dhtest.c 26 KB

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  1. /*
  2. * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
  3. *
  4. * Licensed under the OpenSSL license (the "License"). You may not use
  5. * this file except in compliance with the License. You can obtain a copy
  6. * in the file LICENSE in the source distribution or at
  7. * https://www.openssl.org/source/license.html
  8. */
  9. #include <stdio.h>
  10. #include <stdlib.h>
  11. #include <string.h>
  12. #include "internal/nelem.h"
  13. #include <openssl/crypto.h>
  14. #include <openssl/bio.h>
  15. #include <openssl/bn.h>
  16. #include <openssl/rand.h>
  17. #include <openssl/err.h>
  18. #include "testutil.h"
  19. #ifndef OPENSSL_NO_DH
  20. # include <openssl/dh.h>
  21. static int cb(int p, int n, BN_GENCB *arg);
  22. static int dh_test(void)
  23. {
  24. DH *dh = NULL;
  25. BIGNUM *p = NULL, *q = NULL, *g = NULL;
  26. const BIGNUM *p2, *q2, *g2;
  27. BIGNUM *priv_key = NULL;
  28. const BIGNUM *pub_key2, *priv_key2;
  29. BN_GENCB *_cb = NULL;
  30. DH *a = NULL;
  31. DH *b = NULL;
  32. DH *c = NULL;
  33. const BIGNUM *ap = NULL, *ag = NULL, *apub_key = NULL;
  34. const BIGNUM *bpub_key = NULL, *bpriv_key = NULL;
  35. BIGNUM *bp = NULL, *bg = NULL, *cpriv_key = NULL;
  36. unsigned char *abuf = NULL;
  37. unsigned char *bbuf = NULL;
  38. unsigned char *cbuf = NULL;
  39. int i, alen, blen, clen, aout, bout, cout;
  40. int ret = 0;
  41. if (!TEST_ptr(dh = DH_new())
  42. || !TEST_ptr(p = BN_new())
  43. || !TEST_ptr(q = BN_new())
  44. || !TEST_ptr(g = BN_new())
  45. || !TEST_ptr(priv_key = BN_new()))
  46. goto err1;
  47. /*
  48. * I) basic tests
  49. */
  50. /* using a small predefined Sophie Germain DH group with generator 3 */
  51. if (!TEST_true(BN_set_word(p, 4079L))
  52. || !TEST_true(BN_set_word(q, 2039L))
  53. || !TEST_true(BN_set_word(g, 3L))
  54. || !TEST_true(DH_set0_pqg(dh, p, q, g)))
  55. goto err1;
  56. /* test the combined getter for p, q, and g */
  57. DH_get0_pqg(dh, &p2, &q2, &g2);
  58. if (!TEST_ptr_eq(p2, p)
  59. || !TEST_ptr_eq(q2, q)
  60. || !TEST_ptr_eq(g2, g))
  61. goto err2;
  62. /* test the simple getters for p, q, and g */
  63. if (!TEST_ptr_eq(DH_get0_p(dh), p2)
  64. || !TEST_ptr_eq(DH_get0_q(dh), q2)
  65. || !TEST_ptr_eq(DH_get0_g(dh), g2))
  66. goto err2;
  67. /* set the private key only*/
  68. if (!TEST_true(BN_set_word(priv_key, 1234L))
  69. || !TEST_true(DH_set0_key(dh, NULL, priv_key)))
  70. goto err2;
  71. /* test the combined getter for pub_key and priv_key */
  72. DH_get0_key(dh, &pub_key2, &priv_key2);
  73. if (!TEST_ptr_eq(pub_key2, NULL)
  74. || !TEST_ptr_eq(priv_key2, priv_key))
  75. goto err3;
  76. /* test the simple getters for pub_key and priv_key */
  77. if (!TEST_ptr_eq(DH_get0_pub_key(dh), pub_key2)
  78. || !TEST_ptr_eq(DH_get0_priv_key(dh), priv_key2))
  79. goto err3;
  80. /* now generate a key pair ... */
  81. if (!DH_generate_key(dh))
  82. goto err3;
  83. /* ... and check whether the private key was reused: */
  84. /* test it with the combined getter for pub_key and priv_key */
  85. DH_get0_key(dh, &pub_key2, &priv_key2);
  86. if (!TEST_ptr(pub_key2)
  87. || !TEST_ptr_eq(priv_key2, priv_key))
  88. goto err3;
  89. /* test it the simple getters for pub_key and priv_key */
  90. if (!TEST_ptr_eq(DH_get0_pub_key(dh), pub_key2)
  91. || !TEST_ptr_eq(DH_get0_priv_key(dh), priv_key2))
  92. goto err3;
  93. /* check whether the public key was calculated correctly */
  94. TEST_uint_eq(BN_get_word(pub_key2), 3331L);
  95. /*
  96. * II) key generation
  97. */
  98. /* generate a DH group ... */
  99. if (!TEST_ptr(_cb = BN_GENCB_new()))
  100. goto err3;
  101. BN_GENCB_set(_cb, &cb, NULL);
  102. if (!TEST_ptr(a = DH_new())
  103. || !TEST_true(DH_generate_parameters_ex(a, 64,
  104. DH_GENERATOR_5, _cb)))
  105. goto err3;
  106. /* ... and check whether it is valid */
  107. if (!DH_check(a, &i))
  108. goto err3;
  109. if (!TEST_false(i & DH_CHECK_P_NOT_PRIME)
  110. || !TEST_false(i & DH_CHECK_P_NOT_SAFE_PRIME)
  111. || !TEST_false(i & DH_UNABLE_TO_CHECK_GENERATOR)
  112. || !TEST_false(i & DH_NOT_SUITABLE_GENERATOR))
  113. goto err3;
  114. DH_get0_pqg(a, &ap, NULL, &ag);
  115. /* now create another copy of the DH group for the peer */
  116. if (!TEST_ptr(b = DH_new()))
  117. goto err3;
  118. if (!TEST_ptr(bp = BN_dup(ap))
  119. || !TEST_ptr(bg = BN_dup(ag))
  120. || !TEST_true(DH_set0_pqg(b, bp, NULL, bg)))
  121. goto err3;
  122. bp = bg = NULL;
  123. /*
  124. * III) simulate a key exchange
  125. */
  126. if (!DH_generate_key(a))
  127. goto err3;
  128. DH_get0_key(a, &apub_key, NULL);
  129. if (!DH_generate_key(b))
  130. goto err3;
  131. DH_get0_key(b, &bpub_key, &bpriv_key);
  132. /* Also test with a private-key-only copy of |b|. */
  133. if (!TEST_ptr(c = DHparams_dup(b))
  134. || !TEST_ptr(cpriv_key = BN_dup(bpriv_key))
  135. || !TEST_true(DH_set0_key(c, NULL, cpriv_key)))
  136. goto err3;
  137. cpriv_key = NULL;
  138. alen = DH_size(a);
  139. if (!TEST_ptr(abuf = OPENSSL_malloc(alen))
  140. || !TEST_true((aout = DH_compute_key(abuf, bpub_key, a)) != -1))
  141. goto err3;
  142. blen = DH_size(b);
  143. if (!TEST_ptr(bbuf = OPENSSL_malloc(blen))
  144. || !TEST_true((bout = DH_compute_key(bbuf, apub_key, b)) != -1))
  145. goto err3;
  146. clen = DH_size(c);
  147. if (!TEST_ptr(cbuf = OPENSSL_malloc(clen))
  148. || !TEST_true((cout = DH_compute_key(cbuf, apub_key, c)) != -1))
  149. goto err3;
  150. if (!TEST_true(aout >= 4)
  151. || !TEST_mem_eq(abuf, aout, bbuf, bout)
  152. || !TEST_mem_eq(abuf, aout, cbuf, cout))
  153. goto err3;
  154. ret = 1;
  155. goto success;
  156. err1:
  157. /* an error occurred before p,q,g were assigned to dh */
  158. BN_free(p);
  159. BN_free(q);
  160. BN_free(g);
  161. err2:
  162. /* an error occured before priv_key was assigned to dh */
  163. BN_free(priv_key);
  164. err3:
  165. success:
  166. OPENSSL_free(abuf);
  167. OPENSSL_free(bbuf);
  168. OPENSSL_free(cbuf);
  169. DH_free(b);
  170. DH_free(a);
  171. DH_free(c);
  172. BN_free(bp);
  173. BN_free(bg);
  174. BN_free(cpriv_key);
  175. BN_GENCB_free(_cb);
  176. DH_free(dh);
  177. return ret;
  178. }
  179. static int cb(int p, int n, BN_GENCB *arg)
  180. {
  181. return 1;
  182. }
  183. /* Test data from RFC 5114 */
  184. static const unsigned char dhtest_1024_160_xA[] = {
  185. 0xB9, 0xA3, 0xB3, 0xAE, 0x8F, 0xEF, 0xC1, 0xA2, 0x93, 0x04, 0x96, 0x50,
  186. 0x70, 0x86, 0xF8, 0x45, 0x5D, 0x48, 0x94, 0x3E
  187. };
  188. static const unsigned char dhtest_1024_160_yA[] = {
  189. 0x2A, 0x85, 0x3B, 0x3D, 0x92, 0x19, 0x75, 0x01, 0xB9, 0x01, 0x5B, 0x2D,
  190. 0xEB, 0x3E, 0xD8, 0x4F, 0x5E, 0x02, 0x1D, 0xCC, 0x3E, 0x52, 0xF1, 0x09,
  191. 0xD3, 0x27, 0x3D, 0x2B, 0x75, 0x21, 0x28, 0x1C, 0xBA, 0xBE, 0x0E, 0x76,
  192. 0xFF, 0x57, 0x27, 0xFA, 0x8A, 0xCC, 0xE2, 0x69, 0x56, 0xBA, 0x9A, 0x1F,
  193. 0xCA, 0x26, 0xF2, 0x02, 0x28, 0xD8, 0x69, 0x3F, 0xEB, 0x10, 0x84, 0x1D,
  194. 0x84, 0xA7, 0x36, 0x00, 0x54, 0xEC, 0xE5, 0xA7, 0xF5, 0xB7, 0xA6, 0x1A,
  195. 0xD3, 0xDF, 0xB3, 0xC6, 0x0D, 0x2E, 0x43, 0x10, 0x6D, 0x87, 0x27, 0xDA,
  196. 0x37, 0xDF, 0x9C, 0xCE, 0x95, 0xB4, 0x78, 0x75, 0x5D, 0x06, 0xBC, 0xEA,
  197. 0x8F, 0x9D, 0x45, 0x96, 0x5F, 0x75, 0xA5, 0xF3, 0xD1, 0xDF, 0x37, 0x01,
  198. 0x16, 0x5F, 0xC9, 0xE5, 0x0C, 0x42, 0x79, 0xCE, 0xB0, 0x7F, 0x98, 0x95,
  199. 0x40, 0xAE, 0x96, 0xD5, 0xD8, 0x8E, 0xD7, 0x76
  200. };
  201. static const unsigned char dhtest_1024_160_xB[] = {
  202. 0x93, 0x92, 0xC9, 0xF9, 0xEB, 0x6A, 0x7A, 0x6A, 0x90, 0x22, 0xF7, 0xD8,
  203. 0x3E, 0x72, 0x23, 0xC6, 0x83, 0x5B, 0xBD, 0xDA
  204. };
  205. static const unsigned char dhtest_1024_160_yB[] = {
  206. 0x71, 0x7A, 0x6C, 0xB0, 0x53, 0x37, 0x1F, 0xF4, 0xA3, 0xB9, 0x32, 0x94,
  207. 0x1C, 0x1E, 0x56, 0x63, 0xF8, 0x61, 0xA1, 0xD6, 0xAD, 0x34, 0xAE, 0x66,
  208. 0x57, 0x6D, 0xFB, 0x98, 0xF6, 0xC6, 0xCB, 0xF9, 0xDD, 0xD5, 0xA5, 0x6C,
  209. 0x78, 0x33, 0xF6, 0xBC, 0xFD, 0xFF, 0x09, 0x55, 0x82, 0xAD, 0x86, 0x8E,
  210. 0x44, 0x0E, 0x8D, 0x09, 0xFD, 0x76, 0x9E, 0x3C, 0xEC, 0xCD, 0xC3, 0xD3,
  211. 0xB1, 0xE4, 0xCF, 0xA0, 0x57, 0x77, 0x6C, 0xAA, 0xF9, 0x73, 0x9B, 0x6A,
  212. 0x9F, 0xEE, 0x8E, 0x74, 0x11, 0xF8, 0xD6, 0xDA, 0xC0, 0x9D, 0x6A, 0x4E,
  213. 0xDB, 0x46, 0xCC, 0x2B, 0x5D, 0x52, 0x03, 0x09, 0x0E, 0xAE, 0x61, 0x26,
  214. 0x31, 0x1E, 0x53, 0xFD, 0x2C, 0x14, 0xB5, 0x74, 0xE6, 0xA3, 0x10, 0x9A,
  215. 0x3D, 0xA1, 0xBE, 0x41, 0xBD, 0xCE, 0xAA, 0x18, 0x6F, 0x5C, 0xE0, 0x67,
  216. 0x16, 0xA2, 0xB6, 0xA0, 0x7B, 0x3C, 0x33, 0xFE
  217. };
  218. static const unsigned char dhtest_1024_160_Z[] = {
  219. 0x5C, 0x80, 0x4F, 0x45, 0x4D, 0x30, 0xD9, 0xC4, 0xDF, 0x85, 0x27, 0x1F,
  220. 0x93, 0x52, 0x8C, 0x91, 0xDF, 0x6B, 0x48, 0xAB, 0x5F, 0x80, 0xB3, 0xB5,
  221. 0x9C, 0xAA, 0xC1, 0xB2, 0x8F, 0x8A, 0xCB, 0xA9, 0xCD, 0x3E, 0x39, 0xF3,
  222. 0xCB, 0x61, 0x45, 0x25, 0xD9, 0x52, 0x1D, 0x2E, 0x64, 0x4C, 0x53, 0xB8,
  223. 0x07, 0xB8, 0x10, 0xF3, 0x40, 0x06, 0x2F, 0x25, 0x7D, 0x7D, 0x6F, 0xBF,
  224. 0xE8, 0xD5, 0xE8, 0xF0, 0x72, 0xE9, 0xB6, 0xE9, 0xAF, 0xDA, 0x94, 0x13,
  225. 0xEA, 0xFB, 0x2E, 0x8B, 0x06, 0x99, 0xB1, 0xFB, 0x5A, 0x0C, 0xAC, 0xED,
  226. 0xDE, 0xAE, 0xAD, 0x7E, 0x9C, 0xFB, 0xB3, 0x6A, 0xE2, 0xB4, 0x20, 0x83,
  227. 0x5B, 0xD8, 0x3A, 0x19, 0xFB, 0x0B, 0x5E, 0x96, 0xBF, 0x8F, 0xA4, 0xD0,
  228. 0x9E, 0x34, 0x55, 0x25, 0x16, 0x7E, 0xCD, 0x91, 0x55, 0x41, 0x6F, 0x46,
  229. 0xF4, 0x08, 0xED, 0x31, 0xB6, 0x3C, 0x6E, 0x6D
  230. };
  231. static const unsigned char dhtest_2048_224_xA[] = {
  232. 0x22, 0xE6, 0x26, 0x01, 0xDB, 0xFF, 0xD0, 0x67, 0x08, 0xA6, 0x80, 0xF7,
  233. 0x47, 0xF3, 0x61, 0xF7, 0x6D, 0x8F, 0x4F, 0x72, 0x1A, 0x05, 0x48, 0xE4,
  234. 0x83, 0x29, 0x4B, 0x0C
  235. };
  236. static const unsigned char dhtest_2048_224_yA[] = {
  237. 0x1B, 0x3A, 0x63, 0x45, 0x1B, 0xD8, 0x86, 0xE6, 0x99, 0xE6, 0x7B, 0x49,
  238. 0x4E, 0x28, 0x8B, 0xD7, 0xF8, 0xE0, 0xD3, 0x70, 0xBA, 0xDD, 0xA7, 0xA0,
  239. 0xEF, 0xD2, 0xFD, 0xE7, 0xD8, 0xF6, 0x61, 0x45, 0xCC, 0x9F, 0x28, 0x04,
  240. 0x19, 0x97, 0x5E, 0xB8, 0x08, 0x87, 0x7C, 0x8A, 0x4C, 0x0C, 0x8E, 0x0B,
  241. 0xD4, 0x8D, 0x4A, 0x54, 0x01, 0xEB, 0x1E, 0x87, 0x76, 0xBF, 0xEE, 0xE1,
  242. 0x34, 0xC0, 0x38, 0x31, 0xAC, 0x27, 0x3C, 0xD9, 0xD6, 0x35, 0xAB, 0x0C,
  243. 0xE0, 0x06, 0xA4, 0x2A, 0x88, 0x7E, 0x3F, 0x52, 0xFB, 0x87, 0x66, 0xB6,
  244. 0x50, 0xF3, 0x80, 0x78, 0xBC, 0x8E, 0xE8, 0x58, 0x0C, 0xEF, 0xE2, 0x43,
  245. 0x96, 0x8C, 0xFC, 0x4F, 0x8D, 0xC3, 0xDB, 0x08, 0x45, 0x54, 0x17, 0x1D,
  246. 0x41, 0xBF, 0x2E, 0x86, 0x1B, 0x7B, 0xB4, 0xD6, 0x9D, 0xD0, 0xE0, 0x1E,
  247. 0xA3, 0x87, 0xCB, 0xAA, 0x5C, 0xA6, 0x72, 0xAF, 0xCB, 0xE8, 0xBD, 0xB9,
  248. 0xD6, 0x2D, 0x4C, 0xE1, 0x5F, 0x17, 0xDD, 0x36, 0xF9, 0x1E, 0xD1, 0xEE,
  249. 0xDD, 0x65, 0xCA, 0x4A, 0x06, 0x45, 0x5C, 0xB9, 0x4C, 0xD4, 0x0A, 0x52,
  250. 0xEC, 0x36, 0x0E, 0x84, 0xB3, 0xC9, 0x26, 0xE2, 0x2C, 0x43, 0x80, 0xA3,
  251. 0xBF, 0x30, 0x9D, 0x56, 0x84, 0x97, 0x68, 0xB7, 0xF5, 0x2C, 0xFD, 0xF6,
  252. 0x55, 0xFD, 0x05, 0x3A, 0x7E, 0xF7, 0x06, 0x97, 0x9E, 0x7E, 0x58, 0x06,
  253. 0xB1, 0x7D, 0xFA, 0xE5, 0x3A, 0xD2, 0xA5, 0xBC, 0x56, 0x8E, 0xBB, 0x52,
  254. 0x9A, 0x7A, 0x61, 0xD6, 0x8D, 0x25, 0x6F, 0x8F, 0xC9, 0x7C, 0x07, 0x4A,
  255. 0x86, 0x1D, 0x82, 0x7E, 0x2E, 0xBC, 0x8C, 0x61, 0x34, 0x55, 0x31, 0x15,
  256. 0xB7, 0x0E, 0x71, 0x03, 0x92, 0x0A, 0xA1, 0x6D, 0x85, 0xE5, 0x2B, 0xCB,
  257. 0xAB, 0x8D, 0x78, 0x6A, 0x68, 0x17, 0x8F, 0xA8, 0xFF, 0x7C, 0x2F, 0x5C,
  258. 0x71, 0x64, 0x8D, 0x6F
  259. };
  260. static const unsigned char dhtest_2048_224_xB[] = {
  261. 0x4F, 0xF3, 0xBC, 0x96, 0xC7, 0xFC, 0x6A, 0x6D, 0x71, 0xD3, 0xB3, 0x63,
  262. 0x80, 0x0A, 0x7C, 0xDF, 0xEF, 0x6F, 0xC4, 0x1B, 0x44, 0x17, 0xEA, 0x15,
  263. 0x35, 0x3B, 0x75, 0x90
  264. };
  265. static const unsigned char dhtest_2048_224_yB[] = {
  266. 0x4D, 0xCE, 0xE9, 0x92, 0xA9, 0x76, 0x2A, 0x13, 0xF2, 0xF8, 0x38, 0x44,
  267. 0xAD, 0x3D, 0x77, 0xEE, 0x0E, 0x31, 0xC9, 0x71, 0x8B, 0x3D, 0xB6, 0xC2,
  268. 0x03, 0x5D, 0x39, 0x61, 0x18, 0x2C, 0x3E, 0x0B, 0xA2, 0x47, 0xEC, 0x41,
  269. 0x82, 0xD7, 0x60, 0xCD, 0x48, 0xD9, 0x95, 0x99, 0x97, 0x06, 0x22, 0xA1,
  270. 0x88, 0x1B, 0xBA, 0x2D, 0xC8, 0x22, 0x93, 0x9C, 0x78, 0xC3, 0x91, 0x2C,
  271. 0x66, 0x61, 0xFA, 0x54, 0x38, 0xB2, 0x07, 0x66, 0x22, 0x2B, 0x75, 0xE2,
  272. 0x4C, 0x2E, 0x3A, 0xD0, 0xC7, 0x28, 0x72, 0x36, 0x12, 0x95, 0x25, 0xEE,
  273. 0x15, 0xB5, 0xDD, 0x79, 0x98, 0xAA, 0x04, 0xC4, 0xA9, 0x69, 0x6C, 0xAC,
  274. 0xD7, 0x17, 0x20, 0x83, 0xA9, 0x7A, 0x81, 0x66, 0x4E, 0xAD, 0x2C, 0x47,
  275. 0x9E, 0x44, 0x4E, 0x4C, 0x06, 0x54, 0xCC, 0x19, 0xE2, 0x8D, 0x77, 0x03,
  276. 0xCE, 0xE8, 0xDA, 0xCD, 0x61, 0x26, 0xF5, 0xD6, 0x65, 0xEC, 0x52, 0xC6,
  277. 0x72, 0x55, 0xDB, 0x92, 0x01, 0x4B, 0x03, 0x7E, 0xB6, 0x21, 0xA2, 0xAC,
  278. 0x8E, 0x36, 0x5D, 0xE0, 0x71, 0xFF, 0xC1, 0x40, 0x0A, 0xCF, 0x07, 0x7A,
  279. 0x12, 0x91, 0x3D, 0xD8, 0xDE, 0x89, 0x47, 0x34, 0x37, 0xAB, 0x7B, 0xA3,
  280. 0x46, 0x74, 0x3C, 0x1B, 0x21, 0x5D, 0xD9, 0xC1, 0x21, 0x64, 0xA7, 0xE4,
  281. 0x05, 0x31, 0x18, 0xD1, 0x99, 0xBE, 0xC8, 0xEF, 0x6F, 0xC5, 0x61, 0x17,
  282. 0x0C, 0x84, 0xC8, 0x7D, 0x10, 0xEE, 0x9A, 0x67, 0x4A, 0x1F, 0xA8, 0xFF,
  283. 0xE1, 0x3B, 0xDF, 0xBA, 0x1D, 0x44, 0xDE, 0x48, 0x94, 0x6D, 0x68, 0xDC,
  284. 0x0C, 0xDD, 0x77, 0x76, 0x35, 0xA7, 0xAB, 0x5B, 0xFB, 0x1E, 0x4B, 0xB7,
  285. 0xB8, 0x56, 0xF9, 0x68, 0x27, 0x73, 0x4C, 0x18, 0x41, 0x38, 0xE9, 0x15,
  286. 0xD9, 0xC3, 0x00, 0x2E, 0xBC, 0xE5, 0x31, 0x20, 0x54, 0x6A, 0x7E, 0x20,
  287. 0x02, 0x14, 0x2B, 0x6C
  288. };
  289. static const unsigned char dhtest_2048_224_Z[] = {
  290. 0x34, 0xD9, 0xBD, 0xDC, 0x1B, 0x42, 0x17, 0x6C, 0x31, 0x3F, 0xEA, 0x03,
  291. 0x4C, 0x21, 0x03, 0x4D, 0x07, 0x4A, 0x63, 0x13, 0xBB, 0x4E, 0xCD, 0xB3,
  292. 0x70, 0x3F, 0xFF, 0x42, 0x45, 0x67, 0xA4, 0x6B, 0xDF, 0x75, 0x53, 0x0E,
  293. 0xDE, 0x0A, 0x9D, 0xA5, 0x22, 0x9D, 0xE7, 0xD7, 0x67, 0x32, 0x28, 0x6C,
  294. 0xBC, 0x0F, 0x91, 0xDA, 0x4C, 0x3C, 0x85, 0x2F, 0xC0, 0x99, 0xC6, 0x79,
  295. 0x53, 0x1D, 0x94, 0xC7, 0x8A, 0xB0, 0x3D, 0x9D, 0xEC, 0xB0, 0xA4, 0xE4,
  296. 0xCA, 0x8B, 0x2B, 0xB4, 0x59, 0x1C, 0x40, 0x21, 0xCF, 0x8C, 0xE3, 0xA2,
  297. 0x0A, 0x54, 0x1D, 0x33, 0x99, 0x40, 0x17, 0xD0, 0x20, 0x0A, 0xE2, 0xC9,
  298. 0x51, 0x6E, 0x2F, 0xF5, 0x14, 0x57, 0x79, 0x26, 0x9E, 0x86, 0x2B, 0x0F,
  299. 0xB4, 0x74, 0xA2, 0xD5, 0x6D, 0xC3, 0x1E, 0xD5, 0x69, 0xA7, 0x70, 0x0B,
  300. 0x4C, 0x4A, 0xB1, 0x6B, 0x22, 0xA4, 0x55, 0x13, 0x53, 0x1E, 0xF5, 0x23,
  301. 0xD7, 0x12, 0x12, 0x07, 0x7B, 0x5A, 0x16, 0x9B, 0xDE, 0xFF, 0xAD, 0x7A,
  302. 0xD9, 0x60, 0x82, 0x84, 0xC7, 0x79, 0x5B, 0x6D, 0x5A, 0x51, 0x83, 0xB8,
  303. 0x70, 0x66, 0xDE, 0x17, 0xD8, 0xD6, 0x71, 0xC9, 0xEB, 0xD8, 0xEC, 0x89,
  304. 0x54, 0x4D, 0x45, 0xEC, 0x06, 0x15, 0x93, 0xD4, 0x42, 0xC6, 0x2A, 0xB9,
  305. 0xCE, 0x3B, 0x1C, 0xB9, 0x94, 0x3A, 0x1D, 0x23, 0xA5, 0xEA, 0x3B, 0xCF,
  306. 0x21, 0xA0, 0x14, 0x71, 0xE6, 0x7E, 0x00, 0x3E, 0x7F, 0x8A, 0x69, 0xC7,
  307. 0x28, 0xBE, 0x49, 0x0B, 0x2F, 0xC8, 0x8C, 0xFE, 0xB9, 0x2D, 0xB6, 0xA2,
  308. 0x15, 0xE5, 0xD0, 0x3C, 0x17, 0xC4, 0x64, 0xC9, 0xAC, 0x1A, 0x46, 0xE2,
  309. 0x03, 0xE1, 0x3F, 0x95, 0x29, 0x95, 0xFB, 0x03, 0xC6, 0x9D, 0x3C, 0xC4,
  310. 0x7F, 0xCB, 0x51, 0x0B, 0x69, 0x98, 0xFF, 0xD3, 0xAA, 0x6D, 0xE7, 0x3C,
  311. 0xF9, 0xF6, 0x38, 0x69
  312. };
  313. static const unsigned char dhtest_2048_256_xA[] = {
  314. 0x08, 0x81, 0x38, 0x2C, 0xDB, 0x87, 0x66, 0x0C, 0x6D, 0xC1, 0x3E, 0x61,
  315. 0x49, 0x38, 0xD5, 0xB9, 0xC8, 0xB2, 0xF2, 0x48, 0x58, 0x1C, 0xC5, 0xE3,
  316. 0x1B, 0x35, 0x45, 0x43, 0x97, 0xFC, 0xE5, 0x0E
  317. };
  318. static const unsigned char dhtest_2048_256_yA[] = {
  319. 0x2E, 0x93, 0x80, 0xC8, 0x32, 0x3A, 0xF9, 0x75, 0x45, 0xBC, 0x49, 0x41,
  320. 0xDE, 0xB0, 0xEC, 0x37, 0x42, 0xC6, 0x2F, 0xE0, 0xEC, 0xE8, 0x24, 0xA6,
  321. 0xAB, 0xDB, 0xE6, 0x6C, 0x59, 0xBE, 0xE0, 0x24, 0x29, 0x11, 0xBF, 0xB9,
  322. 0x67, 0x23, 0x5C, 0xEB, 0xA3, 0x5A, 0xE1, 0x3E, 0x4E, 0xC7, 0x52, 0xBE,
  323. 0x63, 0x0B, 0x92, 0xDC, 0x4B, 0xDE, 0x28, 0x47, 0xA9, 0xC6, 0x2C, 0xB8,
  324. 0x15, 0x27, 0x45, 0x42, 0x1F, 0xB7, 0xEB, 0x60, 0xA6, 0x3C, 0x0F, 0xE9,
  325. 0x15, 0x9F, 0xCC, 0xE7, 0x26, 0xCE, 0x7C, 0xD8, 0x52, 0x3D, 0x74, 0x50,
  326. 0x66, 0x7E, 0xF8, 0x40, 0xE4, 0x91, 0x91, 0x21, 0xEB, 0x5F, 0x01, 0xC8,
  327. 0xC9, 0xB0, 0xD3, 0xD6, 0x48, 0xA9, 0x3B, 0xFB, 0x75, 0x68, 0x9E, 0x82,
  328. 0x44, 0xAC, 0x13, 0x4A, 0xF5, 0x44, 0x71, 0x1C, 0xE7, 0x9A, 0x02, 0xDC,
  329. 0xC3, 0x42, 0x26, 0x68, 0x47, 0x80, 0xDD, 0xDC, 0xB4, 0x98, 0x59, 0x41,
  330. 0x06, 0xC3, 0x7F, 0x5B, 0xC7, 0x98, 0x56, 0x48, 0x7A, 0xF5, 0xAB, 0x02,
  331. 0x2A, 0x2E, 0x5E, 0x42, 0xF0, 0x98, 0x97, 0xC1, 0xA8, 0x5A, 0x11, 0xEA,
  332. 0x02, 0x12, 0xAF, 0x04, 0xD9, 0xB4, 0xCE, 0xBC, 0x93, 0x7C, 0x3C, 0x1A,
  333. 0x3E, 0x15, 0xA8, 0xA0, 0x34, 0x2E, 0x33, 0x76, 0x15, 0xC8, 0x4E, 0x7F,
  334. 0xE3, 0xB8, 0xB9, 0xB8, 0x7F, 0xB1, 0xE7, 0x3A, 0x15, 0xAF, 0x12, 0xA3,
  335. 0x0D, 0x74, 0x6E, 0x06, 0xDF, 0xC3, 0x4F, 0x29, 0x0D, 0x79, 0x7C, 0xE5,
  336. 0x1A, 0xA1, 0x3A, 0xA7, 0x85, 0xBF, 0x66, 0x58, 0xAF, 0xF5, 0xE4, 0xB0,
  337. 0x93, 0x00, 0x3C, 0xBE, 0xAF, 0x66, 0x5B, 0x3C, 0x2E, 0x11, 0x3A, 0x3A,
  338. 0x4E, 0x90, 0x52, 0x69, 0x34, 0x1D, 0xC0, 0x71, 0x14, 0x26, 0x68, 0x5F,
  339. 0x4E, 0xF3, 0x7E, 0x86, 0x8A, 0x81, 0x26, 0xFF, 0x3F, 0x22, 0x79, 0xB5,
  340. 0x7C, 0xA6, 0x7E, 0x29
  341. };
  342. static const unsigned char dhtest_2048_256_xB[] = {
  343. 0x7D, 0x62, 0xA7, 0xE3, 0xEF, 0x36, 0xDE, 0x61, 0x7B, 0x13, 0xD1, 0xAF,
  344. 0xB8, 0x2C, 0x78, 0x0D, 0x83, 0xA2, 0x3B, 0xD4, 0xEE, 0x67, 0x05, 0x64,
  345. 0x51, 0x21, 0xF3, 0x71, 0xF5, 0x46, 0xA5, 0x3D
  346. };
  347. static const unsigned char dhtest_2048_256_yB[] = {
  348. 0x57, 0x5F, 0x03, 0x51, 0xBD, 0x2B, 0x1B, 0x81, 0x74, 0x48, 0xBD, 0xF8,
  349. 0x7A, 0x6C, 0x36, 0x2C, 0x1E, 0x28, 0x9D, 0x39, 0x03, 0xA3, 0x0B, 0x98,
  350. 0x32, 0xC5, 0x74, 0x1F, 0xA2, 0x50, 0x36, 0x3E, 0x7A, 0xCB, 0xC7, 0xF7,
  351. 0x7F, 0x3D, 0xAC, 0xBC, 0x1F, 0x13, 0x1A, 0xDD, 0x8E, 0x03, 0x36, 0x7E,
  352. 0xFF, 0x8F, 0xBB, 0xB3, 0xE1, 0xC5, 0x78, 0x44, 0x24, 0x80, 0x9B, 0x25,
  353. 0xAF, 0xE4, 0xD2, 0x26, 0x2A, 0x1A, 0x6F, 0xD2, 0xFA, 0xB6, 0x41, 0x05,
  354. 0xCA, 0x30, 0xA6, 0x74, 0xE0, 0x7F, 0x78, 0x09, 0x85, 0x20, 0x88, 0x63,
  355. 0x2F, 0xC0, 0x49, 0x23, 0x37, 0x91, 0xAD, 0x4E, 0xDD, 0x08, 0x3A, 0x97,
  356. 0x8B, 0x88, 0x3E, 0xE6, 0x18, 0xBC, 0x5E, 0x0D, 0xD0, 0x47, 0x41, 0x5F,
  357. 0x2D, 0x95, 0xE6, 0x83, 0xCF, 0x14, 0x82, 0x6B, 0x5F, 0xBE, 0x10, 0xD3,
  358. 0xCE, 0x41, 0xC6, 0xC1, 0x20, 0xC7, 0x8A, 0xB2, 0x00, 0x08, 0xC6, 0x98,
  359. 0xBF, 0x7F, 0x0B, 0xCA, 0xB9, 0xD7, 0xF4, 0x07, 0xBE, 0xD0, 0xF4, 0x3A,
  360. 0xFB, 0x29, 0x70, 0xF5, 0x7F, 0x8D, 0x12, 0x04, 0x39, 0x63, 0xE6, 0x6D,
  361. 0xDD, 0x32, 0x0D, 0x59, 0x9A, 0xD9, 0x93, 0x6C, 0x8F, 0x44, 0x13, 0x7C,
  362. 0x08, 0xB1, 0x80, 0xEC, 0x5E, 0x98, 0x5C, 0xEB, 0xE1, 0x86, 0xF3, 0xD5,
  363. 0x49, 0x67, 0x7E, 0x80, 0x60, 0x73, 0x31, 0xEE, 0x17, 0xAF, 0x33, 0x80,
  364. 0xA7, 0x25, 0xB0, 0x78, 0x23, 0x17, 0xD7, 0xDD, 0x43, 0xF5, 0x9D, 0x7A,
  365. 0xF9, 0x56, 0x8A, 0x9B, 0xB6, 0x3A, 0x84, 0xD3, 0x65, 0xF9, 0x22, 0x44,
  366. 0xED, 0x12, 0x09, 0x88, 0x21, 0x93, 0x02, 0xF4, 0x29, 0x24, 0xC7, 0xCA,
  367. 0x90, 0xB8, 0x9D, 0x24, 0xF7, 0x1B, 0x0A, 0xB6, 0x97, 0x82, 0x3D, 0x7D,
  368. 0xEB, 0x1A, 0xFF, 0x5B, 0x0E, 0x8E, 0x4A, 0x45, 0xD4, 0x9F, 0x7F, 0x53,
  369. 0x75, 0x7E, 0x19, 0x13
  370. };
  371. static const unsigned char dhtest_2048_256_Z[] = {
  372. 0x86, 0xC7, 0x0B, 0xF8, 0xD0, 0xBB, 0x81, 0xBB, 0x01, 0x07, 0x8A, 0x17,
  373. 0x21, 0x9C, 0xB7, 0xD2, 0x72, 0x03, 0xDB, 0x2A, 0x19, 0xC8, 0x77, 0xF1,
  374. 0xD1, 0xF1, 0x9F, 0xD7, 0xD7, 0x7E, 0xF2, 0x25, 0x46, 0xA6, 0x8F, 0x00,
  375. 0x5A, 0xD5, 0x2D, 0xC8, 0x45, 0x53, 0xB7, 0x8F, 0xC6, 0x03, 0x30, 0xBE,
  376. 0x51, 0xEA, 0x7C, 0x06, 0x72, 0xCA, 0xC1, 0x51, 0x5E, 0x4B, 0x35, 0xC0,
  377. 0x47, 0xB9, 0xA5, 0x51, 0xB8, 0x8F, 0x39, 0xDC, 0x26, 0xDA, 0x14, 0xA0,
  378. 0x9E, 0xF7, 0x47, 0x74, 0xD4, 0x7C, 0x76, 0x2D, 0xD1, 0x77, 0xF9, 0xED,
  379. 0x5B, 0xC2, 0xF1, 0x1E, 0x52, 0xC8, 0x79, 0xBD, 0x95, 0x09, 0x85, 0x04,
  380. 0xCD, 0x9E, 0xEC, 0xD8, 0xA8, 0xF9, 0xB3, 0xEF, 0xBD, 0x1F, 0x00, 0x8A,
  381. 0xC5, 0x85, 0x30, 0x97, 0xD9, 0xD1, 0x83, 0x7F, 0x2B, 0x18, 0xF7, 0x7C,
  382. 0xD7, 0xBE, 0x01, 0xAF, 0x80, 0xA7, 0xC7, 0xB5, 0xEA, 0x3C, 0xA5, 0x4C,
  383. 0xC0, 0x2D, 0x0C, 0x11, 0x6F, 0xEE, 0x3F, 0x95, 0xBB, 0x87, 0x39, 0x93,
  384. 0x85, 0x87, 0x5D, 0x7E, 0x86, 0x74, 0x7E, 0x67, 0x6E, 0x72, 0x89, 0x38,
  385. 0xAC, 0xBF, 0xF7, 0x09, 0x8E, 0x05, 0xBE, 0x4D, 0xCF, 0xB2, 0x40, 0x52,
  386. 0xB8, 0x3A, 0xEF, 0xFB, 0x14, 0x78, 0x3F, 0x02, 0x9A, 0xDB, 0xDE, 0x7F,
  387. 0x53, 0xFA, 0xE9, 0x20, 0x84, 0x22, 0x40, 0x90, 0xE0, 0x07, 0xCE, 0xE9,
  388. 0x4D, 0x4B, 0xF2, 0xBA, 0xCE, 0x9F, 0xFD, 0x4B, 0x57, 0xD2, 0xAF, 0x7C,
  389. 0x72, 0x4D, 0x0C, 0xAA, 0x19, 0xBF, 0x05, 0x01, 0xF6, 0xF1, 0x7B, 0x4A,
  390. 0xA1, 0x0F, 0x42, 0x5E, 0x3E, 0xA7, 0x60, 0x80, 0xB4, 0xB9, 0xD6, 0xB3,
  391. 0xCE, 0xFE, 0xA1, 0x15, 0xB2, 0xCE, 0xB8, 0x78, 0x9B, 0xB8, 0xA3, 0xB0,
  392. 0xEA, 0x87, 0xFE, 0xBE, 0x63, 0xB6, 0xC8, 0xF8, 0x46, 0xEC, 0x6D, 0xB0,
  393. 0xC2, 0x6C, 0x5D, 0x7C
  394. };
  395. static const unsigned char dhtest_rfc5114_2048_224_bad_y[] = {
  396. 0x45, 0x32, 0x5F, 0x51, 0x07, 0xE5, 0xDF, 0x1C, 0xD6, 0x02, 0x82, 0xB3,
  397. 0x32, 0x8F, 0xA4, 0x0F, 0x87, 0xB8, 0x41, 0xFE, 0xB9, 0x35, 0xDE, 0xAD,
  398. 0xC6, 0x26, 0x85, 0xB4, 0xFF, 0x94, 0x8C, 0x12, 0x4C, 0xBF, 0x5B, 0x20,
  399. 0xC4, 0x46, 0xA3, 0x26, 0xEB, 0xA4, 0x25, 0xB7, 0x68, 0x8E, 0xCC, 0x67,
  400. 0xBA, 0xEA, 0x58, 0xD0, 0xF2, 0xE9, 0xD2, 0x24, 0x72, 0x60, 0xDA, 0x88,
  401. 0x18, 0x9C, 0xE0, 0x31, 0x6A, 0xAD, 0x50, 0x6D, 0x94, 0x35, 0x8B, 0x83,
  402. 0x4A, 0x6E, 0xFA, 0x48, 0x73, 0x0F, 0x83, 0x87, 0xFF, 0x6B, 0x66, 0x1F,
  403. 0xA8, 0x82, 0xC6, 0x01, 0xE5, 0x80, 0xB5, 0xB0, 0x52, 0xD0, 0xE9, 0xD8,
  404. 0x72, 0xF9, 0x7D, 0x5B, 0x8B, 0xA5, 0x4C, 0xA5, 0x25, 0x95, 0x74, 0xE2,
  405. 0x7A, 0x61, 0x4E, 0xA7, 0x8F, 0x12, 0xE2, 0xD2, 0x9D, 0x8C, 0x02, 0x70,
  406. 0x34, 0x44, 0x32, 0xC7, 0xB2, 0xF3, 0xB9, 0xFE, 0x17, 0x2B, 0xD6, 0x1F,
  407. 0x8B, 0x7E, 0x4A, 0xFA, 0xA3, 0xB5, 0x3E, 0x7A, 0x81, 0x9A, 0x33, 0x66,
  408. 0x62, 0xA4, 0x50, 0x18, 0x3E, 0xA2, 0x5F, 0x00, 0x07, 0xD8, 0x9B, 0x22,
  409. 0xE4, 0xEC, 0x84, 0xD5, 0xEB, 0x5A, 0xF3, 0x2A, 0x31, 0x23, 0xD8, 0x44,
  410. 0x22, 0x2A, 0x8B, 0x37, 0x44, 0xCC, 0xC6, 0x87, 0x4B, 0xBE, 0x50, 0x9D,
  411. 0x4A, 0xC4, 0x8E, 0x45, 0xCF, 0x72, 0x4D, 0xC0, 0x89, 0xB3, 0x72, 0xED,
  412. 0x33, 0x2C, 0xBC, 0x7F, 0x16, 0x39, 0x3B, 0xEB, 0xD2, 0xDD, 0xA8, 0x01,
  413. 0x73, 0x84, 0x62, 0xB9, 0x29, 0xD2, 0xC9, 0x51, 0x32, 0x9E, 0x7A, 0x6A,
  414. 0xCF, 0xC1, 0x0A, 0xDB, 0x0E, 0xE0, 0x62, 0x77, 0x6F, 0x59, 0x62, 0x72,
  415. 0x5A, 0x69, 0xA6, 0x5B, 0x70, 0xCA, 0x65, 0xC4, 0x95, 0x6F, 0x9A, 0xC2,
  416. 0xDF, 0x72, 0x6D, 0xB1, 0x1E, 0x54, 0x7B, 0x51, 0xB4, 0xEF, 0x7F, 0x89,
  417. 0x93, 0x74, 0x89, 0x59
  418. };
  419. typedef struct {
  420. DH *(*get_param) (void);
  421. const unsigned char *xA;
  422. size_t xA_len;
  423. const unsigned char *yA;
  424. size_t yA_len;
  425. const unsigned char *xB;
  426. size_t xB_len;
  427. const unsigned char *yB;
  428. size_t yB_len;
  429. const unsigned char *Z;
  430. size_t Z_len;
  431. } rfc5114_td;
  432. # define make_rfc5114_td(pre) { \
  433. DH_get_##pre, \
  434. dhtest_##pre##_xA, sizeof(dhtest_##pre##_xA), \
  435. dhtest_##pre##_yA, sizeof(dhtest_##pre##_yA), \
  436. dhtest_##pre##_xB, sizeof(dhtest_##pre##_xB), \
  437. dhtest_##pre##_yB, sizeof(dhtest_##pre##_yB), \
  438. dhtest_##pre##_Z, sizeof(dhtest_##pre##_Z) \
  439. }
  440. static const rfc5114_td rfctd[] = {
  441. make_rfc5114_td(1024_160),
  442. make_rfc5114_td(2048_224),
  443. make_rfc5114_td(2048_256)
  444. };
  445. static int rfc5114_test(void)
  446. {
  447. int i;
  448. DH *dhA = NULL;
  449. DH *dhB = NULL;
  450. unsigned char *Z1 = NULL;
  451. unsigned char *Z2 = NULL;
  452. const rfc5114_td *td = NULL;
  453. BIGNUM *bady = NULL, *priv_key = NULL, *pub_key = NULL;
  454. const BIGNUM *pub_key_tmp;
  455. for (i = 0; i < (int)OSSL_NELEM(rfctd); i++) {
  456. td = rfctd + i;
  457. /* Set up DH structures setting key components */
  458. if (!TEST_ptr(dhA = td->get_param())
  459. || !TEST_ptr(dhB = td->get_param()))
  460. goto bad_err;
  461. if (!TEST_ptr(priv_key = BN_bin2bn(td->xA, td->xA_len, NULL))
  462. || !TEST_ptr(pub_key = BN_bin2bn(td->yA, td->yA_len, NULL))
  463. || !TEST_true(DH_set0_key(dhA, pub_key, priv_key)))
  464. goto bad_err;
  465. if (!TEST_ptr(priv_key = BN_bin2bn(td->xB, td->xB_len, NULL))
  466. || !TEST_ptr(pub_key = BN_bin2bn(td->yB, td->yB_len, NULL))
  467. || !TEST_true( DH_set0_key(dhB, pub_key, priv_key)))
  468. goto bad_err;
  469. priv_key = pub_key = NULL;
  470. if (!TEST_uint_eq(td->Z_len, (size_t)DH_size(dhA))
  471. || !TEST_uint_eq(td->Z_len, (size_t)DH_size(dhB)))
  472. goto err;
  473. if (!TEST_ptr(Z1 = OPENSSL_malloc(DH_size(dhA)))
  474. || !TEST_ptr(Z2 = OPENSSL_malloc(DH_size(dhB))))
  475. goto bad_err;
  476. /*
  477. * Work out shared secrets using both sides and compare with expected
  478. * values.
  479. */
  480. DH_get0_key(dhB, &pub_key_tmp, NULL);
  481. if (!TEST_int_ne(DH_compute_key(Z1, pub_key_tmp, dhA), -1))
  482. goto bad_err;
  483. DH_get0_key(dhA, &pub_key_tmp, NULL);
  484. if (!TEST_int_ne(DH_compute_key(Z2, pub_key_tmp, dhB), -1))
  485. goto bad_err;
  486. if (!TEST_mem_eq(Z1, td->Z_len, td->Z, td->Z_len)
  487. || !TEST_mem_eq(Z2, td->Z_len, td->Z, td->Z_len))
  488. goto err;
  489. DH_free(dhA);
  490. dhA = NULL;
  491. DH_free(dhB);
  492. dhB = NULL;
  493. OPENSSL_free(Z1);
  494. Z1 = NULL;
  495. OPENSSL_free(Z2);
  496. Z2 = NULL;
  497. }
  498. /* Now i == OSSL_NELEM(rfctd) */
  499. /* RFC5114 uses unsafe primes, so now test an invalid y value */
  500. if (!TEST_ptr(dhA = DH_get_2048_224())
  501. || !TEST_ptr(Z1 = OPENSSL_malloc(DH_size(dhA))))
  502. goto bad_err;
  503. if (!TEST_ptr(bady = BN_bin2bn(dhtest_rfc5114_2048_224_bad_y,
  504. sizeof(dhtest_rfc5114_2048_224_bad_y),
  505. NULL)))
  506. goto bad_err;
  507. if (!DH_generate_key(dhA))
  508. goto bad_err;
  509. if (DH_compute_key(Z1, bady, dhA) != -1) {
  510. /*
  511. * DH_compute_key should fail with -1. If we get here we unexpectedly
  512. * allowed an invalid y value
  513. */
  514. goto err;
  515. }
  516. /* We'll have a stale error on the queue from the above test so clear it */
  517. ERR_clear_error();
  518. BN_free(bady);
  519. DH_free(dhA);
  520. OPENSSL_free(Z1);
  521. return 1;
  522. bad_err:
  523. BN_free(bady);
  524. DH_free(dhA);
  525. DH_free(dhB);
  526. BN_free(pub_key);
  527. BN_free(priv_key);
  528. OPENSSL_free(Z1);
  529. OPENSSL_free(Z2);
  530. TEST_error("Initialisation error RFC5114 set %d\n", i + 1);
  531. return 0;
  532. err:
  533. BN_free(bady);
  534. DH_free(dhA);
  535. DH_free(dhB);
  536. OPENSSL_free(Z1);
  537. OPENSSL_free(Z2);
  538. TEST_error("Test failed RFC5114 set %d\n", i + 1);
  539. return 0;
  540. }
  541. #endif
  542. int setup_tests(void)
  543. {
  544. #ifdef OPENSSL_NO_DH
  545. TEST_note("No DH support");
  546. #else
  547. ADD_TEST(dh_test);
  548. ADD_TEST(rfc5114_test);
  549. #endif
  550. return 1;
  551. }