2 /* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
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3 * All rights reserved.
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5 * This package is an SSL implementation written
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6 * by Eric Young (eay@cryptsoft.com).
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7 * The implementation was written so as to conform with Netscapes SSL.
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9 * This library is free for commercial and non-commercial use as long as
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10 * the following conditions are aheared to. The following conditions
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11 * apply to all code found in this distribution, be it the RC4, RSA,
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12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
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13 * included with this distribution is covered by the same copyright terms
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14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
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16 * Copyright remains Eric Young's, and as such any Copyright notices in
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17 * the code are not to be removed.
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18 * If this package is used in a product, Eric Young should be given attribution
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19 * as the author of the parts of the library used.
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20 * This can be in the form of a textual message at program startup or
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21 * in documentation (online or textual) provided with the package.
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23 * Redistribution and use in source and binary forms, with or without
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24 * modification, are permitted provided that the following conditions
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26 * 1. Redistributions of source code must retain the copyright
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27 * notice, this list of conditions and the following disclaimer.
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28 * 2. Redistributions in binary form must reproduce the above copyright
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29 * notice, this list of conditions and the following disclaimer in the
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30 * documentation and/or other materials provided with the distribution.
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31 * 3. All advertising materials mentioning features or use of this software
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32 * must display the following acknowledgement:
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33 * "This product includes cryptographic software written by
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34 * Eric Young (eay@cryptsoft.com)"
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35 * The word 'cryptographic' can be left out if the rouines from the library
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36 * being used are not cryptographic related :-).
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37 * 4. If you include any Windows specific code (or a derivative thereof) from
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38 * the apps directory (application code) you must include an acknowledgement:
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39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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53 * The licence and distribution terms for any publically available version or
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54 * derivative of this code cannot be changed. i.e. this code cannot simply be
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55 * copied and put under another distribution licence
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56 * [including the GNU Public Licence.]
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58 /* ====================================================================
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59 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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61 * Portions of the attached software ("Contribution") are developed by
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62 * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
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64 * The Contribution is licensed pursuant to the Eric Young open source
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65 * license provided above.
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67 * The binary polynomial arithmetic software is originally written by
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68 * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
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75 #include <openssl/e_os2.h>
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76 #ifndef OPENSSL_NO_FP_API
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77 #include <stdio.h> /* FILE */
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79 #include <openssl/ossl_typ.h>
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85 /* These preprocessor symbols control various aspects of the bignum headers and
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86 * library code. They're not defined by any "normal" configuration, as they are
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87 * intended for development and testing purposes. NB: defining all three can be
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88 * useful for debugging application code as well as openssl itself.
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90 * BN_DEBUG - turn on various debugging alterations to the bignum code
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91 * BN_DEBUG_RAND - uses random poisoning of unused words to trip up
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92 * mismanagement of bignum internals. You must also define BN_DEBUG.
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94 /* #define BN_DEBUG */
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95 /* #define BN_DEBUG_RAND */
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97 #define BN_MUL_COMBA
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98 #define BN_SQR_COMBA
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99 #define BN_RECURSION
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101 /* This next option uses the C libraries (2 word)/(1 word) function.
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102 * If it is not defined, I use my C version (which is slower).
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103 * The reason for this flag is that when the particular C compiler
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104 * library routine is used, and the library is linked with a different
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105 * compiler, the library is missing. This mostly happens when the
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106 * library is built with gcc and then linked using normal cc. This would
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107 * be a common occurrence because gcc normally produces code that is
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108 * 2 times faster than system compilers for the big number stuff.
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109 * For machines with only one compiler (or shared libraries), this should
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110 * be on. Again this in only really a problem on machines
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111 * using "long long's", are 32bit, and are not using my assembler code. */
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112 #if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
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113 defined(OPENSSL_SYS_WIN32) || defined(linux)
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119 /* assuming long is 64bit - this is the DEC Alpha
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120 * unsigned long long is only 64 bits :-(, don't define
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121 * BN_LLONG for the DEC Alpha */
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122 #ifdef SIXTY_FOUR_BIT_LONG
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123 #define BN_ULLONG unsigned long long
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124 #define BN_ULONG unsigned long
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125 #define BN_LONG long
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126 #define BN_BITS 128
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128 #define BN_BITS2 64
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129 #define BN_BITS4 32
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130 #define BN_MASK (0xffffffffffffffffffffffffffffffffLL)
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131 #define BN_MASK2 (0xffffffffffffffffL)
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132 #define BN_MASK2l (0xffffffffL)
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133 #define BN_MASK2h (0xffffffff00000000L)
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134 #define BN_MASK2h1 (0xffffffff80000000L)
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135 #define BN_TBIT (0x8000000000000000L)
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136 #define BN_DEC_CONV (10000000000000000000UL)
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137 #define BN_DEC_FMT1 "%lu"
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138 #define BN_DEC_FMT2 "%019lu"
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139 #define BN_DEC_NUM 19
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142 /* This is where the long long data type is 64 bits, but long is 32.
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143 * For machines where there are 64bit registers, this is the mode to use.
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144 * IRIX, on R4000 and above should use this mode, along with the relevant
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145 * assembler code :-). Do NOT define BN_LLONG.
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147 #ifdef SIXTY_FOUR_BIT
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150 #define BN_ULONG unsigned long long
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151 #define BN_LONG long long
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152 #define BN_BITS 128
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154 #define BN_BITS2 64
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155 #define BN_BITS4 32
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156 #define BN_MASK2 (0xffffffffffffffffLL)
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157 #define BN_MASK2l (0xffffffffL)
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158 #define BN_MASK2h (0xffffffff00000000LL)
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159 #define BN_MASK2h1 (0xffffffff80000000LL)
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160 #define BN_TBIT (0x8000000000000000LL)
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161 #define BN_DEC_CONV (10000000000000000000ULL)
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162 #define BN_DEC_FMT1 "%llu"
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163 #define BN_DEC_FMT2 "%019llu"
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164 #define BN_DEC_NUM 19
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167 #ifdef THIRTY_TWO_BIT
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169 # if defined(OPENSSL_SYS_WIN32) && !defined(__GNUC__)
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170 # define BN_ULLONG unsigned __int64
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172 # define BN_ULLONG unsigned long long
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175 #define BN_ULONG unsigned long
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176 #define BN_LONG long
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179 #define BN_BITS2 32
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180 #define BN_BITS4 16
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181 #ifdef OPENSSL_SYS_WIN32
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182 /* VC++ doesn't like the LL suffix */
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183 #define BN_MASK (0xffffffffffffffffL)
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185 #define BN_MASK (0xffffffffffffffffLL)
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187 #define BN_MASK2 (0xffffffffL)
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188 #define BN_MASK2l (0xffff)
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189 #define BN_MASK2h1 (0xffff8000L)
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190 #define BN_MASK2h (0xffff0000L)
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191 #define BN_TBIT (0x80000000L)
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192 #define BN_DEC_CONV (1000000000L)
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193 #define BN_DEC_FMT1 "%lu"
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194 #define BN_DEC_FMT2 "%09lu"
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195 #define BN_DEC_NUM 9
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202 #define BN_ULLONG unsigned long
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203 #define BN_ULONG unsigned short
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204 #define BN_LONG short
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207 #define BN_BITS2 16
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209 #define BN_MASK (0xffffffff)
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210 #define BN_MASK2 (0xffff)
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211 #define BN_MASK2l (0xff)
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212 #define BN_MASK2h1 (0xff80)
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213 #define BN_MASK2h (0xff00)
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214 #define BN_TBIT (0x8000)
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215 #define BN_DEC_CONV (100000)
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216 #define BN_DEC_FMT1 "%u"
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217 #define BN_DEC_FMT2 "%05u"
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218 #define BN_DEC_NUM 5
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225 #define BN_ULLONG unsigned short
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226 #define BN_ULONG unsigned char
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227 #define BN_LONG char
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232 #define BN_MASK (0xffff)
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233 #define BN_MASK2 (0xff)
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234 #define BN_MASK2l (0xf)
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235 #define BN_MASK2h1 (0xf8)
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236 #define BN_MASK2h (0xf0)
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237 #define BN_TBIT (0x80)
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238 #define BN_DEC_CONV (100)
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239 #define BN_DEC_FMT1 "%u"
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240 #define BN_DEC_FMT2 "%02u"
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241 #define BN_DEC_NUM 2
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244 #define BN_DEFAULT_BITS 1280
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246 #define BN_FLG_MALLOCED 0x01
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247 #define BN_FLG_STATIC_DATA 0x02
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248 #define BN_FLG_EXP_CONSTTIME 0x04 /* avoid leaking exponent information through timings
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249 * (BN_mod_exp_mont() will call BN_mod_exp_mont_consttime) */
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250 #ifndef OPENSSL_NO_DEPRECATED
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251 #define BN_FLG_FREE 0x8000 /* used for debuging */
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253 #define BN_set_flags(b,n) ((b)->flags|=(n))
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254 #define BN_get_flags(b,n) ((b)->flags&(n))
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256 /* get a clone of a BIGNUM with changed flags, for *temporary* use only
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257 * (the two BIGNUMs cannot not be used in parallel!) */
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258 #define BN_with_flags(dest,b,n) ((dest)->d=(b)->d, \
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259 (dest)->top=(b)->top, \
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260 (dest)->dmax=(b)->dmax, \
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261 (dest)->neg=(b)->neg, \
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262 (dest)->flags=(((dest)->flags & BN_FLG_MALLOCED) \
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263 | ((b)->flags & ~BN_FLG_MALLOCED) \
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264 | BN_FLG_STATIC_DATA \
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267 /* Already declared in ossl_typ.h */
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269 typedef struct bignum_st BIGNUM;
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270 /* Used for temp variables (declaration hidden in bn_lcl.h) */
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271 typedef struct bignum_ctx BN_CTX;
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272 typedef struct bn_blinding_st BN_BLINDING;
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273 typedef struct bn_mont_ctx_st BN_MONT_CTX;
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274 typedef struct bn_recp_ctx_st BN_RECP_CTX;
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275 typedef struct bn_gencb_st BN_GENCB;
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280 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */
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281 int top; /* Index of last used d +1. */
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282 /* The next are internal book keeping for bn_expand. */
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283 int dmax; /* Size of the d array. */
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284 int neg; /* one if the number is negative */
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288 /* Used for montgomery multiplication */
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289 struct bn_mont_ctx_st
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291 int ri; /* number of bits in R */
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292 BIGNUM RR; /* used to convert to montgomery form */
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293 BIGNUM N; /* The modulus */
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294 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
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295 * (Ni is only stored for bignum algorithm) */
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296 BN_ULONG n0; /* least significant word of Ni */
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300 /* Used for reciprocal division/mod functions
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301 * It cannot be shared between threads
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303 struct bn_recp_ctx_st
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305 BIGNUM N; /* the divisor */
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306 BIGNUM Nr; /* the reciprocal */
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312 /* Used for slow "generation" functions. */
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315 unsigned int ver; /* To handle binary (in)compatibility */
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316 void *arg; /* callback-specific data */
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319 /* if(ver==1) - handles old style callbacks */
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320 void (*cb_1)(int, int, void *);
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321 /* if(ver==2) - new callback style */
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322 int (*cb_2)(int, int, BN_GENCB *);
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325 /* Wrapper function to make using BN_GENCB easier, */
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326 int BN_GENCB_call(BN_GENCB *cb, int a, int b);
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327 /* Macro to populate a BN_GENCB structure with an "old"-style callback */
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328 #define BN_GENCB_set_old(gencb, callback, cb_arg) { \
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329 BN_GENCB *tmp_gencb = (gencb); \
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330 tmp_gencb->ver = 1; \
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331 tmp_gencb->arg = (cb_arg); \
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332 tmp_gencb->cb.cb_1 = (callback); }
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333 /* Macro to populate a BN_GENCB structure with a "new"-style callback */
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334 #define BN_GENCB_set(gencb, callback, cb_arg) { \
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335 BN_GENCB *tmp_gencb = (gencb); \
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336 tmp_gencb->ver = 2; \
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337 tmp_gencb->arg = (cb_arg); \
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338 tmp_gencb->cb.cb_2 = (callback); }
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340 #define BN_prime_checks 0 /* default: select number of iterations
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341 based on the size of the number */
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343 /* number of Miller-Rabin iterations for an error rate of less than 2^-80
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344 * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
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345 * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
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346 * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
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347 * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
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348 #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \
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356 (b) >= 250 ? 12 : \
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357 (b) >= 200 ? 15 : \
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358 (b) >= 150 ? 18 : \
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361 #define BN_num_bytes(a) ((BN_num_bits(a)+7)/8)
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363 /* Note that BN_abs_is_word didn't work reliably for w == 0 until 0.9.8 */
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364 #define BN_abs_is_word(a,w) ((((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w))) || \
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365 (((w) == 0) && ((a)->top == 0)))
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366 #define BN_is_zero(a) ((a)->top == 0)
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367 #define BN_is_one(a) (BN_abs_is_word((a),1) && !(a)->neg)
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368 #define BN_is_word(a,w) (BN_abs_is_word((a),(w)) && (!(w) || !(a)->neg))
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369 #define BN_is_odd(a) (((a)->top > 0) && ((a)->d[0] & 1))
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371 #define BN_one(a) (BN_set_word((a),1))
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372 #define BN_zero_ex(a) \
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374 BIGNUM *_tmp_bn = (a); \
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375 _tmp_bn->top = 0; \
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376 _tmp_bn->neg = 0; \
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378 #ifdef OPENSSL_NO_DEPRECATED
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379 #define BN_zero(a) BN_zero_ex(a)
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381 #define BN_zero(a) (BN_set_word((a),0))
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384 const BIGNUM *BN_value_one(void);
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385 char * BN_options(void);
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386 BN_CTX *BN_CTX_new(void);
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387 #ifndef OPENSSL_NO_DEPRECATED
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388 void BN_CTX_init(BN_CTX *c);
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390 void BN_CTX_free(BN_CTX *c);
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391 void BN_CTX_start(BN_CTX *ctx);
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392 BIGNUM *BN_CTX_get(BN_CTX *ctx);
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393 void BN_CTX_end(BN_CTX *ctx);
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394 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
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395 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
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396 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
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397 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
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398 int BN_num_bits(const BIGNUM *a);
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399 int BN_num_bits_word(BN_ULONG);
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400 BIGNUM *BN_new(void);
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401 void BN_init(BIGNUM *);
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402 void BN_clear_free(BIGNUM *a);
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403 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
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404 void BN_swap(BIGNUM *a, BIGNUM *b);
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405 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
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406 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
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407 BIGNUM *BN_mpi2bn(const unsigned char *s,int len,BIGNUM *ret);
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408 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
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409 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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410 int BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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411 int BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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412 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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413 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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414 int BN_sqr(BIGNUM *r, const BIGNUM *a,BN_CTX *ctx);
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415 /* BN_set_negative(): sets sign of a bignum */
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416 void BN_set_negative(BIGNUM *b, int n);
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417 /* BN_get_negative(): returns 1 if the bignum is < 0 and 0 otherwise */
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418 #define BN_is_negative(a) ((a)->neg != 0)
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420 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
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422 #define BN_mod(rem,m,d,ctx) BN_div(NULL,(rem),(m),(d),(ctx))
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423 int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
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424 int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
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425 int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
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426 int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
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427 int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m);
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428 int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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429 const BIGNUM *m, BN_CTX *ctx);
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430 int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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431 int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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432 int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m);
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433 int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, BN_CTX *ctx);
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434 int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m);
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436 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
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437 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
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438 int BN_mul_word(BIGNUM *a, BN_ULONG w);
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439 int BN_add_word(BIGNUM *a, BN_ULONG w);
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440 int BN_sub_word(BIGNUM *a, BN_ULONG w);
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441 int BN_set_word(BIGNUM *a, BN_ULONG w);
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442 BN_ULONG BN_get_word(const BIGNUM *a);
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444 int BN_cmp(const BIGNUM *a, const BIGNUM *b);
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445 void BN_free(BIGNUM *a);
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446 int BN_is_bit_set(const BIGNUM *a, int n);
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447 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
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448 int BN_lshift1(BIGNUM *r, const BIGNUM *a);
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449 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,BN_CTX *ctx);
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451 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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452 const BIGNUM *m,BN_CTX *ctx);
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453 int BN_mod_exp_mont(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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454 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
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455 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
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456 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);
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457 int BN_mod_exp_mont_word(BIGNUM *r, BN_ULONG a, const BIGNUM *p,
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458 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
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459 int BN_mod_exp2_mont(BIGNUM *r, const BIGNUM *a1, const BIGNUM *p1,
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460 const BIGNUM *a2, const BIGNUM *p2,const BIGNUM *m,
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461 BN_CTX *ctx,BN_MONT_CTX *m_ctx);
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462 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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463 const BIGNUM *m,BN_CTX *ctx);
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465 int BN_mask_bits(BIGNUM *a,int n);
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466 #ifndef OPENSSL_NO_FP_API
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467 int BN_print_fp(FILE *fp, const BIGNUM *a);
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469 #ifdef HEADER_BIO_H
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470 int BN_print(BIO *fp, const BIGNUM *a);
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472 int BN_print(void *fp, const BIGNUM *a);
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474 int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx);
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475 int BN_rshift(BIGNUM *r, const BIGNUM *a, int n);
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476 int BN_rshift1(BIGNUM *r, const BIGNUM *a);
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477 void BN_clear(BIGNUM *a);
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478 BIGNUM *BN_dup(const BIGNUM *a);
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479 int BN_ucmp(const BIGNUM *a, const BIGNUM *b);
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480 int BN_set_bit(BIGNUM *a, int n);
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481 int BN_clear_bit(BIGNUM *a, int n);
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482 char * BN_bn2hex(const BIGNUM *a);
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483 char * BN_bn2dec(const BIGNUM *a);
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484 int BN_hex2bn(BIGNUM **a, const char *str);
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485 int BN_dec2bn(BIGNUM **a, const char *str);
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486 int BN_gcd(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx);
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487 int BN_kronecker(const BIGNUM *a,const BIGNUM *b,BN_CTX *ctx); /* returns -2 for error */
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488 BIGNUM *BN_mod_inverse(BIGNUM *ret,
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489 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
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490 BIGNUM *BN_mod_sqrt(BIGNUM *ret,
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491 const BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
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493 /* Deprecated versions */
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494 #ifndef OPENSSL_NO_DEPRECATED
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495 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,
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496 const BIGNUM *add, const BIGNUM *rem,
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497 void (*callback)(int,int,void *),void *cb_arg);
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498 int BN_is_prime(const BIGNUM *p,int nchecks,
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499 void (*callback)(int,int,void *),
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500 BN_CTX *ctx,void *cb_arg);
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501 int BN_is_prime_fasttest(const BIGNUM *p,int nchecks,
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502 void (*callback)(int,int,void *),BN_CTX *ctx,void *cb_arg,
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503 int do_trial_division);
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504 #endif /* !defined(OPENSSL_NO_DEPRECATED) */
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506 /* Newer versions */
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507 int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
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508 const BIGNUM *rem, BN_GENCB *cb);
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509 int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
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510 int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
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511 int do_trial_division, BN_GENCB *cb);
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513 BN_MONT_CTX *BN_MONT_CTX_new(void );
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514 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
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515 int BN_mod_mul_montgomery(BIGNUM *r,const BIGNUM *a,const BIGNUM *b,
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516 BN_MONT_CTX *mont, BN_CTX *ctx);
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517 #define BN_to_montgomery(r,a,mont,ctx) BN_mod_mul_montgomery(\
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518 (r),(a),&((mont)->RR),(mont),(ctx))
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519 int BN_from_montgomery(BIGNUM *r,const BIGNUM *a,
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520 BN_MONT_CTX *mont, BN_CTX *ctx);
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521 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
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522 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *mod,BN_CTX *ctx);
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523 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
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524 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
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525 const BIGNUM *mod, BN_CTX *ctx);
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527 /* BN_BLINDING flags */
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528 #define BN_BLINDING_NO_UPDATE 0x00000001
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529 #define BN_BLINDING_NO_RECREATE 0x00000002
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531 BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai, BIGNUM *mod);
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532 void BN_BLINDING_free(BN_BLINDING *b);
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533 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
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534 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
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535 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
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536 int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b, BN_CTX *);
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537 int BN_BLINDING_invert_ex(BIGNUM *n, const BIGNUM *r, BN_BLINDING *b, BN_CTX *);
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538 unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
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539 void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
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540 unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
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541 void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
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542 BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
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543 const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
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544 int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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545 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
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546 BN_MONT_CTX *m_ctx);
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548 #ifndef OPENSSL_NO_DEPRECATED
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549 void BN_set_params(int mul,int high,int low,int mont);
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550 int BN_get_params(int which); /* 0, mul, 1 high, 2 low, 3 mont */
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553 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
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554 BN_RECP_CTX *BN_RECP_CTX_new(void);
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555 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
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556 int BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
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557 int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
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558 BN_RECP_CTX *recp,BN_CTX *ctx);
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559 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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560 const BIGNUM *m, BN_CTX *ctx);
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561 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
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562 BN_RECP_CTX *recp, BN_CTX *ctx);
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564 /* Functions for arithmetic over binary polynomials represented by BIGNUMs.
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566 * The BIGNUM::neg property of BIGNUMs representing binary polynomials is
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569 * Note that input arguments are not const so that their bit arrays can
\r
570 * be expanded to the appropriate size if needed.
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573 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); /*r = a + b*/
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574 #define BN_GF2m_sub(r, a, b) BN_GF2m_add(r, a, b)
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575 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p); /*r=a mod p*/
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576 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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577 const BIGNUM *p, BN_CTX *ctx); /* r = (a * b) mod p */
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578 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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579 BN_CTX *ctx); /* r = (a * a) mod p */
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580 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *b, const BIGNUM *p,
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581 BN_CTX *ctx); /* r = (1 / b) mod p */
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582 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
\r
583 const BIGNUM *p, BN_CTX *ctx); /* r = (a / b) mod p */
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584 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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585 const BIGNUM *p, BN_CTX *ctx); /* r = (a ^ b) mod p */
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586 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
\r
587 BN_CTX *ctx); /* r = sqrt(a) mod p */
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588 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
\r
589 BN_CTX *ctx); /* r^2 + r = a mod p */
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590 #define BN_GF2m_cmp(a, b) BN_ucmp((a), (b))
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591 /* Some functions allow for representation of the irreducible polynomials
\r
592 * as an unsigned int[], say p. The irreducible f(t) is then of the form:
\r
593 * t^p[0] + t^p[1] + ... + t^p[k]
\r
594 * where m = p[0] > p[1] > ... > p[k] = 0.
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596 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[]);
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598 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
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599 const unsigned int p[], BN_CTX *ctx); /* r = (a * b) mod p */
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600 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[],
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601 BN_CTX *ctx); /* r = (a * a) mod p */
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602 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *b, const unsigned int p[],
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603 BN_CTX *ctx); /* r = (1 / b) mod p */
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604 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
\r
605 const unsigned int p[], BN_CTX *ctx); /* r = (a / b) mod p */
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606 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
\r
607 const unsigned int p[], BN_CTX *ctx); /* r = (a ^ b) mod p */
\r
608 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a,
\r
609 const unsigned int p[], BN_CTX *ctx); /* r = sqrt(a) mod p */
\r
610 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a,
\r
611 const unsigned int p[], BN_CTX *ctx); /* r^2 + r = a mod p */
\r
612 int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max);
\r
613 int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a);
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615 /* faster mod functions for the 'NIST primes'
\r
617 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
\r
618 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
\r
619 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
\r
620 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
\r
621 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
\r
623 const BIGNUM *BN_get0_nist_prime_192(void);
\r
624 const BIGNUM *BN_get0_nist_prime_224(void);
\r
625 const BIGNUM *BN_get0_nist_prime_256(void);
\r
626 const BIGNUM *BN_get0_nist_prime_384(void);
\r
627 const BIGNUM *BN_get0_nist_prime_521(void);
\r
629 /* library internal functions */
\r
631 #define bn_expand(a,bits) ((((((bits+BN_BITS2-1))/BN_BITS2)) <= (a)->dmax)?\
\r
632 (a):bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2))
\r
633 #define bn_wexpand(a,words) (((words) <= (a)->dmax)?(a):bn_expand2((a),(words)))
\r
634 BIGNUM *bn_expand2(BIGNUM *a, int words);
\r
635 #ifndef OPENSSL_NO_DEPRECATED
\r
636 BIGNUM *bn_dup_expand(const BIGNUM *a, int words); /* unused */
\r
639 /* Bignum consistency macros
\r
640 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
\r
641 * bignum data after direct manipulations on the data. There is also an
\r
642 * "internal" macro, bn_check_top(), for verifying that there are no leading
\r
643 * zeroes. Unfortunately, some auditing is required due to the fact that
\r
644 * bn_fix_top() has become an overabused duct-tape because bignum data is
\r
645 * occasionally passed around in an inconsistent state. So the following
\r
646 * changes have been made to sort this out;
\r
647 * - bn_fix_top()s implementation has been moved to bn_correct_top()
\r
648 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
\r
649 * bn_check_top() is as before.
\r
650 * - if BN_DEBUG *is* defined;
\r
651 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
\r
652 * consistent. (ed: only if BN_DEBUG_RAND is defined)
\r
653 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
\r
654 * The idea is to have debug builds flag up inconsistent bignums when they
\r
655 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
\r
656 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
\r
657 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
\r
658 * was not appropriate, we convert it permanently to bn_check_top() and track
\r
659 * down the cause of the bug. Eventually, no internal code should be using the
\r
660 * bn_fix_top() macro. External applications and libraries should try this with
\r
661 * their own code too, both in terms of building against the openssl headers
\r
662 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
\r
663 * defined. This not only improves external code, it provides more test
\r
664 * coverage for openssl's own code.
\r
669 /* We only need assert() when debugging */
\r
670 #include <assert.h>
\r
672 #ifdef BN_DEBUG_RAND
\r
673 /* To avoid "make update" cvs wars due to BN_DEBUG, use some tricks */
\r
674 #ifndef RAND_pseudo_bytes
\r
675 int RAND_pseudo_bytes(unsigned char *buf,int num);
\r
676 #define BN_DEBUG_TRIX
\r
678 #define bn_pollute(a) \
\r
680 const BIGNUM *_bnum1 = (a); \
\r
681 if(_bnum1->top < _bnum1->dmax) { \
\r
682 unsigned char _tmp_char; \
\r
683 /* We cast away const without the compiler knowing, any \
\r
684 * *genuinely* constant variables that aren't mutable \
\r
685 * wouldn't be constructed with top!=dmax. */ \
\r
686 BN_ULONG *_not_const; \
\r
687 memcpy(&_not_const, &_bnum1->d, sizeof(BN_ULONG*)); \
\r
688 RAND_pseudo_bytes(&_tmp_char, 1); \
\r
689 memset((unsigned char *)(_not_const + _bnum1->top), _tmp_char, \
\r
690 (_bnum1->dmax - _bnum1->top) * sizeof(BN_ULONG)); \
\r
693 #ifdef BN_DEBUG_TRIX
\r
694 #undef RAND_pseudo_bytes
\r
697 #define bn_pollute(a)
\r
699 #define bn_check_top(a) \
\r
701 const BIGNUM *_bnum2 = (a); \
\r
702 assert((_bnum2->top == 0) || \
\r
703 (_bnum2->d[_bnum2->top - 1] != 0)); \
\r
704 bn_pollute(_bnum2); \
\r
707 #define bn_fix_top(a) bn_check_top(a)
\r
709 #else /* !BN_DEBUG */
\r
711 #define bn_pollute(a)
\r
712 #define bn_check_top(a)
\r
713 #define bn_fix_top(a) bn_correct_top(a)
\r
717 #define bn_correct_top(a) \
\r
720 if ((a)->top > 0) \
\r
722 for (ftl= &((a)->d[(a)->top-1]); (a)->top > 0; (a)->top--) \
\r
723 if (*(ftl--)) break; \
\r
728 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
\r
729 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
\r
730 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
\r
731 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
\r
732 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
\r
733 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int num);
\r
735 int BN_bntest_rand(BIGNUM *rnd, int bits, int top,int bottom);
\r
737 /* BEGIN ERROR CODES */
\r
738 /* The following lines are auto generated by the script mkerr.pl. Any changes
\r
739 * made after this point may be overwritten when the script is next run.
\r
741 void ERR_load_BN_strings(void);
\r
743 /* Error codes for the BN functions. */
\r
745 /* Function codes. */
\r
746 #define BN_F_BNRAND 127
\r
747 #define BN_F_BN_BLINDING_CONVERT_EX 100
\r
748 #define BN_F_BN_BLINDING_CREATE_PARAM 128
\r
749 #define BN_F_BN_BLINDING_INVERT_EX 101
\r
750 #define BN_F_BN_BLINDING_NEW 102
\r
751 #define BN_F_BN_BLINDING_UPDATE 103
\r
752 #define BN_F_BN_BN2DEC 104
\r
753 #define BN_F_BN_BN2HEX 105
\r
754 #define BN_F_BN_CTX_GET 116
\r
755 #define BN_F_BN_CTX_NEW 106
\r
756 #define BN_F_BN_CTX_START 129
\r
757 #define BN_F_BN_DIV 107
\r
758 #define BN_F_BN_DIV_RECP 130
\r
759 #define BN_F_BN_EXP 123
\r
760 #define BN_F_BN_EXPAND2 108
\r
761 #define BN_F_BN_EXPAND_INTERNAL 120
\r
762 #define BN_F_BN_GF2M_MOD 131
\r
763 #define BN_F_BN_GF2M_MOD_EXP 132
\r
764 #define BN_F_BN_GF2M_MOD_MUL 133
\r
765 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD 134
\r
766 #define BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR 135
\r
767 #define BN_F_BN_GF2M_MOD_SQR 136
\r
768 #define BN_F_BN_GF2M_MOD_SQRT 137
\r
769 #define BN_F_BN_MOD_EXP2_MONT 118
\r
770 #define BN_F_BN_MOD_EXP_MONT 109
\r
771 #define BN_F_BN_MOD_EXP_MONT_CONSTTIME 124
\r
772 #define BN_F_BN_MOD_EXP_MONT_WORD 117
\r
773 #define BN_F_BN_MOD_EXP_RECP 125
\r
774 #define BN_F_BN_MOD_EXP_SIMPLE 126
\r
775 #define BN_F_BN_MOD_INVERSE 110
\r
776 #define BN_F_BN_MOD_LSHIFT_QUICK 119
\r
777 #define BN_F_BN_MOD_MUL_RECIPROCAL 111
\r
778 #define BN_F_BN_MOD_SQRT 121
\r
779 #define BN_F_BN_MPI2BN 112
\r
780 #define BN_F_BN_NEW 113
\r
781 #define BN_F_BN_RAND 114
\r
782 #define BN_F_BN_RAND_RANGE 122
\r
783 #define BN_F_BN_USUB 115
\r
785 /* Reason codes. */
\r
786 #define BN_R_ARG2_LT_ARG3 100
\r
787 #define BN_R_BAD_RECIPROCAL 101
\r
788 #define BN_R_BIGNUM_TOO_LONG 114
\r
789 #define BN_R_CALLED_WITH_EVEN_MODULUS 102
\r
790 #define BN_R_DIV_BY_ZERO 103
\r
791 #define BN_R_ENCODING_ERROR 104
\r
792 #define BN_R_EXPAND_ON_STATIC_BIGNUM_DATA 105
\r
793 #define BN_R_INPUT_NOT_REDUCED 110
\r
794 #define BN_R_INVALID_LENGTH 106
\r
795 #define BN_R_INVALID_RANGE 115
\r
796 #define BN_R_NOT_A_SQUARE 111
\r
797 #define BN_R_NOT_INITIALIZED 107
\r
798 #define BN_R_NO_INVERSE 108
\r
799 #define BN_R_NO_SOLUTION 116
\r
800 #define BN_R_P_IS_NOT_PRIME 112
\r
801 #define BN_R_TOO_MANY_ITERATIONS 113
\r
802 #define BN_R_TOO_MANY_TEMPORARY_VARIABLES 109
\r