2 * RSA implementation for PuTTY.
13 #define GET_32BIT(cp) \
14 (((unsigned long)(unsigned char)(cp)[0] << 24) | \
15 ((unsigned long)(unsigned char)(cp)[1] << 16) | \
16 ((unsigned long)(unsigned char)(cp)[2] << 8) | \
17 ((unsigned long)(unsigned char)(cp)[3]))
19 #define PUT_32BIT(cp, value) { \
20 (cp)[0] = (unsigned char)((value) >> 24); \
21 (cp)[1] = (unsigned char)((value) >> 16); \
22 (cp)[2] = (unsigned char)((value) >> 8); \
23 (cp)[3] = (unsigned char)(value); }
25 int makekey(unsigned char *data, struct RSAKey *result,
26 unsigned char **keystr, int order)
28 unsigned char *p = data;
33 for (i = 0; i < 4; i++)
34 result->bits = (result->bits << 8) + *p++;
39 * order=0 means exponent then modulus (the keys sent by the
40 * server). order=1 means modulus then exponent (the keys
41 * stored in a keyfile).
45 p += ssh1_read_bignum(p, result ? &result->exponent : NULL);
47 result->bytes = (((p[0] << 8) + p[1]) + 7) / 8;
50 p += ssh1_read_bignum(p, result ? &result->modulus : NULL);
52 p += ssh1_read_bignum(p, result ? &result->exponent : NULL);
57 int makeprivate(unsigned char *data, struct RSAKey *result)
59 return ssh1_read_bignum(data, &result->private_exponent);
62 void rsaencrypt(unsigned char *data, int length, struct RSAKey *key)
68 memmove(data + key->bytes - length, data, length);
72 for (i = 2; i < key->bytes - length - 1; i++) {
74 data[i] = random_byte();
75 } while (data[i] == 0);
77 data[key->bytes - length - 1] = 0;
79 b1 = bignum_from_bytes(data, key->bytes);
81 b2 = modpow(b1, key->exponent, key->modulus);
84 for (i = key->bytes; i--;) {
85 *p++ = bignum_byte(b2, i);
93 * This function is a wrapper on modpow(). It has the same effect
94 * as modpow(), but employs RSA blinding to protect against timing
97 static Bignum rsa_privkey_op(Bignum input, struct RSAKey *key)
99 Bignum random, random_encrypted, random_inverse;
100 Bignum input_blinded, ret_blinded;
104 * Start by inventing a random number chosen uniformly from the
105 * range 2..modulus-1. (We do this by preparing a random number
106 * of the right length and retrying if it's greater than the
107 * modulus, to prevent any potential Bleichenbacher-like
108 * attacks making use of the uneven distribution within the
109 * range that would arise from just reducing our number mod n.
110 * There are timing implications to the potential retries, of
111 * course, but all they tell you is the modulus, which you
115 int bits, byte, bitsleft, v;
116 random = copybn(key->modulus);
118 * Find the topmost set bit. (This function will return its
119 * index plus one.) Then we'll set all bits from that one
120 * downwards randomly.
122 bits = bignum_bitcount(random);
127 bitsleft = 8, byte = random_byte();
131 bignum_set_bit(random, bits, v);
135 * Now check that this number is strictly greater than
136 * zero, and strictly less than modulus.
138 if (bignum_cmp(random, Zero) <= 0 ||
139 bignum_cmp(random, key->modulus) >= 0) {
148 * RSA blinding relies on the fact that (xy)^d mod n is equal
149 * to (x^d mod n) * (y^d mod n) mod n. We invent a random pair
150 * y and y^d; then we multiply x by y, raise to the power e mod
151 * n as usual, and divide by y^d to recover x^d. Thus the
152 * timing of the modpow does not reveal information about x,
153 * but only about xy, which is unpredictable to an attacker.
155 * The clever bit is that we don't have to do a huge modpow to
156 * get y and y^d; we will use the number we just invented as
157 * _y^d_, and use the RSA public exponent to compute y from it,
158 * which is much faster.
160 random_encrypted = modpow(random, key->exponent, key->modulus);
161 random_inverse = modinv(random, key->modulus);
162 input_blinded = modmul(input, random_encrypted, key->modulus);
163 ret_blinded = modpow(input_blinded, key->private_exponent, key->modulus);
164 ret = modmul(ret_blinded, random_inverse, key->modulus);
167 freebn(input_blinded);
168 freebn(random_inverse);
169 freebn(random_encrypted);
175 Bignum rsadecrypt(Bignum input, struct RSAKey *key)
177 return rsa_privkey_op(input, key);
180 int rsastr_len(struct RSAKey *key)
187 mdlen = (bignum_bitcount(md) + 15) / 16;
188 exlen = (bignum_bitcount(ex) + 15) / 16;
189 return 4 * (mdlen + exlen) + 20;
192 void rsastr_fmt(char *str, struct RSAKey *key)
195 int len = 0, i, nibbles;
196 static const char hex[] = "0123456789abcdef";
201 len += sprintf(str + len, "0x");
203 nibbles = (3 + bignum_bitcount(ex)) / 4;
206 for (i = nibbles; i--;)
207 str[len++] = hex[(bignum_byte(ex, i / 2) >> (4 * (i % 2))) & 0xF];
209 len += sprintf(str + len, ",0x");
211 nibbles = (3 + bignum_bitcount(md)) / 4;
214 for (i = nibbles; i--;)
215 str[len++] = hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF];
221 * Generate a fingerprint string for the key. Compatible with the
222 * OpenSSH fingerprint code.
224 void rsa_fingerprint(char *str, int len, struct RSAKey *key)
226 struct MD5Context md5c;
227 unsigned char digest[16];
228 char buffer[16 * 3 + 40];
232 numlen = ssh1_bignum_length(key->modulus) - 2;
233 for (i = numlen; i--;) {
234 unsigned char c = bignum_byte(key->modulus, i);
235 MD5Update(&md5c, &c, 1);
237 numlen = ssh1_bignum_length(key->exponent) - 2;
238 for (i = numlen; i--;) {
239 unsigned char c = bignum_byte(key->exponent, i);
240 MD5Update(&md5c, &c, 1);
242 MD5Final(digest, &md5c);
244 sprintf(buffer, "%d ", bignum_bitcount(key->modulus));
245 for (i = 0; i < 16; i++)
246 sprintf(buffer + strlen(buffer), "%s%02x", i ? ":" : "",
248 strncpy(str, buffer, len);
251 if (key->comment && slen < len - 1) {
253 strncpy(str + slen + 1, key->comment, len - slen - 1);
259 * Verify that the public data in an RSA key matches the private
260 * data. We also check the private data itself: we ensure that p >
261 * q and that iqmp really is the inverse of q mod p.
263 int rsa_verify(struct RSAKey *key)
265 Bignum n, ed, pm1, qm1;
268 /* n must equal pq. */
269 n = bigmul(key->p, key->q);
270 cmp = bignum_cmp(n, key->modulus);
275 /* e * d must be congruent to 1, modulo (p-1) and modulo (q-1). */
276 pm1 = copybn(key->p);
278 ed = modmul(key->exponent, key->private_exponent, pm1);
279 cmp = bignum_cmp(ed, One);
284 qm1 = copybn(key->q);
286 ed = modmul(key->exponent, key->private_exponent, qm1);
287 cmp = bignum_cmp(ed, One);
295 if (bignum_cmp(key->p, key->q) <= 0)
299 * Ensure iqmp * q is congruent to 1, modulo p.
301 n = modmul(key->iqmp, key->q, key->p);
302 cmp = bignum_cmp(n, One);
310 /* Public key blob as used by Pageant: exponent before modulus. */
311 unsigned char *rsa_public_blob(struct RSAKey *key, int *len)
316 length = (ssh1_bignum_length(key->modulus) +
317 ssh1_bignum_length(key->exponent) + 4);
318 ret = smalloc(length);
320 PUT_32BIT(ret, bignum_bitcount(key->modulus));
322 pos += ssh1_write_bignum(ret + pos, key->exponent);
323 pos += ssh1_write_bignum(ret + pos, key->modulus);
329 /* Given a public blob, determine its length. */
330 int rsa_public_blob_len(void *data)
332 unsigned char *p = (unsigned char *)data;
334 p += 4; /* length word */
335 p += ssh1_read_bignum(p, NULL); /* exponent */
336 p += ssh1_read_bignum(p, NULL); /* modulus */
338 return p - (unsigned char *)data;
341 void freersakey(struct RSAKey *key)
344 freebn(key->modulus);
346 freebn(key->exponent);
347 if (key->private_exponent)
348 freebn(key->private_exponent);
353 /* ----------------------------------------------------------------------
354 * Implementation of the ssh-rsa signing key type.
357 static void getstring(char **data, int *datalen, char **p, int *length)
362 *length = GET_32BIT(*data);
365 if (*datalen < *length)
371 static Bignum getmp(char **data, int *datalen)
377 getstring(data, datalen, &p, &length);
380 b = bignum_from_bytes((unsigned char *)p, length);
384 static void *rsa2_newkey(char *data, int len)
390 rsa = smalloc(sizeof(struct RSAKey));
393 getstring(&data, &len, &p, &slen);
395 if (!p || slen != 7 || memcmp(p, "ssh-rsa", 7)) {
399 rsa->exponent = getmp(&data, &len);
400 rsa->modulus = getmp(&data, &len);
401 rsa->private_exponent = NULL;
407 static void rsa2_freekey(void *key)
409 struct RSAKey *rsa = (struct RSAKey *) key;
414 static char *rsa2_fmtkey(void *key)
416 struct RSAKey *rsa = (struct RSAKey *) key;
420 len = rsastr_len(rsa);
426 static unsigned char *rsa2_public_blob(void *key, int *len)
428 struct RSAKey *rsa = (struct RSAKey *) key;
429 int elen, mlen, bloblen;
431 unsigned char *blob, *p;
433 elen = (bignum_bitcount(rsa->exponent) + 8) / 8;
434 mlen = (bignum_bitcount(rsa->modulus) + 8) / 8;
437 * string "ssh-rsa", mpint exp, mpint mod. Total 19+elen+mlen.
438 * (three length fields, 12+7=19).
440 bloblen = 19 + elen + mlen;
441 blob = smalloc(bloblen);
445 memcpy(p, "ssh-rsa", 7);
450 *p++ = bignum_byte(rsa->exponent, i);
454 *p++ = bignum_byte(rsa->modulus, i);
455 assert(p == blob + bloblen);
460 static unsigned char *rsa2_private_blob(void *key, int *len)
462 struct RSAKey *rsa = (struct RSAKey *) key;
463 int dlen, plen, qlen, ulen, bloblen;
465 unsigned char *blob, *p;
467 dlen = (bignum_bitcount(rsa->private_exponent) + 8) / 8;
468 plen = (bignum_bitcount(rsa->p) + 8) / 8;
469 qlen = (bignum_bitcount(rsa->q) + 8) / 8;
470 ulen = (bignum_bitcount(rsa->iqmp) + 8) / 8;
473 * mpint private_exp, mpint p, mpint q, mpint iqmp. Total 16 +
476 bloblen = 16 + dlen + plen + qlen + ulen;
477 blob = smalloc(bloblen);
482 *p++ = bignum_byte(rsa->private_exponent, i);
486 *p++ = bignum_byte(rsa->p, i);
490 *p++ = bignum_byte(rsa->q, i);
494 *p++ = bignum_byte(rsa->iqmp, i);
495 assert(p == blob + bloblen);
500 static void *rsa2_createkey(unsigned char *pub_blob, int pub_len,
501 unsigned char *priv_blob, int priv_len)
504 char *pb = (char *) priv_blob;
506 rsa = rsa2_newkey((char *) pub_blob, pub_len);
507 rsa->private_exponent = getmp(&pb, &priv_len);
508 rsa->p = getmp(&pb, &priv_len);
509 rsa->q = getmp(&pb, &priv_len);
510 rsa->iqmp = getmp(&pb, &priv_len);
512 if (!rsa_verify(rsa)) {
520 static void *rsa2_openssh_createkey(unsigned char **blob, int *len)
522 char **b = (char **) blob;
525 rsa = smalloc(sizeof(struct RSAKey));
530 rsa->modulus = getmp(b, len);
531 rsa->exponent = getmp(b, len);
532 rsa->private_exponent = getmp(b, len);
533 rsa->iqmp = getmp(b, len);
534 rsa->p = getmp(b, len);
535 rsa->q = getmp(b, len);
537 if (!rsa->modulus || !rsa->exponent || !rsa->private_exponent ||
538 !rsa->iqmp || !rsa->p || !rsa->q) {
540 sfree(rsa->exponent);
541 sfree(rsa->private_exponent);
552 static int rsa2_openssh_fmtkey(void *key, unsigned char *blob, int len)
554 struct RSAKey *rsa = (struct RSAKey *) key;
558 ssh2_bignum_length(rsa->modulus) +
559 ssh2_bignum_length(rsa->exponent) +
560 ssh2_bignum_length(rsa->private_exponent) +
561 ssh2_bignum_length(rsa->iqmp) +
562 ssh2_bignum_length(rsa->p) + ssh2_bignum_length(rsa->q);
569 PUT_32BIT(blob+bloblen, ssh2_bignum_length((x))-4); bloblen += 4; \
570 for (i = ssh2_bignum_length((x))-4; i-- ;) blob[bloblen++]=bignum_byte((x),i);
573 ENC(rsa->private_exponent);
581 static char *rsa2_fingerprint(void *key)
583 struct RSAKey *rsa = (struct RSAKey *) key;
584 struct MD5Context md5c;
585 unsigned char digest[16], lenbuf[4];
586 char buffer[16 * 3 + 40];
591 MD5Update(&md5c, (unsigned char *)"\0\0\0\7ssh-rsa", 11);
593 #define ADD_BIGNUM(bignum) \
594 numlen = (bignum_bitcount(bignum)+8)/8; \
595 PUT_32BIT(lenbuf, numlen); MD5Update(&md5c, lenbuf, 4); \
596 for (i = numlen; i-- ;) { \
597 unsigned char c = bignum_byte(bignum, i); \
598 MD5Update(&md5c, &c, 1); \
600 ADD_BIGNUM(rsa->exponent);
601 ADD_BIGNUM(rsa->modulus);
604 MD5Final(digest, &md5c);
606 sprintf(buffer, "ssh-rsa %d ", bignum_bitcount(rsa->modulus));
607 for (i = 0; i < 16; i++)
608 sprintf(buffer + strlen(buffer), "%s%02x", i ? ":" : "",
610 ret = smalloc(strlen(buffer) + 1);
617 * This is the magic ASN.1/DER prefix that goes in the decoded
618 * signature, between the string of FFs and the actual SHA hash
619 * value. The meaning of it is:
621 * 00 -- this marks the end of the FFs; not part of the ASN.1 bit itself
623 * 30 21 -- a constructed SEQUENCE of length 0x21
624 * 30 09 -- a constructed sub-SEQUENCE of length 9
625 * 06 05 -- an object identifier, length 5
626 * 2B 0E 03 02 1A -- object id { 1 3 14 3 2 26 }
627 * (the 1,3 comes from 0x2B = 43 = 40*1+3)
629 * 04 14 -- a primitive OCTET STRING of length 0x14
630 * [0x14 bytes of hash data follows]
632 * The object id in the middle there is listed as `id-sha1' in
633 * ftp://ftp.rsasecurity.com/pub/pkcs/pkcs-1/pkcs-1v2-1d2.asn (the
634 * ASN module for PKCS #1) and its expanded form is as follows:
636 * id-sha1 OBJECT IDENTIFIER ::= {
637 * iso(1) identified-organization(3) oiw(14) secsig(3)
640 static const unsigned char asn1_weird_stuff[] = {
641 0x00, 0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2B,
642 0x0E, 0x03, 0x02, 0x1A, 0x05, 0x00, 0x04, 0x14,
645 #define ASN1_LEN ( (int) sizeof(asn1_weird_stuff) )
647 static int rsa2_verifysig(void *key, char *sig, int siglen,
648 char *data, int datalen)
650 struct RSAKey *rsa = (struct RSAKey *) key;
654 int bytes, i, j, ret;
655 unsigned char hash[20];
657 getstring(&sig, &siglen, &p, &slen);
658 if (!p || slen != 7 || memcmp(p, "ssh-rsa", 7)) {
661 in = getmp(&sig, &siglen);
662 out = modpow(in, rsa->exponent, rsa->modulus);
667 bytes = bignum_bitcount(rsa->modulus) / 8;
668 /* Top (partial) byte should be zero. */
669 if (bignum_byte(out, bytes - 1) != 0)
671 /* First whole byte should be 1. */
672 if (bignum_byte(out, bytes - 2) != 1)
674 /* Most of the rest should be FF. */
675 for (i = bytes - 3; i >= 20 + ASN1_LEN; i--) {
676 if (bignum_byte(out, i) != 0xFF)
679 /* Then we expect to see the asn1_weird_stuff. */
680 for (i = 20 + ASN1_LEN - 1, j = 0; i >= 20; i--, j++) {
681 if (bignum_byte(out, i) != asn1_weird_stuff[j])
684 /* Finally, we expect to see the SHA-1 hash of the signed data. */
685 SHA_Simple(data, datalen, hash);
686 for (i = 19, j = 0; i >= 0; i--, j++) {
687 if (bignum_byte(out, i) != hash[j])
694 static unsigned char *rsa2_sign(void *key, char *data, int datalen,
697 struct RSAKey *rsa = (struct RSAKey *) key;
698 unsigned char *bytes;
700 unsigned char hash[20];
704 SHA_Simple(data, datalen, hash);
706 nbytes = (bignum_bitcount(rsa->modulus) - 1) / 8;
707 bytes = smalloc(nbytes);
710 for (i = 1; i < nbytes - 20 - ASN1_LEN; i++)
712 for (i = nbytes - 20 - ASN1_LEN, j = 0; i < nbytes - 20; i++, j++)
713 bytes[i] = asn1_weird_stuff[j];
714 for (i = nbytes - 20, j = 0; i < nbytes; i++, j++)
717 in = bignum_from_bytes(bytes, nbytes);
720 out = rsa_privkey_op(in, rsa);
723 nbytes = (bignum_bitcount(out) + 7) / 8;
724 bytes = smalloc(4 + 7 + 4 + nbytes);
726 memcpy(bytes + 4, "ssh-rsa", 7);
727 PUT_32BIT(bytes + 4 + 7, nbytes);
728 for (i = 0; i < nbytes; i++)
729 bytes[4 + 7 + 4 + i] = bignum_byte(out, nbytes - 1 - i);
732 *siglen = 4 + 7 + 4 + nbytes;
736 const struct ssh_signkey ssh_rsa = {
743 rsa2_openssh_createkey,