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annotate libtomcrypt/notes/rsa-testvectors/oaep-int.txt @ 1900:6110afb6f581
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| author | Matt Johnston <matt@ucc.asn.au> |
|---|---|
| date | Thu, 24 Mar 2022 12:22:07 +0800 |
| parents | 6dba84798cd5 |
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| rev | line source |
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1 # ================================= |
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2 # WORKED-OUT EXAMPLE FOR RSAES-OAEP |
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3 # ================================= |
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4 # |
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5 # This file gives an example of the process of |
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6 # encrypting and decrypting a message with |
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7 # RSAES-OAEP as specified in PKCS #1 v2.1. |
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8 # |
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9 # The message is a bit string of length 128, |
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10 # while the size of the modulus in the public |
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11 # key is 1024 bits. The second representation |
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12 # of the private key is used, which means that |
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13 # CRT is applied in the decryption process. |
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14 # |
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15 # The underlying hash function is SHA-1; the |
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16 # mask generation function is MGF1 with SHA-1 |
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17 # as specified in PKCS #1 v2.1. |
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18 # |
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19 # This file also contains a demonstration of |
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20 # the RSADP decryption primitive with CRT. |
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21 # Finally, DER encodings of the RSA keys are |
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22 # given at the end of the file. |
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23 # |
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24 # |
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25 # Integers are represented by strings of octets |
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26 # with the leftmost octet being the most |
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27 # significant octet. For example, |
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28 # |
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29 # 9,202,000 = (0x)8c 69 50. |
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30 # |
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31 # ============================================= |
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32 |
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33 # ------------------------------ |
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34 # Components of the RSA Key Pair |
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35 # ------------------------------ |
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36 |
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37 # RSA modulus n: |
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38 bb f8 2f 09 06 82 ce 9c 23 38 ac 2b 9d a8 71 f7 |
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39 36 8d 07 ee d4 10 43 a4 40 d6 b6 f0 74 54 f5 1f |
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40 b8 df ba af 03 5c 02 ab 61 ea 48 ce eb 6f cd 48 |
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41 76 ed 52 0d 60 e1 ec 46 19 71 9d 8a 5b 8b 80 7f |
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42 af b8 e0 a3 df c7 37 72 3e e6 b4 b7 d9 3a 25 84 |
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43 ee 6a 64 9d 06 09 53 74 88 34 b2 45 45 98 39 4e |
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44 e0 aa b1 2d 7b 61 a5 1f 52 7a 9a 41 f6 c1 68 7f |
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45 e2 53 72 98 ca 2a 8f 59 46 f8 e5 fd 09 1d bd cb |
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46 |
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47 # RSA public exponent e: |
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48 (0x)11 |
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49 |
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50 # Prime p: |
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51 ee cf ae 81 b1 b9 b3 c9 08 81 0b 10 a1 b5 60 01 |
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52 99 eb 9f 44 ae f4 fd a4 93 b8 1a 9e 3d 84 f6 32 |
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53 12 4e f0 23 6e 5d 1e 3b 7e 28 fa e7 aa 04 0a 2d |
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54 5b 25 21 76 45 9d 1f 39 75 41 ba 2a 58 fb 65 99 |
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55 |
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56 # Prime q: |
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57 c9 7f b1 f0 27 f4 53 f6 34 12 33 ea aa d1 d9 35 |
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58 3f 6c 42 d0 88 66 b1 d0 5a 0f 20 35 02 8b 9d 86 |
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59 98 40 b4 16 66 b4 2e 92 ea 0d a3 b4 32 04 b5 cf |
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60 ce 33 52 52 4d 04 16 a5 a4 41 e7 00 af 46 15 03 |
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61 |
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62 # p's CRT exponent dP: |
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63 54 49 4c a6 3e ba 03 37 e4 e2 40 23 fc d6 9a 5a |
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64 eb 07 dd dc 01 83 a4 d0 ac 9b 54 b0 51 f2 b1 3e |
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65 d9 49 09 75 ea b7 74 14 ff 59 c1 f7 69 2e 9a 2e |
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66 20 2b 38 fc 91 0a 47 41 74 ad c9 3c 1f 67 c9 81 |
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67 |
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68 # q's CRT exponent dQ: |
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69 47 1e 02 90 ff 0a f0 75 03 51 b7 f8 78 86 4c a9 |
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70 61 ad bd 3a 8a 7e 99 1c 5c 05 56 a9 4c 31 46 a7 |
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71 f9 80 3f 8f 6f 8a e3 42 e9 31 fd 8a e4 7a 22 0d |
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72 1b 99 a4 95 84 98 07 fe 39 f9 24 5a 98 36 da 3d |
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73 |
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74 # CRT coefficient qInv: |
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75 b0 6c 4f da bb 63 01 19 8d 26 5b db ae 94 23 b3 |
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76 80 f2 71 f7 34 53 88 50 93 07 7f cd 39 e2 11 9f |
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77 c9 86 32 15 4f 58 83 b1 67 a9 67 bf 40 2b 4e 9e |
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78 2e 0f 96 56 e6 98 ea 36 66 ed fb 25 79 80 39 f7 |
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79 |
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80 # ---------------------------------- |
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81 # Step-by-step RSAES-OAEP Encryption |
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82 # ---------------------------------- |
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83 |
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84 # Message M to be encrypted: |
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85 d4 36 e9 95 69 fd 32 a7 c8 a0 5b bc 90 d3 2c 49 |
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86 |
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87 # Label L: |
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88 (the empty string) |
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89 |
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90 # lHash = Hash(L) |
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91 # DB = lHash || Padding || M |
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92 # seed = random string of octets |
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93 # dbMask = MGF(seed, length(DB)) |
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94 # maskedDB = DB xor dbMask |
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95 # seedMask = MGF(maskedDB, length(seed)) |
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96 # maskedSeed = seed xor seedMask |
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97 # EM = 0x00 || maskedSeed || maskedDB |
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98 |
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99 # lHash: |
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100 da 39 a3 ee 5e 6b 4b 0d 32 55 bf ef 95 60 18 90 |
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101 af d8 07 09 |
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102 |
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103 # DB: |
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104 da 39 a3 ee 5e 6b 4b 0d 32 55 bf ef 95 60 18 90 |
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105 af d8 07 09 00 00 00 00 00 00 00 00 00 00 00 00 |
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106 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |
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107 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |
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108 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 |
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109 00 00 00 00 00 00 00 00 00 00 01 d4 36 e9 95 69 |
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110 fd 32 a7 c8 a0 5b bc 90 d3 2c 49 |
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111 |
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112 # seed: |
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113 aa fd 12 f6 59 ca e6 34 89 b4 79 e5 07 6d de c2 |
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114 f0 6c b5 8f |
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115 |
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116 # dbMask: |
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117 06 e1 de b2 36 9a a5 a5 c7 07 d8 2c 8e 4e 93 24 |
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118 8a c7 83 de e0 b2 c0 46 26 f5 af f9 3e dc fb 25 |
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119 c9 c2 b3 ff 8a e1 0e 83 9a 2d db 4c dc fe 4f f4 |
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120 77 28 b4 a1 b7 c1 36 2b aa d2 9a b4 8d 28 69 d5 |
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121 02 41 21 43 58 11 59 1b e3 92 f9 82 fb 3e 87 d0 |
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122 95 ae b4 04 48 db 97 2f 3a c1 4e af f4 9c 8c 3b |
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123 7c fc 95 1a 51 ec d1 dd e6 12 64 |
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124 |
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125 # maskedDB: |
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126 dc d8 7d 5c 68 f1 ee a8 f5 52 67 c3 1b 2e 8b b4 |
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127 25 1f 84 d7 e0 b2 c0 46 26 f5 af f9 3e dc fb 25 |
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128 c9 c2 b3 ff 8a e1 0e 83 9a 2d db 4c dc fe 4f f4 |
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129 77 28 b4 a1 b7 c1 36 2b aa d2 9a b4 8d 28 69 d5 |
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130 02 41 21 43 58 11 59 1b e3 92 f9 82 fb 3e 87 d0 |
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131 95 ae b4 04 48 db 97 2f 3a c1 4f 7b c2 75 19 52 |
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132 81 ce 32 d2 f1 b7 6d 4d 35 3e 2d |
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133 |
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134 # seedMask: |
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135 41 87 0b 5a b0 29 e6 57 d9 57 50 b5 4c 28 3c 08 |
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136 72 5d be a9 |
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137 |
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138 # maskedSeed: |
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139 eb 7a 19 ac e9 e3 00 63 50 e3 29 50 4b 45 e2 ca |
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140 82 31 0b 26 |
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141 |
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142 # EM = 00 || maskedSeed || maskedDB: |
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143 00 eb 7a 19 ac e9 e3 00 63 50 e3 29 50 4b 45 e2 |
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144 ca 82 31 0b 26 dc d8 7d 5c 68 f1 ee a8 f5 52 67 |
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145 c3 1b 2e 8b b4 25 1f 84 d7 e0 b2 c0 46 26 f5 af |
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146 f9 3e dc fb 25 c9 c2 b3 ff 8a e1 0e 83 9a 2d db |
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147 4c dc fe 4f f4 77 28 b4 a1 b7 c1 36 2b aa d2 9a |
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148 b4 8d 28 69 d5 02 41 21 43 58 11 59 1b e3 92 f9 |
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149 82 fb 3e 87 d0 95 ae b4 04 48 db 97 2f 3a c1 4f |
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150 7b c2 75 19 52 81 ce 32 d2 f1 b7 6d 4d 35 3e 2d |
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151 |
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152 # Ciphertext, the RSA encryption of EM: |
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153 12 53 e0 4d c0 a5 39 7b b4 4a 7a b8 7e 9b f2 a0 |
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154 39 a3 3d 1e 99 6f c8 2a 94 cc d3 00 74 c9 5d f7 |
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155 63 72 20 17 06 9e 52 68 da 5d 1c 0b 4f 87 2c f6 |
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156 53 c1 1d f8 23 14 a6 79 68 df ea e2 8d ef 04 bb |
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157 6d 84 b1 c3 1d 65 4a 19 70 e5 78 3b d6 eb 96 a0 |
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158 24 c2 ca 2f 4a 90 fe 9f 2e f5 c9 c1 40 e5 bb 48 |
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159 da 95 36 ad 87 00 c8 4f c9 13 0a de a7 4e 55 8d |
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160 51 a7 4d df 85 d8 b5 0d e9 68 38 d6 06 3e 09 55 |
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161 |
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162 # -------------------------------------------- |
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163 # Step-by-step RSAES-OAEP Decryption Using CRT |
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164 # -------------------------------------------- |
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165 |
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166 # c = the integer value of C above |
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167 # m1 = c^dP mod p = (c mod p)^dP mod p |
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168 # m2 = c^dQ mod q = (c mod q)^dQ mod q |
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169 # h = (m1-m2)*qInv mod p |
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170 # m = m2 + q*h = the integer value of EM above |
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171 |
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172 # c mod p: |
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173 de 63 d4 72 35 66 fa a7 59 bf e4 08 82 1d d5 25 |
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174 72 ec 92 85 4d df 87 a2 b6 64 d4 4d aa 37 ca 34 |
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175 6a 05 20 3d 82 ff 2d e8 e3 6c ec 1d 34 f9 8e b6 |
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176 05 e2 a7 d2 6d e7 af 36 9c e4 ec ae 14 e3 56 33 |
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177 |
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178 # c mod q: |
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179 a2 d9 24 de d9 c3 6d 62 3e d9 a6 5b 5d 86 2c fb |
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180 ec 8b 19 9c 64 27 9c 54 14 e6 41 19 6e f1 c9 3c |
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181 50 7a 9b 52 13 88 1a ad 05 b4 cc fa 02 8a c1 ec |
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182 61 42 09 74 bf 16 25 83 6b 0b 7d 05 fb b7 53 36 |
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183 |
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184 # m1: |
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185 89 6c a2 6c d7 e4 87 1c 7f c9 68 a8 ed ea 11 e2 |
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186 71 82 4f 0e 03 65 52 17 94 f1 e9 e9 43 b4 a4 4b |
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187 57 c9 e3 95 a1 46 74 78 f5 26 49 6b 4b b9 1f 1c |
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188 ba ea 90 0f fc 60 2c f0 c6 63 6e ba 84 fc 9f f7 |
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189 |
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190 # m2: |
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191 4e bb 22 75 85 f0 c1 31 2d ca 19 e0 b5 41 db 14 |
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192 99 fb f1 4e 27 0e 69 8e 23 9a 8c 27 a9 6c da 9a |
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193 74 09 74 de 93 7b 5c 9c 93 ea d9 46 2c 65 75 02 |
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194 1a 23 d4 64 99 dc 9f 6b 35 89 75 59 60 8f 19 be |
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195 |
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196 # h: |
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197 01 2b 2b 24 15 0e 76 e1 59 bd 8d db 42 76 e0 7b |
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198 fa c1 88 e0 8d 60 47 cf 0e fb 8a e2 ae bd f2 51 |
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199 c4 0e bc 23 dc fd 4a 34 42 43 94 ad a9 2c fc be |
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200 1b 2e ff bb 60 fd fb 03 35 9a 95 36 8d 98 09 25 |
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201 |
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202 # m: |
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203 00 eb 7a 19 ac e9 e3 00 63 50 e3 29 50 4b 45 e2 |
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204 ca 82 31 0b 26 dc d8 7d 5c 68 f1 ee a8 f5 52 67 |
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205 c3 1b 2e 8b b4 25 1f 84 d7 e0 b2 c0 46 26 f5 af |
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206 f9 3e dc fb 25 c9 c2 b3 ff 8a e1 0e 83 9a 2d db |
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207 4c dc fe 4f f4 77 28 b4 a1 b7 c1 36 2b aa d2 9a |
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208 b4 8d 28 69 d5 02 41 21 43 58 11 59 1b e3 92 f9 |
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209 82 fb 3e 87 d0 95 ae b4 04 48 db 97 2f 3a c1 4f |
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210 7b c2 75 19 52 81 ce 32 d2 f1 b7 6d 4d 35 3e 2d |
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211 |
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212 # The intermediate values in the remaining |
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213 # decryption process are the same as during |
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214 # RSAES-OAEP encryption of M. |
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215 |
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216 # ============================================= |
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217 |
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218 # ======================== |
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219 # DER Encoding of RSA Keys |
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220 # ======================== |
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221 |
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222 # ------------ |
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223 # RSAPublicKey |
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224 # ------------ |
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225 30 81 87 |
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226 # modulus |
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227 02 81 81 |
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228 00 bb f8 2f 09 06 82 ce |
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229 9c 23 38 ac 2b 9d a8 71 |
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230 f7 36 8d 07 ee d4 10 43 |
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231 a4 40 d6 b6 f0 74 54 f5 |
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232 1f b8 df ba af 03 5c 02 |
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233 ab 61 ea 48 ce eb 6f cd |
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234 48 76 ed 52 0d 60 e1 ec |
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235 46 19 71 9d 8a 5b 8b 80 |
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236 7f af b8 e0 a3 df c7 37 |
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237 72 3e e6 b4 b7 d9 3a 25 |
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238 84 ee 6a 64 9d 06 09 53 |
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239 74 88 34 b2 45 45 98 39 |
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240 4e e0 aa b1 2d 7b 61 a5 |
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241 1f 52 7a 9a 41 f6 c1 68 |
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242 7f e2 53 72 98 ca 2a 8f |
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243 59 46 f8 e5 fd 09 1d bd |
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244 cb |
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245 # publicExponent |
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246 02 01 |
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247 11 |
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248 |
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249 # ------------- |
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250 # RSAPrivateKey |
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251 # ------------- |
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252 30 82 02 5b |
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253 # version |
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254 02 01 |
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255 00 |
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256 # modulus |
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257 02 81 81 |
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258 00 bb f8 2f 09 06 82 ce |
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259 9c 23 38 ac 2b 9d a8 71 |
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260 f7 36 8d 07 ee d4 10 43 |
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261 a4 40 d6 b6 f0 74 54 f5 |
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262 1f b8 df ba af 03 5c 02 |
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263 ab 61 ea 48 ce eb 6f cd |
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264 48 76 ed 52 0d 60 e1 ec |
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265 46 19 71 9d 8a 5b 8b 80 |
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266 7f af b8 e0 a3 df c7 37 |
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267 72 3e e6 b4 b7 d9 3a 25 |
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268 84 ee 6a 64 9d 06 09 53 |
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269 74 88 34 b2 45 45 98 39 |
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270 4e e0 aa b1 2d 7b 61 a5 |
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271 1f 52 7a 9a 41 f6 c1 68 |
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272 7f e2 53 72 98 ca 2a 8f |
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273 59 46 f8 e5 fd 09 1d bd |
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274 cb |
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275 # publicExponent |
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276 02 01 |
|
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277 11 |
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278 # privateExponent |
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279 02 81 81 |
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280 00 a5 da fc 53 41 fa f2 |
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281 89 c4 b9 88 db 30 c1 cd |
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282 f8 3f 31 25 1e 06 68 b4 |
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283 27 84 81 38 01 57 96 41 |
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284 b2 94 10 b3 c7 99 8d 6b |
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285 c4 65 74 5e 5c 39 26 69 |
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286 d6 87 0d a2 c0 82 a9 39 |
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287 e3 7f dc b8 2e c9 3e da |
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288 c9 7f f3 ad 59 50 ac cf |
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289 bc 11 1c 76 f1 a9 52 94 |
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290 44 e5 6a af 68 c5 6c 09 |
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291 2c d3 8d c3 be f5 d2 0a |
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292 93 99 26 ed 4f 74 a1 3e |
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293 dd fb e1 a1 ce cc 48 94 |
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294 af 94 28 c2 b7 b8 88 3f |
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295 e4 46 3a 4b c8 5b 1c b3 |
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296 c1 |
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297 # prime1 |
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298 02 41 |
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299 00 ee cf ae 81 b1 b9 b3 |
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300 c9 08 81 0b 10 a1 b5 60 |
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301 01 99 eb 9f 44 ae f4 fd |
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302 a4 93 b8 1a 9e 3d 84 f6 |
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303 32 12 4e f0 23 6e 5d 1e |
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304 3b 7e 28 fa e7 aa 04 0a |
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305 2d 5b 25 21 76 45 9d 1f |
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306 39 75 41 ba 2a 58 fb 65 |
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307 99 |
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308 # prime2 |
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309 02 41 |
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310 00 c9 7f b1 f0 27 f4 53 |
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311 f6 34 12 33 ea aa d1 d9 |
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312 35 3f 6c 42 d0 88 66 b1 |
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313 d0 5a 0f 20 35 02 8b 9d |
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314 86 98 40 b4 16 66 b4 2e |
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315 92 ea 0d a3 b4 32 04 b5 |
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316 cf ce 33 52 52 4d 04 16 |
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317 a5 a4 41 e7 00 af 46 15 |
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318 03 |
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319 # exponent1 |
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320 02 40 |
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321 54 49 4c a6 3e ba 03 37 |
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322 e4 e2 40 23 fc d6 9a 5a |
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323 eb 07 dd dc 01 83 a4 d0 |
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324 ac 9b 54 b0 51 f2 b1 3e |
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325 d9 49 09 75 ea b7 74 14 |
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326 ff 59 c1 f7 69 2e 9a 2e |
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327 20 2b 38 fc 91 0a 47 41 |
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328 74 ad c9 3c 1f 67 c9 81 |
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329 # exponent2 |
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330 02 40 |
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331 47 1e 02 90 ff 0a f0 75 |
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332 03 51 b7 f8 78 86 4c a9 |
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333 61 ad bd 3a 8a 7e 99 1c |
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334 5c 05 56 a9 4c 31 46 a7 |
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335 f9 80 3f 8f 6f 8a e3 42 |
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336 e9 31 fd 8a e4 7a 22 0d |
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337 1b 99 a4 95 84 98 07 fe |
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338 39 f9 24 5a 98 36 da 3d |
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339 # coefficient |
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340 02 41 |
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341 00 b0 6c 4f da bb 63 01 |
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342 19 8d 26 5b db ae 94 23 |
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343 b3 80 f2 71 f7 34 53 88 |
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344 50 93 07 7f cd 39 e2 11 |
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345 9f c9 86 32 15 4f 58 83 |
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346 b1 67 a9 67 bf 40 2b 4e |
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347 9e 2e 0f 96 56 e6 98 ea |
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348 36 66 ed fb 25 79 80 39 |
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349 f7 |
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350 |
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351 # ------------------------ |
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352 # PrivateKeyInfo (PKCS #8) |
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353 # ------------------------ |
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354 30 82 02 75 |
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355 # version |
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356 02 01 |
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357 00 |
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358 # privateKeyAlgorithmIdentifier |
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359 30 0d |
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360 06 09 |
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361 2a 86 48 86 f7 0d 01 01 01 |
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362 # parameters |
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363 05 00 |
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364 # privateKey = RSAPrivateKey encoding |
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365 04 82 02 5f |
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366 # DER encoding of RSAPrivateKey structure |
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367 30 82 02 5b ... 79 80 39 f7 |
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368 |
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369 # ============================================= |