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Table 5-6. Cipher instantiation reference (continued) Cipher AES 256 bits CBC EVP_aes_256_cbc( ) aes-256-cbc AES 256 bits CFB EVP_aes_256_cfb( ) aes-256-cfb AES 256 bits OFB EVP_aes_256_ofb( ) aes-256-ofb Blowfish 128 bits ECB EVP_bf_ecb( ) bf-ecb Blowfish 128 bits CBC EVP_bf_cbc( ) bf-cbc Blowfish 128 bits CFB EVP_bf_cfb( ) bf-cfb Blowfish 128 bits OFB EVP_bf_ofb( ) bf-ofb CAST5 128 bits ECB EVP_cast_ecb( ) cast-ecb CAST5 128 bits CBC EVP_cast_cbc( ) cast-cbc CAST5 128 bits CFB EVP_cast_cfb( ) cast-cfb CAST5 128 bits OFB EVP_cast_ofb( ) cast-ofb DES Effective: 56 bits Actual: 64 bits DES Effective: 56 bits Actual: 64 bits DES Effective: 56 bits Actual: 64 bits DES Effective: 56 bits Actual: 64 bits DESX Effective a: 120 bits Actual: 128 bits 3-key Triple-DES Effective: 112 bits Actual: 192 bits 3-key Triple-DES Effective: 112 bits Actual: 192 bits 3-key Triple-DES Effective: 112 bits Actual: 192 bits 3-key Triple-DES Effective: 112 bits Actual: 192 bits 2-key Triple-DES Effective: 112 bits Actual: 128 bits 2-key Triple-DES Effective: 112 bits Actual: 128 bits 2-key Triple-DES Effective: 112 bits Actual: 128 bits 2-key Triple-DES Effective: 112 bits Actual: 128 bits 224 | Chapter 5: Symmetric Encryption Key strength / actual size (if different) Cipher mode Call for EVP_CIPHER object ECB EVP_des_ecb( ) des-ecb CBC EVP_des_cbc( ) des-cbc CFB EVP_des_cfb( ) des-cfb OFB EVP_des_ofb( ) des-ofb CBC EVP_desx_cbc( ) desx ECB EVP_des_ede3( ) des-ede3 CBC EVP_des_ede3_cbc( ) des-ede3-cbc CFB EVP_des_ede3_cfb( ) des-ede3-cfb OFB EVP_des_ede3_ofb( ) des-ede3-ofb ECB EVP_des_ede( ) des-ede CBC EVP_des_ede_cbc( ) des-ede-cbc CFB EVP_des_ede_cfb( ) des-ede-cfb OFB EVP_des_ede_ofb( ) des-ede-ofb IDEA 128 bits ECB EVP_idea_ecb( ) idea-ecb IDEA 128 bits CBC EVP_idea_cbc( ) idea-cbc This is the Title of the Book, eMatter Edition Copyright © 2007 O’Reilly & Associates, Inc. All rights reserved. Cipher lookup string
Table 5-6. Cipher instantiation reference (continued) Key strength / actual size (if Cipher lookup Cipher different) Cipher mode Call for EVP_CIPHER object string IDEA 128 bits CFB EVP_idea_cfb( ) idea-cfb IDEA 128 bits OFB EVP_idea_ofb( ) idea-ofb RC2 128 bits ECB EVP_rc2_ecb( ) rc2-ecb RC2 128 bits CBC EVP_rc2_cbc( ) rc2-cbc RC2 128 bits CFB EVP_rc2_cfb( ) rc2-cfb RC2 128 bits OFB EVP_rc2_ofb( ) rc2-ofb RC4 40 bits n/a EVP_rc4_40( ) rc4-40 RC4 128 bits n/a EVP_rc4( ) rc4 RC5 128 bits ECB EVP_rc5_32_16_12_ecb( ) rc5-ecb RC5 128 bits CBC EVP_rc5_32_16_12_cbc( ) rc5-cbc RC5 128 bits CFB EVP_rc5_32_16_12_cfb( ) rc5-cfb RC5 128 bits OFB EVP_rc5_32_16_12_ofb( ) rc5-ofb a There are known plaintext attacks against DESX that reduce the effective strength to 60 bits, but these are generally considered infeasible. For stream-based modes (CFB and OFB), encryption and decryption are identical operations. Therefore, EVP_EncryptInit_ex( ) and EVP_DecryptInit_ex( ) are interchangeable in these cases. While RC4 can be set up using these instructions, you must be very careful to set it up securely. We discuss how to do so in Recipe 5.23. Here is an example of setting up an encryption context using 128-bit AES in CBC mode: #include #include /* key must be of size EVP_MAX_KEY_LENGTH. * iv must be of size EVP_MAX_IV_LENGTH. */ EVP_CIPHER_CTX *sample_setup(unsigned char *key, unsigned char *iv) { EVP_CIPHER_CTX *ctx; /* This uses the OpenSSL PRNG . See Recipe 11.9 */ RAND_bytes(key, EVP_MAX_KEY_LENGTH); RAND_bytes(iv, EVP_MAX_IV_LENGTH); if (!(ctx = (EVP_CIPHER_CTX *)malloc(sizeof(EVP_CIPHER_CTX)))) return 0; EVP_CIPHER_CTX_init(ctx); EVP_EncryptInit_ex(ctx, EVP_aes_128_cbc( ), 0, key, iv); return ctx; } Performing Block Cipher Setup (for CBC, CFB, OFB, and ECB Modes) in OpenSSL | 225 This is the Title of the Book, eMatter Edition Copyright © 2007 O’Reilly & Associates, Inc. All rights reserved.
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Secure Programming Cookbook ΤΜ fo
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Secure Programming CookbookΤΜ for
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Table of Contents Foreword . . . .
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5.8 Using a Generic OFB Mode Implem
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8.10 Performing Password-Based Auth
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12.10 Restructuring Arrays 672 12.1
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they are in the top 50% of safe dri
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think you are in, you will probably
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the C programming language, with so
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igger risks than anticipated. You s
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Recipe Compatibility Most of the re
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The O’Reilly web site for the boo
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Chapter 1 CHAPTER 1 Safe Initializa
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using the code in this recipe on Wi
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variables you preserve, be sure to
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ptr = (char *)new_environ + (arr_si
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an impersonation token for a thread
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Creating a new process with a restr
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array that is the Privileges field.
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eturn 0; } if (!LookupAccountName(0
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privileges. We strongly advise agai
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#include #include #include #incl
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sockets provide a means by which fi
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The privman library provides a numb
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The potential for security vulnerab
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It’s important to remember that t
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Discussion execve( ) is the system
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should call pclose( ) to clean up t
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dup2(stdout_pipe[1], 1); close(stdo
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lpCommandLine Any command-line argu
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#include #include #include void
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and a saved user ID. * The effectiv
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See Also Recipes 1.3, 1.4, 2.8 2.2
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of the object, regardless of what t
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There are many other situations whe
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if (!(fd = opendir("."))) break; if
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spc_file_wipe( ) A wrapper around t
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if (pattern_pass(fd, buf, sizeof(bu
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CryptReleaseContext(hProvider, 0);
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2.7 Restricting Access Permissions
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eset the umask between your adjustm
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Locking files on Windows Where Unix
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NFS older than Version 3 in particu
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a loop until all the data is read.
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if (!(hResourceLock = CreateMutex(0
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generator. The code presented here
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access to the filesystem, the poten
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Chapter 3 CHAPTER 3 Input Validatio
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components of the system are truste
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try to use them. For example, what
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To combat malicious uses of “%n
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Discussion Buffer overflows get a l
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Unfortunately, strlcpy( ) and strlc
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The second problem area occurs when
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(see Recipe 3.2). The format-string
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safestr_release( ) or safestr_free(
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Solution Unfortunately, integer coe
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which the records begin. Generally,
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pointer or a different value altoge
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if (!(new_environ = (char **)malloc
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if (spc_environ) free(environ); env
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GetFullPathName( ) requires the len
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if (*c != '%' || !isxdigit(c[1]) ||
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3.10 Preventing Cross-Site Scriptin
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* These are HTML tags that do not t
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*ptr++ = *c; } while (*++c != ’>
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Finally, if you are using the LIKE
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Table 3-2. UTF-8 encoding byte sequ
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the connections to the server. The
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SPC_FD_SET read_mask; for (;;) { sp
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To ensure that you choose the right
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See Also Recipe 13.2 4.2 Generating
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This function takes the following a
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} break; default: if (isspace(p[0])
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*p = 0; return output; } } } The pu
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} return result; case -1: if (stric
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#define MAX_WORDLEN 4 /* len parame
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Discussion This function spc_words2
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4.9 Using Salts, Nonces, and Initia
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the lifetime of the key; the counte
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#include #include #include #incl
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#include #include /* This value n
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} CryptReleaseContext(hProvider, hK
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cryptographic one-way hash from a t
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HMAC_CTX c; unsigned long ctr = 0,
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database does not support binary st
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Remember to use a MAC anytime you e
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For many different reasons, it can
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A more portable but less accurate w
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Chapter 5 CHAPTER 5 Symmetric Encry
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Discussion Be sure to read this dis
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Pentium III, which should give a go
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locations where 40-bit keys or 56-b
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can arise. For general-purpose use,
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or similar mechanism is used. As wi
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shares many properties with CTR mod
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case, the faster of the two algorit
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parison to standard modes. As of th
Page 201 and 202: work, which severely limits portabi
Page 203 and 204: Table 5-4. Implementations for the
Page 205 and 206: Plaintext block 1 Plaintext block 2
Page 207 and 208: typedef struct { SPC_KEY_SCHED ks;
Page 209 and 210: If you are using padding and you kn
Page 211 and 212: This function has the following arg
Page 213 and 214: if (ol) *ol = out - start; return 1
Page 215 and 216: that the state function is always r
Page 217 and 218: Note that this code depends on the
Page 219 and 220: if (!il--) return 1; ctx->nonce[ctx
Page 221 and 222: one block at a time, by encrypting
Page 223 and 224: spc_memset(key,0, kl); memcpy(ctx->
Page 225 and 226: 5.9 Using a Generic CTR Mode Implem
Page 227 and 228: These two functions also erase the
Page 229 and 230: we ignore that because it will alwa
Page 231 and 232: Once those bindings are made, the Z
Page 233 and 234: output Buffer into which the plaint
Page 235 and 236: eturn the number of valid bytes in
Page 237 and 238: In CBC, CFB, and OFB modes, encrypt
Page 239 and 240: void spc_pctr_do_odd(SPC_CTR2_CTX *
Page 241 and 242: 5.15 Performing File or Disk Encryp
Page 243 and 244: Therefore, we’ll show you LION, b
Page 245 and 246: } RC4_set_key(&k, HASH_SZ, (char *)
Page 247 and 248: techniques from Chapter 8), the key
Page 249 and 250: communicate asynchronously (that is
Page 251: key Pointer to the encryption key t
Page 255 and 256: While RC2, RC4, and RC5 support abs
Page 257 and 258: The function EVP_CIPHER_CTX_ctrl( )
Page 259 and 260: Discussion As a reminder, use a raw
Page 261 and 262: ol = 0; if (!(ret = (char *)malloc(
Page 263 and 264: The “official” RC4 key setup fu
Page 265 and 266: Discussion One-time pads are provab
Page 267 and 268: Once a provider context has been su
Page 269 and 270: Table 5-8. Symmetric ciphers suppor
Page 271 and 272: hKey Key to use for performing the
Page 273 and 274: if (!CryptAcquireContext(&hProvider
Page 275 and 276: exportable from key objects, but th
Page 277 and 278: Chapter 6 CHAPTER 6 Hashes and Mess
Page 279 and 280: Generally, you should prefer an enc
Page 281 and 282: See Also Recipes 6.7, 6.8, 6.12 6.2
Page 283 and 284: Noncorrelation It should also be co
Page 285 and 286: Let’s look briefly at the pros an
Page 287 and 288: Solution In most cases, instead of
Page 289 and 290: MAC (which we recommend), we strong
Page 291 and 292: Libraries with cryptographic hash f
Page 293 and 294: #include int main(int argc, char *
Page 295 and 296: See Also Implementations of SHA-256
Page 297 and 298: CryptAcquireContext(&hProvider, 0,
Page 299 and 300: To ensure the best security, we str
Page 301 and 302: if (!(vfy = (unsigned char *)malloc
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you might use a library such as Ope
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Otherwise, you can use the HMAC imp
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if (klen inner[i] ^= key[i]; ctx->o
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OMAC has been explicitly specified
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unsigned char c1[SPC_BLOCK_SZ]; /*
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ing the all-zero data block. Each p
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CMAC is the message-integrity compo
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To postprocess, we encrypt the hash
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6.15 Constructing a Hash Function f
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unsigned char b[SPC_KEY_SZ]; size_t
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Figure 6-2. The Mayas-Meyer-Oseas c
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c->ix = 0; c->tl = 0; } static void
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modes such as CWC and CCM are start
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authentication in a straightforward
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SPC_HMAC_Reset(&ctx); SPC_HMAC_Upda
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divide up the data stream between t
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Chapter 7 CHAPTER 7 Public Key Cryp
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The code presented in this chapter
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Because public key encryption is so
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Solution There’s some debate on t
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7.4 Manipulating Big Numbers Proble
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There’s a similar function for as
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Additionally, you can ask for a ran
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In addition, you might wish to test
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Table 7-2. Math operations supporte
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313, 317, 331, 337, 347, 349, 353,
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for (b = 0; !BN_is_odd(x); b++) BN_
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BIGNUM *dP, *dQ, *qInv; } RSA_PRIVA
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This would map to the hexadecimal v
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compute d. Without those two primes
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The constants that may be used to s
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When using OpenSSL, decryption can
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ecommend using it, unless you are c
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ture is valid. A successful check w
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et = RSA_verify(NID_sha1, hash, 20,
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#define MIN(x,y) ((x) > (y) ? (y) :
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memcpy(signedtext, decrypt, 16); if
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h_ret Optional argument that, if no
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siglen The number of bytes written
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data ready to go into the certifica
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ut it requires you to pass in the l
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LjKQ2r1Yt9foxbHdLKZeClqZuzN7PoEmy+b
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ing in data, pass in a pointer to a
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Table 7-6 lists the FILE object-bas
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Solution The correct method depends
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Use across applications For some pe
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key agreement protocol, where both
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consider slightly more sophisticate
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Kerberos does assume that the envir
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The function used to look up user i
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The group structure that is returne
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found, NULL will be returned, and G
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ReferencedDomainName = (LPTSTR)Loca
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if (errno != EINTR && errno != EAGA
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if (!(spc_host_rulecount % 256)) {
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} else { if (inet_addr(tmp) = = INA
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8.5 Generating Random Passwords and
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for this list is not insignificant.
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file, it may allocate a sizable amo
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On Windows, you can use the standar
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Once getpass( ) or readpassphrase(
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ters typed by the user. Instead, th
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compute the future time at which th
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decrypt the encrypted data. To make
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On systems that support MCF through
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for (i = 0; i < 1000; i++) { MD5_In
Page 435 and 436:
CryptHashData(hHash1, lpszKey, dwKe
Page 437 and 438:
Solution Use the PBKDF2 method of c
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Verifying a password encrypted usin
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c Pointer to an integer that will r
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each of these pieces of information
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server-side part of the authenticat
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8.14 Authenticating with HTTP Cooki
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char *spc_cookie_encode(char *cooki
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• Let the salt be public, in whic
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extra Additional application-specif
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xl Pointer into which the length of
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With a valid socket descriptor in h
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11. The client and the server compu
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Some people like to use a fixed mod
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Often, you’ll want to generate a
Page 465 and 466:
Discussion Remember, authentication
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• Provide the user with some way
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if (!fgets(answer, sizeof(answer),
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uffer = (char *)realloc(buffer, buf
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compromise. If our system has such
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When using RSA, if you’re doing o
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see the confirmation request and th
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Upon receipt of a response to a con
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BOOL SpcConfirmationCreate(LPCTSTR
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Additionally, over time, SSPI-speci
Page 485 and 486:
if (!spc_verify_cert_hostname(SSL_g
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The next step is to call spc_accept
Page 489 and 490:
Discussion Session caching is norma
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if (BIO_do_connect(conn)
Page 493 and 494:
The next step is to connect to the
Page 495 and 496:
DWORD dwHeadersLength = 0; LPSTR lp
Page 497 and 498:
attempt to develop and debug SSL-en
Page 499 and 500:
API for encryption and decryption,
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memcpy(in_data.data, inbuf, inlen);
Page 503 and 504:
*outlen = out_data.length - (blksz
Page 505 and 506:
so. Likewise, any process with the
Page 507 and 508:
struct sockaddr_un *addr_unix; *dom
Page 509 and 510:
error_exit: if (sock) spc_socket_cl
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different ways. On FreeBSD systems,
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msg.msg_iov->iov_base = (void *)&sy
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it’s unique and unpredictable! Yo
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if (mysql_real_connect(mysql, host,
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maintenance. Adding or removing ser
Page 521 and 522:
ut they shouldn’t tolerate reorde
Page 523 and 524:
#define SPC_CLIENT_DISTINGUISHER 0x
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} static void spc_ssock_write( int
Page 527 and 528:
while (mlen) { if ((r = read(fd, ms
Page 529 and 530:
In such cases, you need to be able
Page 531 and 532:
Discussion One of the big motivator
Page 533 and 534:
A digital certificate contains info
Page 535 and 536:
Certificate revocation What happens
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cate as long as it still has its pr
Page 539 and 540:
Currently, OCSP is not nearly as wi
Page 541 and 542:
ple is the permissible uses for a c
Page 543 and 544:
automated email to the address you
Page 545 and 546:
The type of code-signing certificat
Page 547 and 548:
10.3 Using Root Certificates Proble
Page 549 and 550:
Table 10-1. CA certificates, their
Page 551 and 552:
ights of the entity tied to that ce
Page 553 and 554:
10.5 Performing X.509 Certificate V
Page 555 and 556:
sk_X509_free(spc_store->crls); sk_X
Page 557 and 558:
X509_LOOKUP *lookup; store = X509_S
Page 559 and 560:
CertGetIssuerCertificateFromStore(
Page 561 and 562:
HCERTSTORE hCertStore; PCCERT_CONTE
Page 563 and 564:
See Also Recipe 10.11 10.7 Verifyin
Page 565 and 566:
SPC_X509STORE_SSL_VERIFY_NONE This
Page 567 and 568:
verify_flags |= SSL_VERIFY_FAIL_IF_
Page 569 and 570:
int spc_verify_cert_hostname(X509 *
Page 571 and 572:
for (i = 0; !bResult && i < pNameIn
Page 573 and 574:
only work you really need to do is
Page 575 and 576:
digest = EVP_sha1( ); fingerprint_l
Page 577 and 578:
if (cert && (uri = get_distribution
Page 579 and 580:
"\xb3\x9c\x25\xb1\xc3\x2e\x32\x53\x
Page 581 and 582:
headerlen -= (*datalen + 2); if (*d
Page 583 and 584:
In this recipe, we have used a numb
Page 585 and 586:
{ "\x8d\x26\xff\x2f\x31\x6d\x59x\29
Page 587 and 588:
LocalFree(pvStructInfo); return 0;
Page 589 and 590:
lpFullBuffer = lpNewBuffer; lpBuffe
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of tunable variables that affect th
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SPC_OCSPRESULT_CERTIFICATE_VALID =
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* All done. Set the return code bas
Page 597 and 598:
Solution There are essentially thre
Page 599 and 600:
the byte is even, he reduces the nu
Page 601 and 602:
See Also Recipes 11.16, 11.18, 11.1
Page 603 and 604:
11.3 Using the Standard Unix Random
Page 605 and 606:
a pointer to data. Instead, they re
Page 607 and 608:
if (errno = = EINTR) continue; perr
Page 609 and 610:
Here we show how to use this functi
Page 611 and 612:
attacks are a realistic threat, you
Page 613 and 614:
This function never fails (save for
Page 615 and 616:
Using a stream cipher as a generato
Page 617 and 618:
One very safe way to use a cryptogr
Page 619 and 620:
out Buffer into which the random da
Page 621 and 622:
1. Figure out how big a seed you ne
Page 623 and 624:
0x00 Query the amount of entropy be
Page 625 and 626:
strncpy(a.sun_path, EGD_SOCKET_PATH
Page 627 and 628:
} } while (nb = = -1); } } } See Al
Page 629 and 630:
nbytes Number of bytes of entropy t
Page 631 and 632:
See Also • EGADS by Secure Softwa
Page 633 and 634:
If the generator is not seeded with
Page 635 and 636:
Discussion In all cases, you will s
Page 637 and 638:
Solution Because of the way that fl
Page 639 and 640:
double spc_rand_cunifvariate(double
Page 641 and 642:
See Also Recipe 11.11 11.16 Compres
Page 643 and 644:
It would be nice if you did not hav
Page 645 and 646:
For this reason, we think the full
Page 647 and 648:
} int cur_val, i, j, runsz; unsigne
Page 649 and 650:
See Also • NIST Cryptographic Mod
Page 651 and 652:
ecause even if a source does fail c
Page 653 and 654:
you use a seed file, you can just c
Page 655 and 656:
• If you have to accept data from
Page 657 and 658:
with a high-resolution clock (i.e.,
Page 659 and 660:
Collecting entropy from the keyboar
Page 661 and 662:
f[c + 2] = '>'; } else snprintf(bf,
Page 663 and 664:
SpcGatherKeyboardEntropy( ) uses th
Page 665 and 666:
} } if (hWndParent) EnableWindow(hW
Page 667 and 668:
number of bits of entropy has been
Page 669 and 670:
} return TRUE; pDlgData->cbRequeste
Page 671 and 672:
See Also Recipes 11.19, 11.20 11.22
Page 673 and 674:
Discussion We strongly recommend th
Page 675 and 676:
Chapter 12 CHAPTER 12 Anti-Tamperin
Page 677 and 678:
tecture-specific checks to determin
Page 679 and 680:
ure or to examine a hardware valida
Page 681 and 682:
• Detecting modification to a com
Page 683 and 684:
for (j = 8; j > 0; j--) { if (crc &
Page 685 and 686:
#include CRC_START_BLOCK(test) int
Page 687 and 688:
Solution Obfuscating compiled code
Page 689 and 690:
" movl 0f( , %%ebx ), %%eax \n\t" \
Page 691 and 692:
Because library functions are loade
Page 693 and 694:
encoded as a series of 32 Obcode bi
Page 695 and 696:
12.5 Performing Constant Transforms
Page 697 and 698:
12.7 Splitting Variables Problem La
Page 699 and 700:
12.9 Using Function Pointers Proble
Page 701 and 702:
arrays. This array type will hide t
Page 703 and 704:
eak; case SPC_ARRAY_FOLD: index = (
Page 705 and 706:
The following example demonstrates
Page 707 and 708:
Discussion The techniques for hidin
Page 709 and 710:
12.12 Detecting Debuggers Problem S
Page 711 and 712:
Discussion The spc_trap_detect( ) f
Page 713 and 714:
12.14 Detecting Windows Debuggers P
Page 715 and 716:
The int3 interface can also be used
Page 717 and 718:
To demonstrate the effect this macr
Page 719 and 720:
08048388 83 db 83h ; â 08048389 7D
Page 721 and 722:
ine the instruction making the refe
Page 723 and 724:
mprotect(buf, buf_len, PROT_READ |
Page 725 and 726:
eturn 4; } /* get entry point : her
Page 727 and 728:
need to use one of the three ring3
Page 729 and 730:
cates failure, it’s likely that n
Page 731 and 732:
tion gets caught. The only ways to
Page 733 and 734:
memory location will generally stil
Page 735 and 736:
eturn dst; } volatile void *spc_mem
Page 737 and 738:
The mlock( ) system call on Unix im
Page 739 and 740:
Discussion Both C and C++ allow the
Page 741 and 742:
Do not share signal handlers. Sever
Page 743 and 744:
#endif } static int signal_was_caug
Page 745 and 746:
paper reached the widest audience,
Page 747 and 748:
The proper way to handle a program
Page 749 and 750:
handles[0] = cond; handles[1] = mut
Page 751 and 752:
#ifndef WIN32 pool->tids = (pthread
Page 753 and 754:
#define SPC_ACQUIRE_MUTEX(mtx) pthr
Page 755 and 756:
if (socketpool_limit > 0 && socketp
Page 757 and 758:
Table 13-1. Resources that may be l
Page 759 and 760:
ability to run. The default limits
Page 761 and 762:
Note that the structures as present
Page 763 and 764:
access to the machine. This makes i
Page 765:
ing log entries. It is possible, ho
Page 768 and 769:
attacks (continued) capture replay
Page 770 and 771:
CFB (Cipher Feedback) mode, 167, 18
Page 772 and 773:
deriving symmetric keys from a pass
Page 774 and 775:
EVP_CIPHER_CTX_set_padding( ), 227
Page 776 and 777:
integrity checking cipher modes, 16
Page 778 and 779:
message digests (continued) desirab
Page 780 and 781:
parallelizing MACs, 304 parent and
Page 782 and 783:
RAND_bytes( ), 604 RAND_load_file(
Page 784 and 785:
session ID context, 461 session IDs
Page 786 and 787:
spc_gather_keyboard_entropy( ), 631
Page 788 and 789:
symmetric cryptography, 116-154 alg
Page 790 and 791:
Windows (continued) Win 2000, restr
Page 792:
oads. They will often travel up to
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