
< nbytes
; i
++, j
++)
804 in
= bignum_from_bytes(bytes
, nbytes
);
807 out
= rsa_privkey_op(in
, rsa
);
810 nbytes
= (bignum_bitcount(out
) + 7) / 8;
811 bytes
= snewn(4 + 7 + 4 + nbytes
, unsigned char);
813 memcpy(bytes
+ 4, "ssh-rsa", 7);
814 PUT_32BIT(bytes
+ 4 + 7, nbytes
);
815 for (i
= 0; i
< nbytes
; i
++)
816 bytes
[4 + 7 + 4 + i
] = bignum_byte(out
, nbytes
- 1 - i
);
819 *siglen
= 4 + 7 + 4 + nbytes
;
823 const struct ssh_signkey ssh_rsa
= {
830 rsa2_openssh_createkey
,