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, int len, struct RSAKey *result,
26 unsigned char **keystr, int order)
28 unsigned char *p = data;
36 for (i = 0; i < 4; i++)
37 result->bits = (result->bits << 8) + *p++;
44 * order=0 means exponent then modulus (the keys sent by the
45 * server). order=1 means modulus then exponent (the keys
46 * stored in a keyfile).
50 n = ssh1_read_bignum(p, len, result ? &result->exponent : NULL);
56 n = ssh1_read_bignum(p, len, result ? &result->modulus : NULL);
57 if (n < 0 || (result && bignum_bitcount(result->modulus) == 0)) return -1;
59 result->bytes = n - 2;
66 n = ssh1_read_bignum(p, len, result ? &result->exponent : NULL);
74 int makeprivate(unsigned char *data, int len, struct RSAKey *result)
76 return ssh1_read_bignum(data, len, &result->private_exponent);
79 int rsaencrypt(unsigned char *data, int length, struct RSAKey *key)
85 if (key->bytes < length + 4)
86 return 0; /* RSA key too short! */
88 memmove(data + key->bytes - length, data, length);
92 for (i = 2; i < key->bytes - length - 1; i++) {
94 data[i] = random_byte();
95 } while (data[i] == 0);
97 data[key->bytes - length - 1] = 0;
99 b1 = bignum_from_bytes(data, key->bytes);
101 b2 = modpow(b1, key->exponent, key->modulus);
104 for (i = key->bytes; i--;) {
105 *p++ = bignum_byte(b2, i);
114 static void sha512_mpint(SHA512_State * s, Bignum b)
116 unsigned char lenbuf[4];
118 len = (bignum_bitcount(b) + 8) / 8;
119 PUT_32BIT(lenbuf, len);
120 SHA512_Bytes(s, lenbuf, 4);
122 lenbuf[0] = bignum_byte(b, len);
123 SHA512_Bytes(s, lenbuf, 1);
125 memset(lenbuf, 0, sizeof(lenbuf));
129 * This function is a wrapper on modpow(). It has the same effect
130 * as modpow(), but employs RSA blinding to protect against timing
133 static Bignum rsa_privkey_op(Bignum input, struct RSAKey *key)
135 Bignum random, random_encrypted, random_inverse;
136 Bignum input_blinded, ret_blinded;
140 unsigned char digest512[64];
141 int digestused = lenof(digest512);
145 * Start by inventing a random number chosen uniformly from the
146 * range 2..modulus-1. (We do this by preparing a random number
147 * of the right length and retrying if it's greater than the
148 * modulus, to prevent any potential Bleichenbacher-like
149 * attacks making use of the uneven distribution within the
150 * range that would arise from just reducing our number mod n.
151 * There are timing implications to the potential retries, of
152 * course, but all they tell you is the modulus, which you
155 * To preserve determinism and avoid Pageant needing to share
156 * the random number pool, we actually generate this `random'
157 * number by hashing stuff with the private key.
160 int bits, byte, bitsleft, v;
161 random = copybn(key->modulus);
163 * Find the topmost set bit. (This function will return its
164 * index plus one.) Then we'll set all bits from that one
165 * downwards randomly.
167 bits = bignum_bitcount(random);
174 * Conceptually the following few lines are equivalent to
175 * byte = random_byte();
177 if (digestused >= lenof(digest512)) {
178 unsigned char seqbuf[4];
179 PUT_32BIT(seqbuf, hashseq);
181 SHA512_Bytes(&ss, "RSA deterministic blinding", 26);
182 SHA512_Bytes(&ss, seqbuf, sizeof(seqbuf));
183 sha512_mpint(&ss, key->private_exponent);
184 SHA512_Final(&ss, digest512);
188 * Now hash that digest plus the signature
192 SHA512_Bytes(&ss, digest512, sizeof(digest512));
193 sha512_mpint(&ss, input);
194 SHA512_Final(&ss, digest512);
198 byte = digest512[digestused++];
203 bignum_set_bit(random, bits, v);
207 * Now check that this number is strictly greater than
208 * zero, and strictly less than modulus.
210 if (bignum_cmp(random, Zero) <= 0 ||
211 bignum_cmp(random, key->modulus) >= 0) {
220 * RSA blinding relies on the fact that (xy)^d mod n is equal
221 * to (x^d mod n) * (y^d mod n) mod n. We invent a random pair
222 * y and y^d; then we multiply x by y, raise to the power d mod
223 * n as usual, and divide by y^d to recover x^d. Thus an
224 * attacker can't correlate the timing of the modpow with the
225 * input, because they don't know anything about the number
226 * that was input to the actual modpow.
228 * The clever bit is that we don't have to do a huge modpow to
229 * get y and y^d; we will use the number we just invented as
230 * _y^d_, and use the _public_ exponent to compute (y^d)^e = y
231 * from it, which is much faster to do.
233 random_encrypted = modpow(random, key->exponent, key->modulus);
234 random_inverse = modinv(random, key->modulus);
235 input_blinded = modmul(input, random_encrypted, key->modulus);
236 ret_blinded = modpow(input_blinded, key->private_exponent, key->modulus);
237 ret = modmul(ret_blinded, random_inverse, key->modulus);
240 freebn(input_blinded);
241 freebn(random_inverse);
242 freebn(random_encrypted);
248 Bignum rsadecrypt(Bignum input, struct RSAKey *key)
250 return rsa_privkey_op(input, key);
253 int rsastr_len(struct RSAKey *key)
260 mdlen = (bignum_bitcount(md) + 15) / 16;
261 exlen = (bignum_bitcount(ex) + 15) / 16;
262 return 4 * (mdlen + exlen) + 20;
265 void rsastr_fmt(char *str, struct RSAKey *key)
268 int len = 0, i, nibbles;
269 static const char hex[] = "0123456789abcdef";
274 len += sprintf(str + len, "0x");
276 nibbles = (3 + bignum_bitcount(ex)) / 4;
279 for (i = nibbles; i--;)
280 str[len++] = hex[(bignum_byte(ex, i / 2) >> (4 * (i % 2))) & 0xF];
282 len += sprintf(str + len, ",0x");
284 nibbles = (3 + bignum_bitcount(md)) / 4;
287 for (i = nibbles; i--;)
288 str[len++] = hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF];
294 * Generate a fingerprint string for the key. Compatible with the
295 * OpenSSH fingerprint code.
297 void rsa_fingerprint(char *str, int len, struct RSAKey *key)
299 struct MD5Context md5c;
300 unsigned char digest[16];
301 char buffer[16 * 3 + 40];
305 numlen = ssh1_bignum_length(key->modulus) - 2;
306 for (i = numlen; i--;) {
307 unsigned char c = bignum_byte(key->modulus, i);
308 MD5Update(&md5c, &c, 1);
310 numlen = ssh1_bignum_length(key->exponent) - 2;
311 for (i = numlen; i--;) {
312 unsigned char c = bignum_byte(key->exponent, i);
313 MD5Update(&md5c, &c, 1);
315 MD5Final(digest, &md5c);
317 sprintf(buffer, "%d ", bignum_bitcount(key->modulus));
318 for (i = 0; i < 16; i++)
319 sprintf(buffer + strlen(buffer), "%s%02x", i ? ":" : "",
321 strncpy(str, buffer, len);
324 if (key->comment && slen < len - 1) {
326 strncpy(str + slen + 1, key->comment, len - slen - 1);
332 * Verify that the public data in an RSA key matches the private
333 * data. We also check the private data itself: we ensure that p >
334 * q and that iqmp really is the inverse of q mod p.
336 int rsa_verify(struct RSAKey *key)
338 Bignum n, ed, pm1, qm1;
341 /* n must equal pq. */
342 n = bigmul(key->p, key->q);
343 cmp = bignum_cmp(n, key->modulus);
348 /* e * d must be congruent to 1, modulo (p-1) and modulo (q-1). */
349 pm1 = copybn(key->p);
351 ed = modmul(key->exponent, key->private_exponent, pm1);
352 cmp = bignum_cmp(ed, One);
357 qm1 = copybn(key->q);
359 ed = modmul(key->exponent, key->private_exponent, qm1);
360 cmp = bignum_cmp(ed, One);
368 if (bignum_cmp(key->p, key->q) <= 0)
372 * Ensure iqmp * q is congruent to 1, modulo p.
374 n = modmul(key->iqmp, key->q, key->p);
375 cmp = bignum_cmp(n, One);
383 /* Public key blob as used by Pageant: exponent before modulus. */
384 unsigned char *rsa_public_blob(struct RSAKey *key, int *len)
389 length = (ssh1_bignum_length(key->modulus) +
390 ssh1_bignum_length(key->exponent) + 4);
391 ret = snewn(length, unsigned char);
393 PUT_32BIT(ret, bignum_bitcount(key->modulus));
395 pos += ssh1_write_bignum(ret + pos, key->exponent);
396 pos += ssh1_write_bignum(ret + pos, key->modulus);
402 /* Given a public blob, determine its length. */
403 int rsa_public_blob_len(void *data, int maxlen)
405 unsigned char *p = (unsigned char *)data;
410 p += 4; /* length word */
413 n = ssh1_read_bignum(p, maxlen, NULL); /* exponent */
418 n = ssh1_read_bignum(p, maxlen, NULL); /* modulus */
423 return p - (unsigned char *)data;
426 void freersakey(struct RSAKey *key)
429 freebn(key->modulus);
431 freebn(key->exponent);
432 if (key->private_exponent)
433 freebn(key->private_exponent);
438 /* ----------------------------------------------------------------------
439 * Implementation of the ssh-rsa signing key type.
442 static void getstring(char **data, int *datalen, char **p, int *length)
447 *length = GET_32BIT(*data);
450 if (*datalen < *length)
456 static Bignum getmp(char **data, int *datalen)
462 getstring(data, datalen, &p, &length);
465 b = bignum_from_bytes((unsigned char *)p, length);
469 static void *rsa2_newkey(char *data, int len)
475 rsa = snew(struct RSAKey);
478 getstring(&data, &len, &p, &slen);
480 if (!p || slen != 7 || memcmp(p, "ssh-rsa", 7)) {
484 rsa->exponent = getmp(&data, &len);
485 rsa->modulus = getmp(&data, &len);
486 rsa->private_exponent = NULL;
492 static void rsa2_freekey(void *key)
494 struct RSAKey *rsa = (struct RSAKey *) key;
499 static char *rsa2_fmtkey(void *key)
501 struct RSAKey *rsa = (struct RSAKey *) key;
505 len = rsastr_len(rsa);
506 p = snewn(len, char);
511 static unsigned char *rsa2_public_blob(void *key, int *len)
513 struct RSAKey *rsa = (struct RSAKey *) key;
514 int elen, mlen, bloblen;
516 unsigned char *blob, *p;
518 elen = (bignum_bitcount(rsa->exponent) + 8) / 8;
519 mlen = (bignum_bitcount(rsa->modulus) + 8) / 8;
522 * string "ssh-rsa", mpint exp, mpint mod. Total 19+elen+mlen.
523 * (three length fields, 12+7=19).
525 bloblen = 19 + elen + mlen;
526 blob = snewn(bloblen, unsigned char);
530 memcpy(p, "ssh-rsa", 7);
535 *p++ = bignum_byte(rsa->exponent, i);
539 *p++ = bignum_byte(rsa->modulus, i);
540 assert(p == blob + bloblen);
545 static unsigned char *rsa2_private_blob(void *key, int *len)
547 struct RSAKey *rsa = (struct RSAKey *) key;
548 int dlen, plen, qlen, ulen, bloblen;
550 unsigned char *blob, *p;
552 dlen = (bignum_bitcount(rsa->private_exponent) + 8) / 8;
553 plen = (bignum_bitcount(rsa->p) + 8) / 8;
554 qlen = (bignum_bitcount(rsa->q) + 8) / 8;
555 ulen = (bignum_bitcount(rsa->iqmp) + 8) / 8;
558 * mpint private_exp, mpint p, mpint q, mpint iqmp. Total 16 +
561 bloblen = 16 + dlen + plen + qlen + ulen;
562 blob = snewn(bloblen, unsigned char);
567 *p++ = bignum_byte(rsa->private_exponent, i);
571 *p++ = bignum_byte(rsa->p, i);
575 *p++ = bignum_byte(rsa->q, i);
579 *p++ = bignum_byte(rsa->iqmp, i);
580 assert(p == blob + bloblen);
585 static void *rsa2_createkey(unsigned char *pub_blob, int pub_len,
586 unsigned char *priv_blob, int priv_len)
589 char *pb = (char *) priv_blob;
591 rsa = rsa2_newkey((char *) pub_blob, pub_len);
592 rsa->private_exponent = getmp(&pb, &priv_len);
593 rsa->p = getmp(&pb, &priv_len);
594 rsa->q = getmp(&pb, &priv_len);
595 rsa->iqmp = getmp(&pb, &priv_len);
597 if (!rsa_verify(rsa)) {
605 static void *rsa2_openssh_createkey(unsigned char **blob, int *len)
607 char **b = (char **) blob;
610 rsa = snew(struct RSAKey);
615 rsa->modulus = getmp(b, len);
616 rsa->exponent = getmp(b, len);
617 rsa->private_exponent = getmp(b, len);
618 rsa->iqmp = getmp(b, len);
619 rsa->p = getmp(b, len);
620 rsa->q = getmp(b, len);
622 if (!rsa->modulus || !rsa->exponent || !rsa->private_exponent ||
623 !rsa->iqmp || !rsa->p || !rsa->q) {
625 sfree(rsa->exponent);
626 sfree(rsa->private_exponent);
637 static int rsa2_openssh_fmtkey(void *key, unsigned char *blob, int len)
639 struct RSAKey *rsa = (struct RSAKey *) key;
643 ssh2_bignum_length(rsa->modulus) +
644 ssh2_bignum_length(rsa->exponent) +
645 ssh2_bignum_length(rsa->private_exponent) +
646 ssh2_bignum_length(rsa->iqmp) +
647 ssh2_bignum_length(rsa->p) + ssh2_bignum_length(rsa->q);
654 PUT_32BIT(blob+bloblen, ssh2_bignum_length((x))-4); bloblen += 4; \
655 for (i = ssh2_bignum_length((x))-4; i-- ;) blob[bloblen++]=bignum_byte((x),i);
658 ENC(rsa->private_exponent);
666 static int rsa2_pubkey_bits(void *blob, int len)
671 rsa = rsa2_newkey((char *) blob, len);
672 ret = bignum_bitcount(rsa->modulus);
678 static char *rsa2_fingerprint(void *key)
680 struct RSAKey *rsa = (struct RSAKey *) key;
681 struct MD5Context md5c;
682 unsigned char digest[16], lenbuf[4];
683 char buffer[16 * 3 + 40];
688 MD5Update(&md5c, (unsigned char *)"\0\0\0\7ssh-rsa", 11);
690 #define ADD_BIGNUM(bignum) \
691 numlen = (bignum_bitcount(bignum)+8)/8; \
692 PUT_32BIT(lenbuf, numlen); MD5Update(&md5c, lenbuf, 4); \
693 for (i = numlen; i-- ;) { \
694 unsigned char c = bignum_byte(bignum, i); \
695 MD5Update(&md5c, &c, 1); \
697 ADD_BIGNUM(rsa->exponent);
698 ADD_BIGNUM(rsa->modulus);
701 MD5Final(digest, &md5c);
703 sprintf(buffer, "ssh-rsa %d ", bignum_bitcount(rsa->modulus));
704 for (i = 0; i < 16; i++)
705 sprintf(buffer + strlen(buffer), "%s%02x", i ? ":" : "",
707 ret = snewn(strlen(buffer) + 1, char);
714 * This is the magic ASN.1/DER prefix that goes in the decoded
715 * signature, between the string of FFs and the actual SHA hash
716 * value. The meaning of it is:
718 * 00 -- this marks the end of the FFs; not part of the ASN.1 bit itself
720 * 30 21 -- a constructed SEQUENCE of length 0x21
721 * 30 09 -- a constructed sub-SEQUENCE of length 9
722 * 06 05 -- an object identifier, length 5
723 * 2B 0E 03 02 1A -- object id { 1 3 14 3 2 26 }
724 * (the 1,3 comes from 0x2B = 43 = 40*1+3)
726 * 04 14 -- a primitive OCTET STRING of length 0x14
727 * [0x14 bytes of hash data follows]
729 * The object id in the middle there is listed as `id-sha1' in
730 * ftp://ftp.rsasecurity.com/pub/pkcs/pkcs-1/pkcs-1v2-1d2.asn (the
731 * ASN module for PKCS #1) and its expanded form is as follows:
733 * id-sha1 OBJECT IDENTIFIER ::= {
734 * iso(1) identified-organization(3) oiw(14) secsig(3)
737 static const unsigned char asn1_weird_stuff[] = {
738 0x00, 0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2B,
739 0x0E, 0x03, 0x02, 0x1A, 0x05, 0x00, 0x04, 0x14,
742 #define ASN1_LEN ( (int) sizeof(asn1_weird_stuff) )
744 static int rsa2_verifysig(void *key, char *sig, int siglen,
745 char *data, int datalen)
747 struct RSAKey *rsa = (struct RSAKey *) key;
751 int bytes, i, j, ret;
752 unsigned char hash[20];
754 getstring(&sig, &siglen, &p, &slen);
755 if (!p || slen != 7 || memcmp(p, "ssh-rsa", 7)) {
758 in = getmp(&sig, &siglen);
759 out = modpow(in, rsa->exponent, rsa->modulus);
764 bytes = (bignum_bitcount(rsa->modulus)+7) / 8;
765 /* Top (partial) byte should be zero. */
766 if (bignum_byte(out, bytes - 1) != 0)
768 /* First whole byte should be 1. */
769 if (bignum_byte(out, bytes - 2) != 1)
771 /* Most of the rest should be FF. */
772 for (i = bytes - 3; i >= 20 + ASN1_LEN; i--) {
773 if (bignum_byte(out, i) != 0xFF)
776 /* Then we expect to see the asn1_weird_stuff. */
777 for (i = 20 + ASN1_LEN - 1, j = 0; i >= 20; i--, j++) {
778 if (bignum_byte(out, i) != asn1_weird_stuff[j])
781 /* Finally, we expect to see the SHA-1 hash of the signed data. */
782 SHA_Simple(data, datalen, hash);
783 for (i = 19, j = 0; i >= 0; i--, j++) {
784 if (bignum_byte(out, i) != hash[j])
792 static unsigned char *rsa2_sign(void *key, char *data, int datalen,
795 struct RSAKey *rsa = (struct RSAKey *) key;
796 unsigned char *bytes;
798 unsigned char hash[20];
802 SHA_Simple(data, datalen, hash);
804 nbytes = (bignum_bitcount(rsa->modulus) - 1) / 8;
805 assert(1 <= nbytes - 20 - ASN1_LEN);
806 bytes = snewn(nbytes, unsigned char);
809 for (i = 1; i < nbytes - 20 - ASN1_LEN; i++)
811 for (i = nbytes - 20 - ASN1_LEN, j = 0; i < nbytes - 20; i++, j++)
812 bytes[i] = asn1_weird_stuff[j];
813 for (i = nbytes - 20, j = 0; i < nbytes; i++, j++)
816 in = bignum_from_bytes(bytes, nbytes);
819 out = rsa_privkey_op(in, rsa);
822 nbytes = (bignum_bitcount(out) + 7) / 8;
823 bytes = snewn(4 + 7 + 4 + nbytes, unsigned char);
825 memcpy(bytes + 4, "ssh-rsa", 7);
826 PUT_32BIT(bytes + 4 + 7, nbytes);
827 for (i = 0; i < nbytes; i++)
828 bytes[4 + 7 + 4 + i] = bignum_byte(out, nbytes - 1 - i);
831 *siglen = 4 + 7 + 4 + nbytes;
835 const struct ssh_signkey ssh_rsa = {
842 rsa2_openssh_createkey,