CR50: add support for RSA key generation

Prime generation uses a sieve to amortize division
with small primes.  Otherwise this a standard
Miller-Rabin implementation.

BRANCH=none
BUG=chrome-os-partner:43025,chrome-os-partner:47524
TEST=tests under test/tpm2 pass

Change-Id: I9f84d1f9c911f6146e4bd80296f75157a191552d
Signed-off-by: nagendra modadugu <ngm@google.com>
Reviewed-on: https://chromium-review.googlesource.com/335222
Commit-Ready: Nagendra Modadugu <ngm@google.com>
Tested-by: Nagendra Modadugu <ngm@google.com>
Reviewed-by: Nagendra Modadugu <ngm@google.com>

2 files changed, 515 insertions, 2 deletions

diff --git a/test/tpm_test/ftdi_spi_tpm.c b/test/tpm_test/ftdi_spi_tpm.c
index 752e80bed4..2b9f30992a 100644
--- a/test/tpm_test/ftdi_spi_tpm.c
+++ b/test/tpm_test/ftdi_spi_tpm.c
@@ -272,8 +272,8 @@ int FtdiSpiInit(uint32_t freq, int enable_debug)
 	return true;
 }
 
-/* This is in seconds. */
-#define MAX_STATUS_TIMEOUT 120
+/* This is in seconds (prime generation may take several minutes). */
+#define MAX_STATUS_TIMEOUT 900
 static int WaitForStatus(uint32_t statusMask, uint32_t statusExpected)
 {
 	uint32_t status;
diff --git a/test/tpm_test/rsa_test.py b/test/tpm_test/rsa_test.py
index 14982d5380..6ee474c579 100644
--- a/test/tpm_test/rsa_test.py
+++ b/test/tpm_test/rsa_test.py
@@ -5,7 +5,9 @@
 
 """Module for testing rsa functions using extended commands."""
 
+import binascii
 import hashlib
+import rsa
 import struct
 
 import subcmd
@@ -19,11 +21,13 @@ _RSA_OPCODES = {
   'VERIFY': 0x03,
   'KEYGEN': 0x04,
   'KEYTEST': 0x05,
+  'PRIMEGEN': 0x06
 }
 
 
 # TPM2 ALG codes.
 _RSA_PADDING = {
+  'NONE': 0x00,
   'PKCS1-SSA': 0x14,
   'PKCS1-ES': 0x15,
   'PKCS1-PSS': 0x16,
@@ -103,6 +107,7 @@ def _verify_cmd(padding, hashing, key_len, sig, msg):
                                 ml=struct.pack('>H', sig_len), msg=sig,
                                 dl=struct.pack('>H', digest_len), dig=digest)
 
+
 def _keytest_cmd(key_len):
   op = _RSA_OPCODES['KEYTEST']
   return _RSA_CMD_FORMAT.format(o=op, p=0, h=_HASH['NONE'],
@@ -111,6 +116,447 @@ def _keytest_cmd(key_len):
                                 dl='', dig='')
 
 
+def _keygen_cmd(key_len, e):
+  op = _RSA_OPCODES['KEYGEN']
+  padding = _RSA_PADDING['NONE']
+  hashing = _HASH['NONE']
+  return _RSA_CMD_FORMAT.format(o=op, p=padding, h=hashing,
+                                kl=struct.pack('>H', key_len),
+                                ml=struct.pack('>H', 0), msg='',
+                                dl=struct.pack('>H', 0), dig='')
+
+
+def _primegen_cmd(seed):
+  op = _RSA_OPCODES['PRIMEGEN']
+  padding = _RSA_PADDING['NONE']
+  hashing = _HASH['NONE']
+  return _RSA_CMD_FORMAT.format(o=op, p=padding, h=hashing,
+                                kl=struct.pack('>H', len(seed) * 8 * 2),
+                                ml=struct.pack('>H', len(seed)), msg=seed,
+                                dl=struct.pack('>H', 0), dig='')
+
+_PRIMES = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
+           59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131,
+           137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
+           211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
+           283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373,
+           379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457,
+           461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
+           563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
+           643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
+           739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827,
+           829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
+           937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
+           1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
+           1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171,
+           1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,
+           1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319,
+           1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429,
+           1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489,
+           1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571,
+           1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,
+           1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
+           1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
+           1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
+           1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
+           2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083,
+           2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153,
+           2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
+           2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341,
+           2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
+           2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521,
+           2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
+           2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689,
+           2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753,
+           2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843,
+           2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,
+           2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037,
+           3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
+           3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229,
+           3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,
+           3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407,
+           3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
+           3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
+           3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671,
+           3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761,
+           3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
+           3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929,
+           3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021,
+           4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127,
+           4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219,
+           4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,
+           4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
+           4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507,
+           4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
+           4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679,
+           4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789,
+           4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903,
+           4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973,
+           4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059,
+           5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167,
+           5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273,
+           5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
+           5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
+           5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531,
+           5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651,
+           5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737,
+           5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827,
+           5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897,
+           5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037,
+           6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121,
+           6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217,
+           6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
+           6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
+           6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491,
+           6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599,
+           6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
+           6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793,
+           6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883,
+           6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977,
+           6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069,
+           7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193,
+           7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
+           7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417,
+           7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517,
+           7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583,
+           7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681,
+           7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759,
+           7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879,
+           7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993,
+           8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093,
+           8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209,
+           8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291,
+           8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389,
+           8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521,
+           8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623,
+           8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699,
+           8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783,
+           8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867,
+           8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999,
+           9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091,
+           9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187,
+           9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283,
+           9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391,
+           9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463,
+           9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551,
+           9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677,
+           9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769,
+           9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857,
+           9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949,
+           9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079,
+           10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159,
+           10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253,
+           10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331,
+           10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433,
+           10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529,
+           10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631,
+           10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723,
+           10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837,
+           10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909,
+           10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027,
+           11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117,
+           11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213,
+           11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311,
+           11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411,
+           11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497,
+           11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617,
+           11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719,
+           11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821,
+           11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909,
+           11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981,
+           11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097,
+           12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163,
+           12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269,
+           12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377,
+           12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457,
+           12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539,
+           12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613,
+           12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703,
+           12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809,
+           12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911,
+           12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983,
+           13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093,
+           13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171,
+           13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267,
+           13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381,
+           13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469,
+           13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591,
+           13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687,
+           13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757,
+           13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859,
+           13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931,
+           13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051,
+           14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159,
+           14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293,
+           14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401,
+           14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479,
+           14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561,
+           14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657,
+           14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747,
+           14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827,
+           14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923,
+           14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031,
+           15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131,
+           15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227,
+           15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299,
+           15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377,
+           15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467,
+           15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581,
+           15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661,
+           15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749,
+           15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823,
+           15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923,
+           15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061,
+           16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127,
+           16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231,
+           16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361,
+           16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451,
+           16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561,
+           16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657,
+           16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759,
+           16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883,
+           16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979,
+           16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047,
+           17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167,
+           17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291,
+           17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377,
+           17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449,
+           17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539,
+           17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627,
+           17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747,
+           17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851,
+           17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939,
+           17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043,
+           18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127,
+           18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217,
+           18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301,
+           18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397,
+           18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481,
+           18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587,
+           18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719,
+           18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839,
+           18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973,
+           18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079,
+           19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207,
+           19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289,
+           19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403,
+           19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463,
+           19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543,
+           19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681,
+           19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759,
+           19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861,
+           19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963,
+           19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047,
+           20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129,
+           20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231,
+           20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341,
+           20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411,
+           20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533,
+           20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641,
+           20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749,
+           20753, 20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873,
+           20879, 20887, 20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959,
+           20963, 20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21031,
+           21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149,
+           21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227,
+           21247, 21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341, 21347,
+           21377, 21379, 21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467,
+           21481, 21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523, 21529,
+           21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601, 21611,
+           21613, 21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713, 21727,
+           21737, 21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817,
+           21821, 21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911,
+           21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, 22013, 22027,
+           22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, 22093,
+           22109, 22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171,
+           22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283,
+           22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397,
+           22409, 22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511,
+           22531, 22541, 22543, 22549, 22567, 22571, 22573, 22613, 22619, 22621,
+           22637, 22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709,
+           22717, 22721, 22727, 22739, 22741, 22751, 22769, 22777, 22783, 22787,
+           22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907,
+           22921, 22937, 22943, 22961, 22963, 22973, 22993, 23003, 23011, 23017,
+           23021, 23027, 23029, 23039, 23041, 23053, 23057, 23059, 23063, 23071,
+           23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, 23189,
+           23197, 23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291, 23293,
+           23297, 23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399,
+           23417, 23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539,
+           23549, 23557, 23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609,
+           23623, 23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687, 23689,
+           23719, 23741, 23743, 23747, 23753, 23761, 23767, 23773, 23789, 23801,
+           23813, 23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879, 23887,
+           23893, 23899, 23909, 23911, 23917, 23929, 23957, 23971, 23977, 23981,
+           23993, 24001, 24007, 24019, 24023, 24029, 24043, 24049, 24061, 24071,
+           24077, 24083, 24091, 24097, 24103, 24107, 24109, 24113, 24121, 24133,
+           24137, 24151, 24169, 24179, 24181, 24197, 24203, 24223, 24229, 24239,
+           24247, 24251, 24281, 24317, 24329, 24337, 24359, 24371, 24373, 24379,
+           24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481,
+           24499, 24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611,
+           24623, 24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733,
+           24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821, 24841, 24847,
+           24851, 24859, 24877, 24889, 24907, 24917, 24919, 24923, 24943, 24953,
+           24967, 24971, 24977, 24979, 24989, 25013, 25031, 25033, 25037, 25057,
+           25073, 25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163,
+           25169, 25171, 25183, 25189, 25219, 25229, 25237, 25243, 25247, 25253,
+           25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357,
+           25367, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457,
+           25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583,
+           25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667,
+           25673, 25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763,
+           25771, 25793, 25799, 25801, 25819, 25841, 25847, 25849, 25867, 25873,
+           25889, 25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969,
+           25981, 25997, 25999, 26003, 26017, 26021, 26029, 26041, 26053, 26083,
+           26099, 26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177,
+           26183, 26189, 26203, 26209, 26227, 26237, 26249, 26251, 26261, 26263,
+           26267, 26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371,
+           26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459,
+           26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, 26591,
+           26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693,
+           26699, 26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759,
+           26777, 26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863,
+           26879, 26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953,
+           26959, 26981, 26987, 26993, 27011, 27017, 27031, 27043, 27059, 27061,
+           27067, 27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143, 27179,
+           27191, 27197, 27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281,
+           27283, 27299, 27329, 27337, 27361, 27367, 27397, 27407, 27409, 27427,
+           27431, 27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527, 27529,
+           27539, 27541, 27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653,
+           27673, 27689, 27691, 27697, 27701, 27733, 27737, 27739, 27743, 27749,
+           27751, 27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809,
+           27817, 27823, 27827, 27847, 27851, 27883, 27893, 27901, 27917, 27919,
+           27941, 27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019,
+           28027, 28031, 28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109,
+           28111, 28123, 28151, 28163, 28181, 28183, 28201, 28211, 28219, 28229,
+           28277, 28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351,
+           28387, 28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463,
+           28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547, 28549, 28559,
+           28571, 28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627,
+           28631, 28643, 28649, 28657, 28661, 28663, 28669, 28687, 28697, 28703,
+           28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, 28807,
+           28813, 28817, 28837, 28843, 28859, 28867, 28871, 28879, 28901, 28909,
+           28921, 28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021, 29023,
+           29027, 29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137,
+           29147, 29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221,
+           29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311, 29327, 29333,
+           29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411, 29423,
+           29429, 29437, 29443, 29453, 29473, 29483, 29501, 29527, 29531, 29537,
+           29567, 29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641,
+           29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761,
+           29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879,
+           29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, 30013,
+           30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113,
+           30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203,
+           30211, 30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313,
+           30319, 30323, 30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431,
+           30449, 30467, 30469, 30491, 30493, 30497, 30509, 30517, 30529, 30539,
+           30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, 30661,
+           30671, 30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757, 30763,
+           30773, 30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853,
+           30859, 30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949,
+           30971, 30977, 30983, 31013, 31019, 31033, 31039, 31051, 31063, 31069,
+           31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159,
+           31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247,
+           31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327,
+           31333, 31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477,
+           31481, 31489, 31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567,
+           31573, 31583, 31601, 31607, 31627, 31643, 31649, 31657, 31663, 31667,
+           31687, 31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769, 31771,
+           31793, 31799, 31817, 31847, 31849, 31859, 31873, 31883, 31891, 31907,
+           31957, 31963, 31973, 31981, 31991, 32003, 32009, 32027, 32029, 32051,
+           32057, 32059, 32063, 32069, 32077, 32083, 32089, 32099, 32117, 32119,
+           32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213, 32233,
+           32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, 32323,
+           32327, 32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381, 32401,
+           32411, 32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497,
+           32503, 32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579,
+           32587, 32603, 32609, 32611, 32621, 32633, 32647, 32653, 32687, 32693,
+           32707, 32713, 32717, 32719, 32749, 32771, 32779, 32783, 32789, 32797,
+           32801, 32803, 32831, 32833, 32839, 32843, 32869, 32887, 32909, 32911,
+           32917, 32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993,
+           32999, 33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073, 33083,
+           33091, 33107, 33113, 33119, 33149, 33151, 33161, 33179, 33181, 33191,
+           33199, 33203, 33211, 33223, 33247, 33287, 33289, 33301, 33311, 33317,
+           33329, 33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, 33403,
+           33409, 33413, 33427, 33457, 33461, 33469, 33479, 33487, 33493, 33503,
+           33521, 33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589,
+           33599, 33601, 33613, 33617, 33619, 33623, 33629, 33637, 33641, 33647,
+           33679, 33703, 33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769,
+           33773, 33791, 33797, 33809, 33811, 33827, 33829, 33851, 33857, 33863,
+           33871, 33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961, 33967,
+           33997, 34019, 34031, 34033, 34039, 34057, 34061, 34123, 34127, 34129,
+           34141, 34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231,
+           34253, 34259, 34261, 34267, 34273, 34283, 34297, 34301, 34303, 34313,
+           34319, 34327, 34337, 34351, 34361, 34367, 34369, 34381, 34403, 34421,
+           34429, 34439, 34457, 34469, 34471, 34483, 34487, 34499, 34501, 34511,
+           34513, 34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607,
+           34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703,
+           34721, 34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819,
+           34841, 34843, 34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919,
+           34939, 34949, 34961, 34963, 34981, 35023, 35027, 35051, 35053, 35059,
+           35069, 35081, 35083, 35089, 35099, 35107, 35111, 35117, 35129, 35141,
+           35149, 35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257, 35267,
+           35279, 35281, 35291, 35311, 35317, 35323, 35327, 35339, 35353, 35363,
+           35381, 35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449, 35461,
+           35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, 35543, 35569,
+           35573, 35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729, 35731,
+           35747, 35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837,
+           35839, 35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933,
+           35951, 35963, 35969, 35977, 35983, 35993, 35999, 36007, 36011, 36013,
+           36017, 36037, 36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131,
+           36137, 36151, 36161, 36187, 36191, 36209, 36217, 36229, 36241, 36251,
+           36263, 36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341, 36343,
+           36353, 36373, 36383, 36389, 36433, 36451, 36457, 36467, 36469, 36473,
+           36479, 36493, 36497, 36523, 36527, 36529, 36541, 36551, 36559, 36563,
+           36571, 36583, 36587, 36599, 36607, 36629, 36637, 36643, 36653, 36671,
+           36677, 36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761,
+           36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833, 36847,
+           36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929,
+           36931, 36943, 36947, 36973, 36979, 36997, 37003, 37013, 37019, 37021,
+           37039, 37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159,
+           37171, 37181, 37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273,
+           37277, 37307, 37309, 37313, 37321, 37337, 37339, 37357, 37361, 37363,
+           37369, 37379, 37397, 37409, 37423, 37441, 37447, 37463, 37483, 37489,
+           37493, 37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561,
+           37567, 37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643,
+           37649, 37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781, 37783,
+           37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871, 37879, 37889,
+           37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, 37997,
+           38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153,
+           38167, 38177, 38183, 38189, 38197, 38201, 38219, 38231, 38237, 38239,
+           38261, 38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329,
+           38333, 38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459,
+           38461, 38501, 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609,
+           38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699,
+           38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783,
+           38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873]
+
+
+def _prime_from_seed(seed):
+  ROUNDS = 7
+
+  def _window(s, primes):
+    w = [0] * 4096
+    for i in primes:
+      rem = s % i
+      if rem != 0:
+        rem = i - rem
+      for j in range(rem, len(w), i):
+        w[j] = 1
+    return w
+
+  # Set LSB, and top two bits.
+  candidate = chr(ord(seed[0]) | 192) + seed[1:-1] + chr(ord(seed[-1]) | 1)
+  candidate = int(binascii.b2a_hex(candidate), 16)
+  assert len(bin(candidate)[2:]) == len(seed) * 8
+  w = _window(candidate, _PRIMES[:4096])
+  for i, bit in enumerate(w):
+    if not bit:
+      if rsa.prime.randomized_primality_testing(candidate + i, ROUNDS):
+        return candidate + i
+  return None
+
+
 #
 # TEST VECTORS.
 #
@@ -135,6 +581,19 @@ _KEYTEST_INPUTS = (
   (2048,),
 )
 
+_KEYGEN_INPUTS = (
+  (768, 65537),
+)
+
+
+_PRIMEGEN_INPUTS = (
+  768,
+  768,
+  768,
+  768,
+  768
+)
+
 def _encrypt_tests(tpm):
   msg = 'Hello CR50!'
 
@@ -198,7 +657,61 @@ def _keytest_tests(tpm):
     print('%sSUCCESS: %s' % (utils.cursor_back(), test_name))
 
 
+def _keygen_tests(tpm):
+  for data in _KEYGEN_INPUTS:
+    key_len, e = data
+    test_name = 'RSA-KEYGEN:%d:%d' % data
+    cmd = _keygen_cmd(key_len, e)
+
+    wrapped_response = tpm.command(tpm.wrap_ext_command(subcmd.RSA, cmd))
+    result = tpm.unwrap_ext_response(subcmd.RSA, wrapped_response)
+    result_len = len(result)
+    if result_len != int(key_len / 8 * 1.5):
+      raise subcmd.TpmTestError('%s error:%s' % (
+        test_name, utils.hex_dump(result)))
+
+    N = int(binascii.b2a_hex(result[0:result_len * 2 / 3]), 16)
+    p = int(binascii.b2a_hex(result[result_len * 2 / 3:]), 16)
+    q = N / p
+    if not rsa.prime.is_prime(p):
+      raise subcmd.TpmTestError('%s error:%s' % (
+          test_name, utils.hex_dump(result)))
+    if not rsa.prime.is_prime(q):
+      raise subcmd.TpmTestError('%s error:%s' % (
+          test_name, utils.hex_dump(result)))
+    print('%sSUCCESS: %s' % (utils.cursor_back(), test_name))
+
+
+def _primegen_tests(tpm):
+  for data in _PRIMEGEN_INPUTS:
+    key_len = data
+    test_name = 'RSA-PRIMEGEN:%d' % data
+    seed = rsa.randnum.read_random_bits(key_len / 2)
+    assert len(seed) == key_len / 16
+    # dcrypto interface is little-endian.
+    cmd = _primegen_cmd(seed[::-1])
+
+    wrapped_response = tpm.command(tpm.wrap_ext_command(subcmd.RSA, cmd))
+    result = tpm.unwrap_ext_response(subcmd.RSA, wrapped_response)
+    result_len = len(result)
+    if result_len != key_len / 16:
+      raise subcmd.TpmTestError('%s error:%s' % (
+        test_name, utils.hex_dump(result)))
+
+    p = int(binascii.b2a_hex(result[::-1]), 16)
+    if not rsa.prime.is_prime(p):
+      raise subcmd.TpmTestError('%s error:%s' % (
+          test_name, utils.hex_dump(result)))
+    calculated = _prime_from_seed(seed)
+    if p != calculated:
+      raise subcmd.TpmTestError('%s error:%s' % (
+          test_name, utils.hex_dump(result)))
+    print('%sSUCCESS: %s' % (utils.cursor_back(), test_name))
+
+
 def rsa_test(tpm):
   _encrypt_tests(tpm)
   _sign_tests(tpm)
   _keytest_tests(tpm)
+  _keygen_tests(tpm)
+  _primegen_tests(tpm)