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 * I have seen key blobs in the wild which were generated with
357 * p < q, so instead of rejecting the key in this case we
358 * should instead flip them round into the canonical order of
359 * p > q. This also involves regenerating iqmp.
361 if (bignum_cmp(key->p, key->q) <= 0) {
367 key->iqmp = modinv(key->q, key->p);
371 * Ensure iqmp * q is congruent to 1, modulo p.
373 n = modmul(key->iqmp, key->q, key->p);
374 cmp = bignum_cmp(n, One);
382 /* Public key blob as used by Pageant: exponent before modulus. */
383 unsigned char *rsa_public_blob(struct RSAKey *key, int *len)
388 length = (ssh1_bignum_length(key->modulus) +
389 ssh1_bignum_length(key->exponent) + 4);
390 ret = snewn(length, unsigned char);
392 PUT_32BIT(ret, bignum_bitcount(key->modulus));
394 pos += ssh1_write_bignum(ret + pos, key->exponent);
395 pos += ssh1_write_bignum(ret + pos, key->modulus);
401 /* Given a public blob, determine its length. */
402 int rsa_public_blob_len(void *data, int maxlen)
404 unsigned char *p = (unsigned char *)data;
409 p += 4; /* length word */
412 n = ssh1_read_bignum(p, maxlen, NULL); /* exponent */
417 n = ssh1_read_bignum(p, maxlen, NULL); /* modulus */
422 return p - (unsigned char *)data;
425 void freersakey(struct RSAKey *key)
428 freebn(key->modulus);
430 freebn(key->exponent);
431 if (key->private_exponent)
432 freebn(key->private_exponent);
443 /* ----------------------------------------------------------------------
444 * Implementation of the ssh-rsa signing key type.
447 static void getstring(char **data, int *datalen, char **p, int *length)
452 *length = GET_32BIT(*data);
455 if (*datalen < *length)
461 static Bignum getmp(char **data, int *datalen)
467 getstring(data, datalen, &p, &length);
470 b = bignum_from_bytes((unsigned char *)p, length);
474 static void *rsa2_newkey(char *data, int len)
480 rsa = snew(struct RSAKey);
483 getstring(&data, &len, &p, &slen);
485 if (!p || slen != 7 || memcmp(p, "ssh-rsa", 7)) {
489 rsa->exponent = getmp(&data, &len);
490 rsa->modulus = getmp(&data, &len);
491 rsa->private_exponent = NULL;
497 static void rsa2_freekey(void *key)
499 struct RSAKey *rsa = (struct RSAKey *) key;
504 static char *rsa2_fmtkey(void *key)
506 struct RSAKey *rsa = (struct RSAKey *) key;
510 len = rsastr_len(rsa);
511 p = snewn(len, char);
516 static unsigned char *rsa2_public_blob(void *key, int *len)
518 struct RSAKey *rsa = (struct RSAKey *) key;
519 int elen, mlen, bloblen;
521 unsigned char *blob, *p;
523 elen = (bignum_bitcount(rsa->exponent) + 8) / 8;
524 mlen = (bignum_bitcount(rsa->modulus) + 8) / 8;
527 * string "ssh-rsa", mpint exp, mpint mod. Total 19+elen+mlen.
528 * (three length fields, 12+7=19).
530 bloblen = 19 + elen + mlen;
531 blob = snewn(bloblen, unsigned char);
535 memcpy(p, "ssh-rsa", 7);
540 *p++ = bignum_byte(rsa->exponent, i);
544 *p++ = bignum_byte(rsa->modulus, i);
545 assert(p == blob + bloblen);
550 static unsigned char *rsa2_private_blob(void *key, int *len)
552 struct RSAKey *rsa = (struct RSAKey *) key;
553 int dlen, plen, qlen, ulen, bloblen;
555 unsigned char *blob, *p;
557 dlen = (bignum_bitcount(rsa->private_exponent) + 8) / 8;
558 plen = (bignum_bitcount(rsa->p) + 8) / 8;
559 qlen = (bignum_bitcount(rsa->q) + 8) / 8;
560 ulen = (bignum_bitcount(rsa->iqmp) + 8) / 8;
563 * mpint private_exp, mpint p, mpint q, mpint iqmp. Total 16 +
566 bloblen = 16 + dlen + plen + qlen + ulen;
567 blob = snewn(bloblen, unsigned char);
572 *p++ = bignum_byte(rsa->private_exponent, i);
576 *p++ = bignum_byte(rsa->p, i);
580 *p++ = bignum_byte(rsa->q, i);
584 *p++ = bignum_byte(rsa->iqmp, i);
585 assert(p == blob + bloblen);
590 static void *rsa2_createkey(unsigned char *pub_blob, int pub_len,
591 unsigned char *priv_blob, int priv_len)
594 char *pb = (char *) priv_blob;
596 rsa = rsa2_newkey((char *) pub_blob, pub_len);
597 rsa->private_exponent = getmp(&pb, &priv_len);
598 rsa->p = getmp(&pb, &priv_len);
599 rsa->q = getmp(&pb, &priv_len);
600 rsa->iqmp = getmp(&pb, &priv_len);
602 if (!rsa_verify(rsa)) {
610 static void *rsa2_openssh_createkey(unsigned char **blob, int *len)
612 char **b = (char **) blob;
615 rsa = snew(struct RSAKey);
620 rsa->modulus = getmp(b, len);
621 rsa->exponent = getmp(b, len);
622 rsa->private_exponent = getmp(b, len);
623 rsa->iqmp = getmp(b, len);
624 rsa->p = getmp(b, len);
625 rsa->q = getmp(b, len);
627 if (!rsa->modulus || !rsa->exponent || !rsa->private_exponent ||
628 !rsa->iqmp || !rsa->p || !rsa->q) {
630 sfree(rsa->exponent);
631 sfree(rsa->private_exponent);
642 static int rsa2_openssh_fmtkey(void *key, unsigned char *blob, int len)
644 struct RSAKey *rsa = (struct RSAKey *) key;
648 ssh2_bignum_length(rsa->modulus) +
649 ssh2_bignum_length(rsa->exponent) +
650 ssh2_bignum_length(rsa->private_exponent) +
651 ssh2_bignum_length(rsa->iqmp) +
652 ssh2_bignum_length(rsa->p) + ssh2_bignum_length(rsa->q);
659 PUT_32BIT(blob+bloblen, ssh2_bignum_length((x))-4); bloblen += 4; \
660 for (i = ssh2_bignum_length((x))-4; i-- ;) blob[bloblen++]=bignum_byte((x),i);
663 ENC(rsa->private_exponent);
671 static int rsa2_pubkey_bits(void *blob, int len)
676 rsa = rsa2_newkey((char *) blob, len);
677 ret = bignum_bitcount(rsa->modulus);
683 static char *rsa2_fingerprint(void *key)
685 struct RSAKey *rsa = (struct RSAKey *) key;
686 struct MD5Context md5c;
687 unsigned char digest[16], lenbuf[4];
688 char buffer[16 * 3 + 40];
693 MD5Update(&md5c, (unsigned char *)"\0\0\0\7ssh-rsa", 11);
695 #define ADD_BIGNUM(bignum) \
696 numlen = (bignum_bitcount(bignum)+8)/8; \
697 PUT_32BIT(lenbuf, numlen); MD5Update(&md5c, lenbuf, 4); \
698 for (i = numlen; i-- ;) { \
699 unsigned char c = bignum_byte(bignum, i); \
700 MD5Update(&md5c, &c, 1); \
702 ADD_BIGNUM(rsa->exponent);
703 ADD_BIGNUM(rsa->modulus);
706 MD5Final(digest, &md5c);
708 sprintf(buffer, "ssh-rsa %d ", bignum_bitcount(rsa->modulus));
709 for (i = 0; i < 16; i++)
710 sprintf(buffer + strlen(buffer), "%s%02x", i ? ":" : "",
712 ret = snewn(strlen(buffer) + 1, char);
719 * This is the magic ASN.1/DER prefix that goes in the decoded
720 * signature, between the string of FFs and the actual SHA hash
721 * value. The meaning of it is:
723 * 00 -- this marks the end of the FFs; not part of the ASN.1 bit itself
725 * 30 21 -- a constructed SEQUENCE of length 0x21
726 * 30 09 -- a constructed sub-SEQUENCE of length 9
727 * 06 05 -- an object identifier, length 5
728 * 2B 0E 03 02 1A -- object id { 1 3 14 3 2 26 }
729 * (the 1,3 comes from 0x2B = 43 = 40*1+3)
731 * 04 14 -- a primitive OCTET STRING of length 0x14
732 * [0x14 bytes of hash data follows]
734 * The object id in the middle there is listed as `id-sha1' in
735 * ftp://ftp.rsasecurity.com/pub/pkcs/pkcs-1/pkcs-1v2-1d2.asn (the
736 * ASN module for PKCS #1) and its expanded form is as follows:
738 * id-sha1 OBJECT IDENTIFIER ::= {
739 * iso(1) identified-organization(3) oiw(14) secsig(3)
742 static const unsigned char asn1_weird_stuff[] = {
743 0x00, 0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2B,
744 0x0E, 0x03, 0x02, 0x1A, 0x05, 0x00, 0x04, 0x14,
747 #define ASN1_LEN ( (int) sizeof(asn1_weird_stuff) )
749 static int rsa2_verifysig(void *key, char *sig, int siglen,
750 char *data, int datalen)
752 struct RSAKey *rsa = (struct RSAKey *) key;
756 int bytes, i, j, ret;
757 unsigned char hash[20];
759 getstring(&sig, &siglen, &p, &slen);
760 if (!p || slen != 7 || memcmp(p, "ssh-rsa", 7)) {
763 in = getmp(&sig, &siglen);
764 out = modpow(in, rsa->exponent, rsa->modulus);
769 bytes = (bignum_bitcount(rsa->modulus)+7) / 8;
770 /* Top (partial) byte should be zero. */
771 if (bignum_byte(out, bytes - 1) != 0)
773 /* First whole byte should be 1. */
774 if (bignum_byte(out, bytes - 2) != 1)
776 /* Most of the rest should be FF. */
777 for (i = bytes - 3; i >= 20 + ASN1_LEN; i--) {
778 if (bignum_byte(out, i) != 0xFF)
781 /* Then we expect to see the asn1_weird_stuff. */
782 for (i = 20 + ASN1_LEN - 1, j = 0; i >= 20; i--, j++) {
783 if (bignum_byte(out, i) != asn1_weird_stuff[j])
786 /* Finally, we expect to see the SHA-1 hash of the signed data. */
787 SHA_Simple(data, datalen, hash);
788 for (i = 19, j = 0; i >= 0; i--, j++) {
789 if (bignum_byte(out, i) != hash[j])
797 static unsigned char *rsa2_sign(void *key, char *data, int datalen,
800 struct RSAKey *rsa = (struct RSAKey *) key;
801 unsigned char *bytes;
803 unsigned char hash[20];
807 SHA_Simple(data, datalen, hash);
809 nbytes = (bignum_bitcount(rsa->modulus) - 1) / 8;
810 assert(1 <= nbytes - 20 - ASN1_LEN);
811 bytes = snewn(nbytes, unsigned char);
814 for (i = 1; i < nbytes - 20 - ASN1_LEN; i++)
816 for (i = nbytes - 20 - ASN1_LEN, j = 0; i < nbytes - 20; i++, j++)
817 bytes[i] = asn1_weird_stuff[j];
818 for (i = nbytes - 20, j = 0; i < nbytes; i++, j++)
821 in = bignum_from_bytes(bytes, nbytes);
824 out = rsa_privkey_op(in, rsa);
827 nbytes = (bignum_bitcount(out) + 7) / 8;
828 bytes = snewn(4 + 7 + 4 + nbytes, unsigned char);
830 memcpy(bytes + 4, "ssh-rsa", 7);
831 PUT_32BIT(bytes + 4 + 7, nbytes);
832 for (i = 0; i < nbytes; i++)
833 bytes[4 + 7 + 4 + i] = bignum_byte(out, nbytes - 1 - i);
836 *siglen = 4 + 7 + 4 + nbytes;
840 const struct ssh_signkey ssh_rsa = {
847 rsa2_openssh_createkey,
857 void *ssh_rsakex_newkey(char *data, int len)
859 return rsa2_newkey(data, len);
862 void ssh_rsakex_freekey(void *key)
867 int ssh_rsakex_klen(void *key)
869 struct RSAKey *rsa = (struct RSAKey *) key;
871 return bignum_bitcount(rsa->modulus);
874 static void oaep_mask(const struct ssh_hash *h, void *seed, int seedlen,
875 void *vdata, int datalen)
877 unsigned char *data = (unsigned char *)vdata;
880 while (datalen > 0) {
881 int i, max = (datalen > h->hlen ? h->hlen : datalen);
883 unsigned char counter[4], hash[SSH2_KEX_MAX_HASH_LEN];
885 assert(h->hlen <= SSH2_KEX_MAX_HASH_LEN);
886 PUT_32BIT(counter, count);
888 h->bytes(s, seed, seedlen);
889 h->bytes(s, counter, 4);
893 for (i = 0; i < max; i++)
901 void ssh_rsakex_encrypt(const struct ssh_hash *h, unsigned char *in, int inlen,
902 unsigned char *out, int outlen,
906 struct RSAKey *rsa = (struct RSAKey *) key;
909 const int HLEN = h->hlen;
912 * Here we encrypt using RSAES-OAEP. Essentially this means:
914 * - we have a SHA-based `mask generation function' which
915 * creates a pseudo-random stream of mask data
916 * deterministically from an input chunk of data.
918 * - we have a random chunk of data called a seed.
920 * - we use the seed to generate a mask which we XOR with our
923 * - then we use _the masked plaintext_ to generate a mask
924 * which we XOR with the seed.
926 * - then we concatenate the masked seed and the masked
927 * plaintext, and RSA-encrypt that lot.
929 * The result is that the data input to the encryption function
930 * is random-looking and (hopefully) contains no exploitable
931 * structure such as PKCS1-v1_5 does.
933 * For a precise specification, see RFC 3447, section 7.1.1.
934 * Some of the variable names below are derived from that, so
935 * it'd probably help to read it anyway.
938 /* k denotes the length in octets of the RSA modulus. */
939 k = (7 + bignum_bitcount(rsa->modulus)) / 8;
941 /* The length of the input data must be at most k - 2hLen - 2. */
942 assert(inlen > 0 && inlen <= k - 2*HLEN - 2);
944 /* The length of the output data wants to be precisely k. */
948 * Now perform EME-OAEP encoding. First set up all the unmasked
951 /* Leading byte zero. */
953 /* At position 1, the seed: HLEN bytes of random data. */
954 for (i = 0; i < HLEN; i++)
955 out[i + 1] = random_byte();
956 /* At position 1+HLEN, the data block DB, consisting of: */
957 /* The hash of the label (we only support an empty label here) */
958 h->final(h->init(), out + HLEN + 1);
959 /* A bunch of zero octets */
960 memset(out + 2*HLEN + 1, 0, outlen - (2*HLEN + 1));
961 /* A single 1 octet, followed by the input message data. */
962 out[outlen - inlen - 1] = 1;
963 memcpy(out + outlen - inlen, in, inlen);
966 * Now use the seed data to mask the block DB.
968 oaep_mask(h, out+1, HLEN, out+HLEN+1, outlen-HLEN-1);
971 * And now use the masked DB to mask the seed itself.
973 oaep_mask(h, out+HLEN+1, outlen-HLEN-1, out+1, HLEN);
976 * Now `out' contains precisely the data we want to
979 b1 = bignum_from_bytes(out, outlen);
980 b2 = modpow(b1, rsa->exponent, rsa->modulus);
982 for (i = outlen; i--;) {
983 *p++ = bignum_byte(b2, i);
993 static const struct ssh_kex ssh_rsa_kex_sha1 = {
994 "rsa1024-sha1", NULL, KEXTYPE_RSA, NULL, NULL, 0, 0, &ssh_sha1
997 static const struct ssh_kex ssh_rsa_kex_sha256 = {
998 "rsa2048-sha256", NULL, KEXTYPE_RSA, NULL, NULL, 0, 0, &ssh_sha256
1001 static const struct ssh_kex *const rsa_kex_list[] = {
1002 &ssh_rsa_kex_sha256,
1006 const struct ssh_kexes ssh_rsa_kex = {
1007 sizeof(rsa_kex_list) / sizeof(*rsa_kex_list),