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@ -53,9 +53,9 @@ For example, for the abridged version of the transport », the…">
<h1><a class="anchor" href="#1-request-req-pq-multi" id="1-request-req-pq-multi" name="1-request-req-pq-multi"><i class="anchor-icon"></i></a>1. request req_pq_multi</h1>
<!-- start req_pq_multi -->
<p>Sent payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 00 00 00 00 00 00 00 00 00 00 00 00 13 90 9C 64
0010 | 14 00 00 00 F1 8E 7E BE A1 F9 B9 D5 B1 C7 24 55
0020 | 20 11 1F B7 30 1C 95 C0</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 00 00 00 00 C4 90 9C 64
0010 | 14 00 00 00 F1 8E 7E BE DF D6 01 C3 D4 AD 9E 9F
0020 | 59 2A 9E 0E 97 B3 E6 03</code></pre>
<p>Payload serialization:</p>
<pre><code>req_pq_multi#be7e8ef1 nonce:int128 = ResPQ;</code></pre>
<table class="table">
@ -77,7 +77,7 @@ For example, for the abridged version of the transport », the…">
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>0000000013909C64</code></td>
<td><code>00000000C4909C64</code></td>
<td>Exact <code>unixtime*2^32</code>, <code>+(4*N)</code> if N messages with the same message ID were already generated</td>
</tr>
<tr>
@ -95,7 +95,7 @@ For example, for the abridged version of the transport », the…">
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Random number</td>
</tr>
</tbody>
@ -104,11 +104,11 @@ For example, for the abridged version of the transport », the…">
<h1><a class="anchor" href="#2-response-respq" id="2-response-respq" name="2-response-respq"><i class="anchor-icon"></i></a>2. response respq</h1>
<!-- start resPQ -->
<p>Received payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 A8 D4 9C 13 90 9C 64
0010 | 78 00 00 00 63 24 16 05 A1 F9 B9 D5 B1 C7 24 55
0020 | 20 11 1F B7 30 1C 95 C0 70 EA 28 24 B9 2F 73 9F
0030 | 4C 26 45 7B 02 94 8D CA 08 28 6C A9 D9 90 2D A7
0040 | ED 00 00 00 15 C4 B5 1C 03 00 00 00 A5 B7 F7 09
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 84 C1 D8 C4 90 9C 64
0010 | 5C 00 00 00 63 24 16 05 DF D6 01 C3 D4 AD 9E 9F
0020 | 59 2A 9E 0E 97 B3 E6 03 74 8B 67 63 BB E5 93 96
0030 | D6 24 9A 28 79 1F F0 70 08 1B 0A 05 21 4E 98 91
0040 | CB 00 00 00 15 C4 B5 1C 03 00 00 00 A5 B7 F7 09
0050 | 35 5F C3 0B 21 6B E8 6C 02 2B B4 C3 85 FD 64 DE
0060 | 85 1D 9D D0</code></pre>
<p>Payload serialization:</p>
@ -132,13 +132,13 @@ For example, for the abridged version of the transport », the…">
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>01A8D49C13909C64</code></td>
<td><code>0184C1D8C4909C64</code></td>
<td>Exact <code>unixtime*2^32</code>, <code>+(4*N)</code> if N messages with the same message ID were already generated</td>
</tr>
<tr>
<td>message_length</td>
<td>16, 4</td>
<td><code>78000000</code> (120 in decimal)</td>
<td><code>5C000000</code> (92 in decimal)</td>
<td>Message body length</td>
</tr>
<tr>
@ -150,19 +150,19 @@ For example, for the abridged version of the transport », the…">
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Server-generated random number</td>
</tr>
<tr>
<td>pq</td>
<td>56, 12</td>
<td><code>08286CA9D9902DA7ED000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 2912889810893776877</td>
<td><code>081B0A05214E9891CB000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1948375429401842123</td>
<td>Single-byte prefix denoting length, an 8-byte string, and three bytes of padding</td>
</tr>
<tr>
@ -207,20 +207,20 @@ For example, for the abridged version of the transport », the…">
<!-- end fingerprints -->
<h1><a class="anchor" href="#21-decompose-p-and-q" id="21-decompose-p-and-q" name="21-decompose-p-and-q"><i class="anchor-icon"></i></a>2.1. decompose p and q</h1>
<!-- start pq -->
<pre><code>pq = 2912889810893776877</code></pre>
<p>Decompose into 2 prime cofactors: <code>1567638131 * 1858139167 = 2912889810893776877</code></p>
<pre><code>p = 1567638131
q = 1858139167</code></pre>
<pre><code>pq = 1948375429401842123</code></pre>
<p>Decompose into 2 prime cofactors: <code>1272587959 * 1531033997 = 1948375429401842123</code></p>
<pre><code>p = 1272587959
q = 1531033997</code></pre>
<!-- end pq -->
<h1><a class="anchor" href="#22-encrypted-data-generation" id="22-encrypted-data-generation" name="22-encrypted-data-generation"><i class="anchor-icon"></i></a>2.2. encrypted_data generation</h1>
<!-- start p_q_inner_data_dc -->
<p>Generated payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 95 5F F5 A9 08 28 6C A9 D9 90 2D A7 ED 00 00 00
0010 | 04 5D 70 42 73 00 00 00 04 6E C0 F4 1F 00 00 00
0020 | A1 F9 B9 D5 B1 C7 24 55 20 11 1F B7 30 1C 95 C0
0030 | 70 EA 28 24 B9 2F 73 9F 4C 26 45 7B 02 94 8D CA
0040 | F6 CB F0 39 C5 6D 79 01 6C 22 33 6A C3 4A C3 CC
0050 | C6 CF 1F 11 32 3A CB FC CB 06 62 7E 94 BB C3 59
<pre><code>0000 | 95 5F F5 A9 08 1B 0A 05 21 4E 98 91 CB 00 00 00
0010 | 04 4B DA 26 B7 00 00 00 04 5B 41 B9 8D 00 00 00
0020 | DF D6 01 C3 D4 AD 9E 9F 59 2A 9E 0E 97 B3 E6 03
0030 | 74 8B 67 63 BB E5 93 96 D6 24 9A 28 79 1F F0 70
0040 | 16 CE AD 6A 85 3A 5B C4 68 E8 1E 7C 54 EC 20 97
0050 | C8 95 5D 1C C6 1F 6B 5F 13 4E 56 46 78 4C C0 81
0060 | 02 00 00 00</code></pre>
<p>Payload serialization:</p>
<pre><code>p_q_inner_data_dc#a9f55f95 pq:string p:string q:string nonce:int128 server_nonce:int128 new_nonce:int256 dc:int = P_Q_inner_data;
@ -246,37 +246,37 @@ p_q_inner_data_temp#3c6a84d4 pq:string p:string q:string nonce:int128 server_non
<tr>
<td>pq</td>
<td>4, 12</td>
<td><code>08286CA9D9902DA7ED000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 2912889810893776877</td>
<td><code>081B0A05214E9891CB000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1948375429401842123</td>
<td>Single-byte prefix denoting length, 8-byte string, and three bytes of padding</td>
</tr>
<tr>
<td>p</td>
<td>16, 8</td>
<td><code>045D704273000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1567638131</td>
<td><code>044BDA26B7000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1272587959</td>
<td>First prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding</td>
</tr>
<tr>
<td>q</td>
<td>24, 8</td>
<td><code>046EC0F41F000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1858139167</td>
<td><code>045B41B98D000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1531033997</td>
<td>Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding</td>
</tr>
<tr>
<td>nonce</td>
<td>32, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>48, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>new_nonce</td>
<td>64, 32</td>
<td><code>F6CBF039C56D79016C22336AC34AC3CC</code> <code>C6CF1F11323ACBFCCB06627E94BBC359</code></td>
<td><code>16CEAD6A853A5BC468E81E7C54EC2097</code> <code>C8955D1CC61F6B5F134E5646784CC081</code></td>
<td>Client-generated random number</td>
</tr>
<tr>
@ -291,39 +291,39 @@ p_q_inner_data_temp#3c6a84d4 pq:string p:string q:string nonce:int128 server_non
<p>The serialization of <em>P_Q_inner_data</em> produces <strong>data</strong>, which is used to generate <strong>encrypted_data</strong> as specified in <a href="/mtproto/auth_key">step 4.1</a>.<br>
These are the inputs to the algorithm specified in <a href="/mtproto/auth_key">step 4.1</a>:</p>
<!-- start p_q_inner_data_input -->
<pre><code>data = 955FF5A908286CA9D9902DA7ED000000045D704273000000046EC0F41F000000A1F9B9D5B1C7245520111FB7301C95C070EA2824B92F739F4C26457B02948DCAF6CBF039C56D79016C22336AC34AC3CCC6CF1F11323ACBFCCB06627E94BBC35902000000
random_padding_bytes = C00B71D54D522A134D231AEE7DD68B5290D97FA57F4C2A735C4A5FC2044F28D9C361D1E16F70C6A33477F27B5EF538D532398E3A34BE17192389F2C3F214F8F2A50C9646E1143EA5B5C421DE5A2F8A20FBDC3F3C08D706F13EDA3BB9</code></pre>
<pre><code>data = 955FF5A9081B0A05214E9891CB000000044BDA26B7000000045B41B98D000000DFD601C3D4AD9E9F592A9E0E97B3E603748B6763BBE59396D6249A28791FF07016CEAD6A853A5BC468E81E7C54EC2097C8955D1CC61F6B5F134E5646784CC08102000000
random_padding_bytes = 0A82901E4C955DEF7CB1FF0A698F2E1AF69116524EA5E8DFCEC0A5EAE4536B99D061DA8BFF2103419464FD69303912D9D62F377CC3245D7347AA1D0F8F8FE881C97EE2DFB2BDBE2E2D88FAAE42594F29D1770E17B44CF4B67CB36486</code></pre>
<!-- end p_q_inner_data_input -->
<p>And this is the output:</p>
<!-- start p_q_inner_data_output -->
<pre><code>encrypted_data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code></pre>
<pre><code>encrypted_data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code></pre>
<!-- end p_q_inner_data_output -->
<p>The length of the final string is 256 bytes.</p>
<h1><a class="anchor" href="#3-request-req-dh-params" id="3-request-req-dh-params" name="3-request-req-dh-params"><i class="anchor-icon"></i></a>3. request req_dh_params</h1>
<!-- start req_DH_params -->
<p>Sent payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 00 00 00 00 00 00 00 00 04 00 00 00 13 90 9C 64
0010 | 40 01 00 00 BE E4 12 D7 A1 F9 B9 D5 B1 C7 24 55
0020 | 20 11 1F B7 30 1C 95 C0 70 EA 28 24 B9 2F 73 9F
0030 | 4C 26 45 7B 02 94 8D CA 04 5D 70 42 73 00 00 00
0040 | 04 6E C0 F4 1F 00 00 00 85 FD 64 DE 85 1D 9D D0
0050 | FE 00 01 00 C5 76 24 03 05 C4 E6 2F 0D 4C 1C 7D
0060 | A7 6D 16 A3 F0 52 9C 38 CC 8A C0 87 C3 A0 98 D4
0070 | 4B 4A 6D 96 E0 50 82 17 EE E9 87 E0 92 F0 79 FE
0080 | 61 ED 02 D7 3B 51 3E 61 2D 1C A3 91 D3 DF F3 AF
0090 | EE 09 19 B4 5A 5E 5F 80 67 75 17 54 3A 26 24 E4
00A0 | 6E 23 85 64 11 83 11 EA BB 00 2E CE 73 BA D0 10
00B0 | C1 DA B4 9F 42 2F F7 00 35 17 72 C0 17 72 14 07
00C0 | B6 05 8F 68 4A 65 C2 71 B6 18 AD 30 B6 FF AC 6F
00D0 | 27 AA 39 F7 42 5E 6C 20 AB 1B 3F 3C EF 22 88 63
00E0 | F8 8D 0E E7 24 09 A5 E7 37 C9 28 56 2C F4 FC A9
00F0 | C2 15 8F BD 92 99 11 26 73 5E 7C 0A 03 6C E4 98
0100 | C9 67 50 17 C1 01 37 AB 1D 05 84 CB 7D 75 97 5D
0110 | E4 F3 D3 74 6B 84 16 AC DA 10 3A 75 3C 0B 24 9D
0120 | 0D 29 D0 E0 E8 12 06 B5 6B C5 83 33 3D EA BE A2
0130 | 03 D7 E4 2A 19 68 0F 4C 39 96 E4 08 E3 69 D2 08
0140 | 53 3C 2C 6E E9 D1 57 4F 37 22 BC D9 EC 15 78 9E
0150 | E2 85 94 2A</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 04 00 00 00 C4 90 9C 64
0010 | 40 01 00 00 BE E4 12 D7 DF D6 01 C3 D4 AD 9E 9F
0020 | 59 2A 9E 0E 97 B3 E6 03 74 8B 67 63 BB E5 93 96
0030 | D6 24 9A 28 79 1F F0 70 04 4B DA 26 B7 00 00 00
0040 | 04 5B 41 B9 8D 00 00 00 85 FD 64 DE 85 1D 9D D0
0050 | FE 00 01 00 C7 B3 79 DA F9 91 44 7C 61 EE E3 4A
0060 | 01 38 05 31 44 E1 FD B4 DD AF A9 19 09 DD F3 5E
0070 | B7 62 DC 35 D1 DE 3F 14 7E 4A 6D C4 4B 70 88 B1
0080 | 3A 68 BA 10 3C 62 11 49 57 85 90 BD D2 2C BE C0
0090 | A6 10 14 AF EE C5 16 23 36 2A ED A4 34 9A E0 F3
00A0 | 55 94 D8 94 17 75 AB 5E 64 6C AB B2 6A 32 14 E7
00B0 | 87 3C 45 83 0E 4A 64 C7 22 C7 E6 0D 17 F9 5D F8
00C0 | 2E CA 38 31 83 CA 1B FA B4 54 5F 27 06 86 0F 61
00D0 | B6 37 27 77 A8 5E DF 44 78 32 27 E3 82 18 35 C7
00E0 | 86 03 11 53 69 E2 EC 01 E7 88 CA B6 24 42 6F 73
00F0 | CD 4B 7B A1 BC A9 AC 83 1A 92 FC A8 78 BE 70 1B
0100 | 12 77 2D EF 1A 7B 38 54 F7 0C 96 F3 85 6B 50 B2
0110 | CC F7 75 E4 F6 61 79 0C FC 3B 44 D4 15 43 2E 00
0120 | D6 D2 A9 8B F9 D7 09 A2 C6 C4 3B D3 01 4D 5F 81
0130 | 02 5D 4A 1B 68 97 70 04 70 8E F7 CB 3F AE 68 F4
0140 | 24 8F 26 A2 C5 2A EB F1 8F 48 47 84 51 D7 46 1D
0150 | 09 02 4A 10</code></pre>
<p>Payload serialization:</p>
<pre><code>req_DH_params#d712e4be nonce:int128 server_nonce:int128 p:string q:string public_key_fingerprint:long encrypted_data:string = Server_DH_Params;</code></pre>
<table class="table">
@ -345,7 +345,7 @@ random_padding_bytes = C00B71D54D522A134D231AEE7DD68B5290D97FA57F4C2A735C4A5FC20
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>0400000013909C64</code></td>
<td><code>04000000C4909C64</code></td>
<td>Exact <code>unixtime*2^32</code>, <code>+(4*N)</code> if N messages with the same message ID were already generated</td>
</tr>
<tr>
@ -363,25 +363,25 @@ random_padding_bytes = C00B71D54D522A134D231AEE7DD68B5290D97FA57F4C2A735C4A5FC20
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>p</td>
<td>56, 8</td>
<td><code>045D704273000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1567638131</td>
<td><code>044BDA26B7000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1272587959</td>
<td>First prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding</td>
</tr>
<tr>
<td>q</td>
<td>64, 8</td>
<td><code>046EC0F41F000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1858139167</td>
<td><code>045B41B98D000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1531033997</td>
<td>Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding</td>
</tr>
<tr>
@ -393,7 +393,7 @@ random_padding_bytes = C00B71D54D522A134D231AEE7DD68B5290D97FA57F4C2A735C4A5FC20
<tr>
<td>encrypted_data</td>
<td>80, 260</td>
<td><code>FE000100C576240305C4E62F0D4C1C7D</code> <code>A76D16A3F0529C38CC8AC087C3A098D4</code> <code>4B4A6D96E0508217EEE987E092F079FE</code> <code>61ED02D73B513E612D1CA391D3DFF3AF</code> <code>EE0919B45A5E5F80677517543A2624E4</code> <code>6E238564118311EABB002ECE73BAD010</code> <code>C1DAB49F422FF700351772C017721407</code> <code>B6058F684A65C271B618AD30B6FFAC6F</code> <code>27AA39F7425E6C20AB1B3F3CEF228863</code> <code>F88D0EE72409A5E737C928562CF4FCA9</code> <code>C2158FBD92991126735E7C0A036CE498</code> <code>C9675017C10137AB1D0584CB7D75975D</code> <code>E4F3D3746B8416ACDA103A753C0B249D</code> <code>0D29D0E0E81206B56BC583333DEABEA2</code> <code>03D7E42A19680F4C3996E408E369D208</code> <code>533C2C6EE9D1574F3722BCD9EC15789EE285942A</code></td>
<td><code>FE000100C7B379DAF991447C61EEE34A</code> <code>0138053144E1FDB4DDAFA91909DDF35E</code> <code>B762DC35D1DE3F147E4A6DC44B7088B1</code> <code>3A68BA103C621149578590BDD22CBEC0</code> <code>A61014AFEEC51623362AEDA4349AE0F3</code> <code>5594D8941775AB5E646CABB26A3214E7</code> <code>873C45830E4A64C722C7E60D17F95DF8</code> <code>2ECA383183CA1BFAB4545F2706860F61</code> <code>B6372777A85EDF44783227E3821835C7</code> <code>8603115369E2EC01E788CAB624426F73</code> <code>CD4B7BA1BCA9AC831A92FCA878BE701B</code> <code>12772DEF1A7B3854F70C96F3856B50B2</code> <code>CCF775E4F661790CFC3B44D415432E00</code> <code>D6D2A98BF9D709A2C6C43BD3014D5F81</code> <code>025D4A1B68977004708EF7CB3FAE68F4</code> <code>248F26A2C52AEBF18F48478451D7461D</code><br> <code>09024A10</code></td>
<td>See <a href="#generation-of-encrypted-data">Generation of encrypted_data »</a></td>
</tr>
</tbody>
@ -402,47 +402,47 @@ random_padding_bytes = C00B71D54D522A134D231AEE7DD68B5290D97FA57F4C2A735C4A5FC20
<h1><a class="anchor" href="#4-response-server-dh-params-ok" id="4-response-server-dh-params-ok" name="4-response-server-dh-params-ok"><i class="anchor-icon"></i></a>4. response server_dh_params_ok</h1>
<!-- start server_DH_params_ok -->
<p>Received payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 C0 2E 41 14 90 9C 64
0010 | A0 02 00 00 5C 07 E8 D0 A1 F9 B9 D5 B1 C7 24 55
0020 | 20 11 1F B7 30 1C 95 C0 70 EA 28 24 B9 2F 73 9F
0030 | 4C 26 45 7B 02 94 8D CA FE 50 02 00 A3 7D DE 27
0040 | DD 2C D8 36 5E 53 A4 4D 45 8F AE C7 07 B8 4F FD
0050 | 0D 1D C6 0F 93 EB 8D EE 86 40 8C DE 4D 4A CC 01
0060 | DE F4 1C A8 F3 F5 53 0C A6 7C 07 C6 0F 80 B3 73
0070 | EB 00 95 4B BA 8D CA 2F EB CC 73 37 48 55 DC AC
0080 | E3 4A 58 4F 83 54 43 B1 4C F6 1B B8 D5 02 32 31
0090 | 5B 84 23 C4 86 09 B4 F9 43 00 AA 85 AC DD 37 AE
00A0 | 48 33 CF 72 62 FD 78 F9 E9 CF 55 91 CC B1 37 16
00B0 | 8C CB 51 C2 32 D0 99 3F B9 13 EB F3 84 28 BA 71
00C0 | 4C 7C 44 3B 54 34 BF F6 EB C2 64 9C D5 2B E1 0D
00D0 | 91 AF EB A2 9E 8F F1 CA E7 90 5E 05 25 04 50 E9
00E0 | D4 A8 2D 32 20 A9 4D E8 CE DA 2F 5B 30 E5 AA 1E
00F0 | E5 FD 30 B4 F8 41 1D 98 1B FD 73 22 65 08 01 49
0100 | 0E BC 4B 06 94 24 93 DB B2 E3 D6 1A EF 42 8E D9
0110 | 63 E1 69 6C 26 42 02 24 65 D2 E4 57 FD F9 70 FC
0120 | 54 A1 68 48 3B 26 E4 57 DA 08 A3 FA 17 BC 17 54
0130 | E6 03 CD F7 17 C6 37 C2 A4 71 6E 86 8E 98 DA 8C
0140 | EE 3C 11 34 62 0C 12 A0 A0 12 9F 13 6C D1 E1 F4
0150 | 4A C1 F6 E9 DB AB 69 A8 DE 5C 1E 98 12 04 95 5E
0160 | E6 D1 47 CF 12 2B C6 D9 69 3C CC 31 C8 46 2B 20
0170 | 51 23 08 52 5C 42 A2 44 4B 00 23 F3 1F 84 91 99
0180 | 21 11 D1 F7 0D 15 B0 60 BC 12 9A 98 C4 8B 1D 3C
0190 | F7 82 F0 80 8D 24 79 CA 42 16 4F FB 92 FD 2C 2D
01A0 | CF EB 56 E4 95 3E CB 49 68 29 E6 FF BA 59 FF F5
01B0 | D8 A6 6E 43 82 D3 AF 89 BC A5 14 38 34 EA 4B 2C
01C0 | 30 C7 DE 8D 65 A3 2F A6 39 0D 57 F7 D5 02 57 8F
01D0 | BA 76 16 20 0D 5B 2E 5B 12 A8 99 B8 EB 10 C9 EF
01E0 | 48 35 C3 B5 ED 95 42 7F 06 3F 0A FD 19 63 AD F6
01F0 | 5C BC 1F EC 55 CC 28 22 DD DE 4A 7E EB DC AD 6E
0200 | AB AD B0 CF 51 A3 D0 FA 5A 14 1B 31 BB E5 75 18
0210 | 7E 6D 7C CC 57 97 7D 2E 7D 86 AA 50 5F 10 F5 00
0220 | 34 58 63 75 DC F2 2B 9C 91 B5 B4 B0 11 51 97 1E
0230 | 20 E1 01 E3 54 18 DF 6C 1E 89 6C BC DF 61 77 FF
0240 | 90 03 B0 DF 21 75 F7 A4 DC 61 C6 FD 7A 76 54 AE
0250 | 50 4C DC A0 1A 22 31 4B 88 D5 4A 1B A4 D6 D4 90
0260 | AB FA 71 DA 42 89 3C D8 28 45 FE 55 DA C2 68 B2
0270 | 00 1D 2B 07 AF 47 B5 09 2F 2B 4A 7D FD D0 98 48
0280 | 0D 53 41 9D 52 DD 93 42 E6 E3 F7 E1</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 64 D0 69 C5 90 9C 64
0010 | C4 02 00 00 5C 07 E8 D0 DF D6 01 C3 D4 AD 9E 9F
0020 | 59 2A 9E 0E 97 B3 E6 03 74 8B 67 63 BB E5 93 96
0030 | D6 24 9A 28 79 1F F0 70 FE 50 02 00 94 1D B6 38
0040 | 9B B2 12 EE 21 EF DC 8F CB F2 2F 9D 12 85 3E 32
0050 | 0D CC C7 98 5D 4E E8 01 A5 B6 71 51 2E C6 22 83
0060 | 30 24 58 49 E5 D1 98 0A B5 D0 13 23 79 36 E7 61
0070 | 30 15 4D 9F 74 2C 8F 49 DB E6 CA B4 50 AC 88 A7
0080 | 4D 38 E7 E1 C1 77 E5 7E BB 4A A5 34 BA 93 DF 89
0090 | 23 BE 4B 1D 60 53 3A 5D DF 80 DD B6 6C E7 BA FA
00A0 | 64 8A 6B FC 79 B6 41 42 1B DD 30 B4 99 2F BB 18
00B0 | 71 F9 4C D8 6F 5C 49 53 E7 54 07 50 EF 5B 80 C0
00C0 | E3 4C A1 59 64 E8 F4 0D C8 7D 39 B6 A5 EC 27 0F
00D0 | FB 84 C7 76 8A FE 7C 03 A0 F2 36 77 28 68 7C 36
00E0 | 42 CE A7 32 51 75 4A C0 28 55 6A ED D2 83 FF 18
00F0 | DB 65 A2 D6 B0 A8 0B 93 F2 ED B5 64 4A BD 97 76
0100 | 2A 5D E6 44 9E 29 C9 DA 78 EF EA EB F0 F6 C9 7E
0110 | 2F 52 F9 9E 99 C9 B8 61 7D 8B B5 BF 76 9F 4B F4
0120 | 29 E6 32 F4 64 D1 C6 55 97 F3 92 B1 19 00 BE 6C
0130 | 78 D2 1C F1 BA BC 49 91 F0 BA 55 7A 57 FF EA 04
0140 | 16 09 E5 03 85 6B FF FD F7 3D 2A 20 39 20 39 C1
0150 | EB 8E 21 A3 BA 95 CC 85 26 7D 00 49 9B 63 9A B2
0160 | F7 34 5E 92 76 D4 20 6C 15 1C 2A A3 A0 00 01 6D
0170 | B8 30 9A 5F 54 E2 65 A6 F4 BE AC 0B DB 48 6D 2A
0180 | CD 53 9C 1D D1 0E 5F 74 96 58 2A 52 48 CD D7 DD
0190 | C8 E6 D4 94 CB 7B BD A2 E9 C7 40 2C 32 70 03 B9
01A0 | 2D 7A A8 BB 77 95 1F D5 83 C1 48 E3 C5 DC 82 C0
01B0 | EE 0C 11 F0 E6 B2 59 0F 3A 13 49 D9 07 6C DE 62
01C0 | C3 A1 62 BA 0E FD 90 60 EC 7F B8 FE F9 DA AB FF
01D0 | F8 6D 4F DC 56 79 CF F1 65 C9 33 DF BF 81 C2 5F
01E0 | 6E DC B2 87 30 17 95 60 A9 34 27 2A 94 4A 64 A2
01F0 | 87 B1 01 ED 18 E8 B0 12 1C 24 EB F6 C0 53 A0 F7
0200 | FB 38 95 8F CC 63 60 D5 2F 66 70 14 99 01 6C 18
0210 | 36 3A 95 D3 AA C8 32 1E ED 62 09 FD 54 B8 6E 13
0220 | 61 E6 CA 2B BE F6 03 C6 6D 4E 8C 73 2D D9 1B EA
0230 | 01 19 13 44 0E 94 77 11 A4 7D 05 2C C7 DB EB 3C
0240 | 4E FF 09 F8 1F C3 8F CD 34 9A E7 9E CE 98 51 AC
0250 | 8F A5 61 1C DC D8 07 85 DD 7F 50 EE 2A 65 2D 32
0260 | E3 D0 FD D6 D9 A7 D1 17 14 B0 4F 6D 4F 50 7F 5B
0270 | E5 04 2C 24 A7 B9 21 AB 1B 1D 0E 8B 3A D2 77 18
0280 | F7 19 8C 34 D9 EA CA 57 E7 95 AC 60</code></pre>
<p>Payload serialization:</p>
<pre><code>server_DH_params_fail#79cb045d nonce:int128 server_nonce:int128 new_nonce_hash:int128 = Server_DH_Params;
server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:string = Server_DH_Params;</code></pre>
@ -465,13 +465,13 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>01C02E4114909C64</code></td>
<td><code>0164D069C5909C64</code></td>
<td>Exact <code>unixtime*2^32</code>, <code>+(4*N)</code> if N messages with the same message ID were already generated</td>
</tr>
<tr>
<td>message_length</td>
<td>16, 4</td>
<td><code>A0020000</code> (672 in decimal)</td>
<td><code>C4020000</code> (708 in decimal)</td>
<td>Message body length</td>
</tr>
<tr>
@ -483,19 +483,19 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>encrypted_answer</td>
<td>56, 596</td>
<td><code>FE500200A37DDE27DD2CD8365E53A44D</code> <code>458FAEC707B84FFD0D1DC60F93EB8DEE</code> <code>86408CDE4D4ACC01DEF41CA8F3F5530C</code> <code>A67C07C60F80B373EB00954BBA8DCA2F</code> <code>EBCC73374855DCACE34A584F835443B1</code> <code>4CF61BB8D50232315B8423C48609B4F9</code> <code>4300AA85ACDD37AE4833CF7262FD78F9</code> <code>E9CF5591CCB137168CCB51C232D0993F</code> <code>B913EBF38428BA714C7C443B5434BFF6</code> <code>EBC2649CD52BE10D91AFEBA29E8FF1CA</code> <code>E7905E05250450E9D4A82D3220A94DE8</code> <code>CEDA2F5B30E5AA1EE5FD30B4F8411D98</code> <code>1BFD7322650801490EBC4B06942493DB</code> <code>B2E3D61AEF428ED963E1696C26420224</code> <code>65D2E457FDF970FC54A168483B26E457</code> <code>DA08A3FA17BC1754E603CDF717C637C2</code> <code>A4716E868E98DA8CEE3C1134620C12A0</code> <code>A0129F136CD1E1F44AC1F6E9DBAB69A8</code> <code>DE5C1E981204955EE6D147CF122BC6D9</code> <code>693CCC31C8462B20512308525C42A244</code> <code>4B0023F31F8491992111D1F70D15B060</code> <code>BC129A98C48B1D3CF782F0808D2479CA</code> <code>42164FFB92FD2C2DCFEB56E4953ECB49</code> <code>6829E6FFBA59FFF5D8A66E4382D3AF89</code> <code>BCA5143834EA4B2C30C7DE8D65A32FA6</code> <code>390D57F7D502578FBA7616200D5B2E5B</code> <code>12A899B8EB10C9EF4835C3B5ED95427F</code> <code>063F0AFD1963ADF65CBC1FEC55CC2822</code> <code>DDDE4A7EEBDCAD6EABADB0CF51A3D0FA</code> <code>5A141B31BBE575187E6D7CCC57977D2E</code> <code>7D86AA505F10F50034586375DCF22B9C</code> <code>91B5B4B01151971E20E101E35418DF6C</code> <code>1E896CBCDF6177FF9003B0DF2175F7A4</code> <code>DC61C6FD7A7654AE504CDCA01A22314B</code> <code>88D54A1BA4D6D490ABFA71DA42893CD8</code> <code>2845FE55DAC268B2001D2B07AF47B509</code> <code>2F2B4A7DFDD098480D53419D52DD9342E6E3F7E1</code></td>
<td><code>FE500200941DB6389BB212EE21EFDC8F</code> <code>CBF22F9D12853E320DCCC7985D4EE801</code> <code>A5B671512EC6228330245849E5D1980A</code> <code>B5D013237936E76130154D9F742C8F49</code> <code>DBE6CAB450AC88A74D38E7E1C177E57E</code> <code>BB4AA534BA93DF8923BE4B1D60533A5D</code> <code>DF80DDB66CE7BAFA648A6BFC79B64142</code> <code>1BDD30B4992FBB1871F94CD86F5C4953</code> <code>E7540750EF5B80C0E34CA15964E8F40D</code> <code>C87D39B6A5EC270FFB84C7768AFE7C03</code> <code>A0F2367728687C3642CEA73251754AC0</code> <code>28556AEDD283FF18DB65A2D6B0A80B93</code> <code>F2EDB5644ABD97762A5DE6449E29C9DA</code> <code>78EFEAEBF0F6C97E2F52F99E99C9B861</code> <code>7D8BB5BF769F4BF429E632F464D1C655</code> <code>97F392B11900BE6C78D21CF1BABC4991</code> <code>F0BA557A57FFEA041609E503856BFFFD</code> <code>F73D2A20392039C1EB8E21A3BA95CC85</code> <code>267D00499B639AB2F7345E9276D4206C</code> <code>151C2AA3A000016DB8309A5F54E265A6</code> <code>F4BEAC0BDB486D2ACD539C1DD10E5F74</code> <code>96582A5248CDD7DDC8E6D494CB7BBDA2</code> <code>E9C7402C327003B92D7AA8BB77951FD5</code> <code>83C148E3C5DC82C0EE0C11F0E6B2590F</code> <code>3A1349D9076CDE62C3A162BA0EFD9060</code> <code>EC7FB8FEF9DAABFFF86D4FDC5679CFF1</code> <code>65C933DFBF81C25F6EDCB28730179560</code> <code>A934272A944A64A287B101ED18E8B012</code> <code>1C24EBF6C053A0F7FB38958FCC6360D5</code> <code>2F66701499016C18363A95D3AAC8321E</code> <code>ED6209FD54B86E1361E6CA2BBEF603C6</code> <code>6D4E8C732DD91BEA011913440E947711</code> <code>A47D052CC7DBEB3C4EFF09F81FC38FCD</code> <code>349AE79ECE9851AC8FA5611CDCD80785</code> <code>DD7F50EE2A652D32E3D0FDD6D9A7D117</code> <code>14B04F6D4F507F5BE5042C24A7B921AB</code> <code>1B1D0E8B3AD27718F7198C34D9EACA57</code><br> <code>E795AC60</code></td>
<td>See <a href="#conversion-of-encrypted-answer-into-answer">Decomposition of encrypted_answer »</a></td>
</tr>
</tbody>
@ -505,9 +505,9 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
<p>Decrypt <code>encrypted_answer</code> using the process specified in step 5.</p>
<!-- start server_DH_inner_data -->
<p>Generated payload (excluding transport headers/trailers):</p>
<pre><code>0000 | BA 0D 89 B5 A1 F9 B9 D5 B1 C7 24 55 20 11 1F B7
0010 | 30 1C 95 C0 70 EA 28 24 B9 2F 73 9F 4C 26 45 7B
0020 | 02 94 8D CA 03 00 00 00 FE 00 01 00 C7 1C AE B9
<pre><code>0000 | BA 0D 89 B5 DF D6 01 C3 D4 AD 9E 9F 59 2A 9E 0E
0010 | 97 B3 E6 03 74 8B 67 63 BB E5 93 96 D6 24 9A 28
0020 | 79 1F F0 70 03 00 00 00 FE 00 01 00 C7 1C AE B9
0030 | C6 B1 C9 04 8E 6C 52 2F 70 F1 3F 73 98 0D 40 23
0040 | 8E 3E 21 C1 49 34 D0 37 56 3D 93 0F 48 19 8A 0A
0050 | A7 C1 40 58 22 94 93 D2 25 30 F4 DB FA 33 6F 6E
@ -524,23 +524,23 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
0100 | F4 7B F9 59 D9 56 85 0C E9 29 85 1F 0D 81 15 F6
0110 | 35 B1 05 EE 2E 4E 15 D0 4B 24 54 BF 6F 4F AD F0
0120 | 34 B1 04 03 11 9C D8 E3 B9 2F CC 5B FE 00 01 00
0130 | 09 0D 87 8A 77 0D 8B C3 9F D6 65 02 CC 47 E2 9A
0140 | AE FF D1 27 DD 15 11 90 70 34 FF 46 76 27 A1 76
0150 | 20 B6 C3 21 E5 C0 4F D3 D4 CE 55 D5 F0 EF 86 14
0160 | F8 89 F4 02 EB FC 70 3E 49 94 51 EC 42 69 F1 AB
0170 | 16 88 57 EE 07 38 DB 48 F7 AE 04 22 BC B9 6E 13
0180 | 1D 27 DA 0F 07 DE D6 01 A5 9A 3E 2C 1F 90 F4 DF
0190 | C9 A2 E4 92 44 06 5B 78 59 23 2D F5 65 0F 0F F2
01A0 | 66 40 C5 23 E6 9F 34 DB 38 38 18 BC B8 26 A1 2F
01B0 | EF B9 84 7C 59 11 A6 23 0D 16 FD F6 C3 79 BF 0C
01C0 | 7D E2 2C CD 57 D5 DC F6 A7 4A AC 3F 8E 88 8B A6
01D0 | 7E AD 2C 7F A6 19 72 9B F0 E4 72 B3 8E C6 B9 AE
01E0 | 45 08 A6 BA E5 20 D9 66 11 EC 65 DD AF 4A 95 CE
01F0 | D2 16 B9 96 A1 EB 50 89 AF 75 E2 4F 5F D2 E5 5E
0200 | 71 69 A3 6C 58 9F A1 31 51 2B C9 49 66 7C BD 73
0210 | B7 97 5D 61 44 A9 E3 8B 0C B1 3F D9 3C 06 ED A8
0220 | 4F 84 3C F5 83 71 88 17 E1 54 D8 A5 08 B7 F2 66
0230 | 14 90 9C 64</code></pre>
0130 | 79 0F 9F 6E E3 E6 FF 34 9C DF EC E3 86 C8 1B 49
0140 | 2A F8 7B 0D B1 00 CB 7C D9 6E E2 9A 6F 74 1A FF
0150 | A7 8F 6A 48 7C 89 80 11 FF 3B 64 7E 3E 1B 79 BC
0160 | AA C2 74 7E 10 FA FA B3 69 AD BA 9E E6 7F DD 31
0170 | 67 9C D3 35 6B 06 9F E3 1F 80 B2 5F 15 D4 6E 86
0180 | 64 03 0E 4B EA 40 7A A8 90 22 C7 CB A2 7B AA E5
0190 | 87 46 5D 8F B5 C0 0B A0 5B 74 92 43 94 1A 11 59
01A0 | 8B 48 45 B4 80 C4 4C 38 0F F8 AC 87 4E FB 22 51
01B0 | 84 17 43 23 28 AD 26 36 29 07 D1 B4 65 0C 02 65
01C0 | 95 49 9F 53 55 82 11 FC 08 D8 00 72 98 00 B6 CF
01D0 | EC 22 F0 E9 EB 56 4C A7 7E 7A 7F 97 D1 A9 21 65
01E0 | 90 1F 65 2A AC DC 09 80 BD F8 A1 F1 0A 09 7D C8
01F0 | 49 0D FA 27 1A 16 DF B0 AB 2D FB 10 28 6F 6E 12
0200 | 03 AB 0A 92 5C DE DE D4 BB 94 00 43 4D 47 C5 90
0210 | 08 E9 67 96 3B E1 1D 5E 12 F5 8B 8B 37 14 88 3F
0220 | 7A 02 48 66 DB 59 3A 32 68 F3 98 CE D9 53 98 37
0230 | C5 90 9C 64</code></pre>
<p>Payload serialization:</p>
<pre><code>server_DH_inner_data#b5890dba nonce:int128 server_nonce:int128 g:int dh_prime:string g_a:string server_time:int = Server_DH_inner_data;</code></pre>
<table class="table">
@ -562,13 +562,13 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
<tr>
<td>nonce</td>
<td>4, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>20, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
@ -580,19 +580,19 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
<tr>
<td>dh_prime</td>
<td>40, 260</td>
<td><code>FE000100C71CAEB9C6B1C9048E6C522F</code> <code>70F13F73980D40238E3E21C14934D037</code> <code>563D930F48198A0AA7C14058229493D2</code> <code>2530F4DBFA336F6E0AC925139543AED4</code> <code>4CCE7C3720FD51F69458705AC68CD4FE</code> <code>6B6B13ABDC9746512969328454F18FAF</code> <code>8C595F642477FE96BB2A941D5BCD1D4A</code> <code>C8CC49880708FA9B378E3C4F3A9060BE</code> <code>E67CF9A4A4A695811051907E162753B5</code> <code>6B0F6B410DBA74D8A84B2A14B3144E0E</code> <code>F1284754FD17ED950D5965B4B9DD4658</code> <code>2DB1178D169C6BC465B0D6FF9CA3928F</code> <code>EF5B9AE4E418FC15E83EBEA0F87FA9FF</code> <code>5EED70050DED2849F47BF959D956850C</code> <code>E929851F0D8115F635B105EE2E4E15D0</code> <code>4B2454BF6F4FADF034B10403119CD8E3B92FCC5B</code></td>
<td><code>FE000100C71CAEB9C6B1C9048E6C522F</code> <code>70F13F73980D40238E3E21C14934D037</code> <code>563D930F48198A0AA7C14058229493D2</code> <code>2530F4DBFA336F6E0AC925139543AED4</code> <code>4CCE7C3720FD51F69458705AC68CD4FE</code> <code>6B6B13ABDC9746512969328454F18FAF</code> <code>8C595F642477FE96BB2A941D5BCD1D4A</code> <code>C8CC49880708FA9B378E3C4F3A9060BE</code> <code>E67CF9A4A4A695811051907E162753B5</code> <code>6B0F6B410DBA74D8A84B2A14B3144E0E</code> <code>F1284754FD17ED950D5965B4B9DD4658</code> <code>2DB1178D169C6BC465B0D6FF9CA3928F</code> <code>EF5B9AE4E418FC15E83EBEA0F87FA9FF</code> <code>5EED70050DED2849F47BF959D956850C</code> <code>E929851F0D8115F635B105EE2E4E15D0</code> <code>4B2454BF6F4FADF034B10403119CD8E3</code><br> <code>B92FCC5B</code></td>
<td>2048-bit prime, in big-endian byte order, to be checked as specified in the auth key docs</td>
</tr>
<tr>
<td>g_a</td>
<td>300, 260</td>
<td><code>FE000100090D878A770D8BC39FD66502</code> <code>CC47E29AAEFFD127DD1511907034FF46</code> <code>7627A17620B6C321E5C04FD3D4CE55D5</code> <code>F0EF8614F889F402EBFC703E499451EC</code> <code>4269F1AB168857EE0738DB48F7AE0422</code> <code>BCB96E131D27DA0F07DED601A59A3E2C</code> <code>1F90F4DFC9A2E49244065B7859232DF5</code> <code>650F0FF26640C523E69F34DB383818BC</code> <code>B826A12FEFB9847C5911A6230D16FDF6</code> <code>C379BF0C7DE22CCD57D5DCF6A74AAC3F</code> <code>8E888BA67EAD2C7FA619729BF0E472B3</code> <code>8EC6B9AE4508A6BAE520D96611EC65DD</code> <code>AF4A95CED216B996A1EB5089AF75E24F</code> <code>5FD2E55E7169A36C589FA131512BC949</code> <code>667CBD73B7975D6144A9E38B0CB13FD9</code> <code>3C06EDA84F843CF583718817E154D8A508B7F266</code></td>
<td><code>FE000100790F9F6EE3E6FF349CDFECE3</code> <code>86C81B492AF87B0DB100CB7CD96EE29A</code> <code>6F741AFFA78F6A487C898011FF3B647E</code> <code>3E1B79BCAAC2747E10FAFAB369ADBA9E</code> <code>E67FDD31679CD3356B069FE31F80B25F</code> <code>15D46E8664030E4BEA407AA89022C7CB</code> <code>A27BAAE587465D8FB5C00BA05B749243</code> <code>941A11598B4845B480C44C380FF8AC87</code> <code>4EFB22518417432328AD26362907D1B4</code> <code>650C026595499F53558211FC08D80072</code> <code>9800B6CFEC22F0E9EB564CA77E7A7F97</code> <code>D1A92165901F652AACDC0980BDF8A1F1</code> <code>0A097DC8490DFA271A16DFB0AB2DFB10</code> <code>286F6E1203AB0A925CDEDED4BB940043</code> <code>4D47C59008E967963BE11D5E12F58B8B</code> <code>3714883F7A024866DB593A3268F398CE</code><br> <code>D9539837</code></td>
<td><code>g_a</code> diffie-hellman parameter</td>
</tr>
<tr>
<td>server_time</td>
<td>560, 4</td>
<td><code>14909C64</code> (1687982100 in decimal)</td>
<td><code>C5909C64</code> (1687982277 in decimal)</td>
<td>Server time</td>
</tr>
</tbody>
@ -601,34 +601,34 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
<h1><a class="anchor" href="#42-generate-diffie-helman-parameters" id="42-generate-diffie-helman-parameters" name="42-generate-diffie-helman-parameters"><i class="anchor-icon"></i></a>4.2. generate diffie-helman parameters</h1>
<p>First, generate a secure random 2048-bit number b:</p>
<!-- start b -->
<pre><code>b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code></pre>
<pre><code>b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code></pre>
<!-- end b -->
<p>Then compute <code>g_b = pow(g, b) mod dh_prime</code></p>
<!-- start g_b -->
<pre><code>g_b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code></pre>
<pre><code>g_b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code></pre>
<!-- end g_b -->
<h1><a class="anchor" href="#43-generation-of-encrypted-data" id="43-generation-of-encrypted-data" name="43-generation-of-encrypted-data"><i class="anchor-icon"></i></a>4.3 generation of encrypted_data</h1>
<!-- start client_DH_inner_data -->
<p>Generated payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 54 B6 43 66 A1 F9 B9 D5 B1 C7 24 55 20 11 1F B7
0010 | 30 1C 95 C0 70 EA 28 24 B9 2F 73 9F 4C 26 45 7B
0020 | 02 94 8D CA 00 00 00 00 00 00 00 00 FE 00 01 00
0030 | 03 6B 95 C4 61 9B E4 5D A0 74 82 AF F8 54 39 E8
0040 | 98 23 44 A9 7F 94 B0 44 DB 2F 56 26 A6 E7 E3 B4
0050 | CD F5 B8 17 A1 BF 5F 5E 36 A5 28 EB 21 CB D6 1E
0060 | 8F E6 9C 4D CF 4F 5B F1 1C 0E 6B E0 A9 09 74 49
0070 | 02 35 27 DB CB C7 67 EB DB E4 43 B8 8D 67 70 09
0080 | 47 23 F9 9F 39 F6 4C A2 99 1A C9 E5 E2 F4 70 BB
0090 | 52 06 81 64 E8 46 F5 E7 86 B4 96 8B B3 59 40 B4
00A0 | D4 1C 9F 75 4C 85 C4 E4 0F C1 7E 90 D0 76 D4 2F
00B0 | 55 15 4E 05 86 F0 EC 67 CF D6 E8 23 4B 82 F5 D5
00C0 | 04 20 EF C1 21 D8 EF 1D 79 70 B7 FC 3A 7C 48 33
00D0 | 4D 73 39 56 6A 46 2C DC 6D 67 AF CF E6 43 CE A2
00E0 | 0F 1C 2E FE 09 D9 E8 C5 B4 3D 5A C6 67 15 76 01
00F0 | C2 1D A1 0D C6 03 57 B7 49 6C 88 0E 1E 17 2E AB
0100 | F1 65 31 6A 02 3C 19 64 E0 1B 2A A1 23 92 7F 0C
0110 | 12 12 55 8B 87 2E 9E C5 C7 F7 E4 F6 E8 2F 65 7B
0120 | F3 6B EE 66 D3 C3 11 E9 34 2F C1 BB E4 0B CA F0</code></pre>
<pre><code>0000 | 54 B6 43 66 DF D6 01 C3 D4 AD 9E 9F 59 2A 9E 0E
0010 | 97 B3 E6 03 74 8B 67 63 BB E5 93 96 D6 24 9A 28
0020 | 79 1F F0 70 00 00 00 00 00 00 00 00 FE 00 01 00
0030 | B5 84 1C D8 24 62 61 CF BD 6F DA 1C 4B F6 4E 7E
0040 | CC C8 2C 19 EA B8 6C 59 D9 86 C4 29 D6 A0 D5 20
0050 | 4C 54 7C 74 ED 6A B6 1E 28 A4 AA 9A 39 FA 67 6D
0060 | 14 C1 C9 FA CC E9 B9 D3 05 6A 34 09 34 08 CE C2
0070 | 8E ED F5 F0 9A C3 F2 64 51 37 D9 1F 50 E4 FE 6A
0080 | 35 8A 24 50 7E B3 E8 AB 94 31 2D 80 13 C4 74 0E
0090 | 49 2C 0A 5E 90 2E 2E 46 0C FA 96 05 5C 86 82 C3
00A0 | B2 20 D0 E1 66 18 84 FC E5 25 D3 AD 8E D7 B2 3D
00B0 | 3B 34 1B DF B1 D5 DD 98 8F 36 3A 48 73 0E C1 56
00C0 | 53 13 B2 0A D2 86 FD 7E 36 31 7E 3D 87 0E 92 A9
00D0 | AE BA B8 35 83 3F 02 3A 18 51 68 92 2F A7 BC EA
00E0 | 7D 5F 4F 0B 1B 7D BD 10 F0 81 8D 7F 9A 4A 94 96
00F0 | 1E A4 59 74 15 E4 57 CD 57 5E 30 9B 73 22 5F 20
0100 | 5C D2 D6 79 18 C0 0C 17 04 12 CD 43 0D 6A 34 3D
0110 | 06 1C 4B AD 7A C1 49 CC 4E C5 F1 91 0F 3A 0C 09
0120 | D1 84 C9 F1 23 FC A7 1C 51 E8 34 19 E9 E5 F6 4D</code></pre>
<p>Payload serialization:</p>
<pre><code>client_DH_inner_data#6643b654 nonce:int128 server_nonce:int128 retry_id:long g_b:string = Client_DH_Inner_Data;</code></pre>
<table class="table">
@ -650,19 +650,19 @@ server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:s
<tr>
<td>nonce</td>
<td>4, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>20, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>g_b</td>
<td>36, 260</td>
<td><code>FE000100036B95C4619BE45DA07482AF</code> <code>F85439E8982344A97F94B044DB2F5626</code> <code>A6E7E3B4CDF5B817A1BF5F5E36A528EB</code> <code>21CBD61E8FE69C4DCF4F5BF11C0E6BE0</code> <code>A9097449023527DBCBC767EBDBE443B8</code> <code>8D6770094723F99F39F64CA2991AC9E5</code> <code>E2F470BB52068164E846F5E786B4968B</code> <code>B35940B4D41C9F754C85C4E40FC17E90</code> <code>D076D42F55154E0586F0EC67CFD6E823</code> <code>4B82F5D50420EFC121D8EF1D7970B7FC</code> <code>3A7C48334D7339566A462CDC6D67AFCF</code> <code>E643CEA20F1C2EFE09D9E8C5B43D5AC6</code> <code>67157601C21DA10DC60357B7496C880E</code> <code>1E172EABF165316A023C1964E01B2AA1</code> <code>23927F0C1212558B872E9EC5C7F7E4F6</code> <code>E82F657BF36BEE66D3C311E9342FC1BBE40BCAF0</code></td>
<td><code>FE000100B5841CD8246261CFBD6FDA1C</code> <code>4BF64E7ECCC82C19EAB86C59D986C429</code> <code>D6A0D5204C547C74ED6AB61E28A4AA9A</code> <code>39FA676D14C1C9FACCE9B9D3056A3409</code> <code>3408CEC28EEDF5F09AC3F2645137D91F</code> <code>50E4FE6A358A24507EB3E8AB94312D80</code> <code>13C4740E492C0A5E902E2E460CFA9605</code> <code>5C8682C3B220D0E1661884FCE525D3AD</code> <code>8ED7B23D3B341BDFB1D5DD988F363A48</code> <code>730EC1565313B20AD286FD7E36317E3D</code> <code>870E92A9AEBAB835833F023A18516892</code> <code>2FA7BCEA7D5F4F0B1B7DBD10F0818D7F</code> <code>9A4A94961EA4597415E457CD575E309B</code> <code>73225F205CD2D67918C00C170412CD43</code> <code>0D6A343D061C4BAD7AC149CC4EC5F191</code> <code>0F3A0C09D184C9F123FCA71C51E83419</code><br> <code>E9E5F64D</code></td>
<td><code>pow(g, b) mod dh_prime</code></td>
</tr>
<tr>
@ -681,31 +681,31 @@ AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv) = 928A4957D0463B525
<h1><a class="anchor" href="#5-request-set-client-dh-params" id="5-request-set-client-dh-params" name="5-request-set-client-dh-params"><i class="anchor-icon"></i></a>5. request set_client_dh_params</h1>
<!-- start set_client_DH_params -->
<p>Sent payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 00 00 00 00 00 00 00 00 00 00 00 00 14 90 9C 64
0010 | 78 01 00 00 1F 5F 04 F5 A1 F9 B9 D5 B1 C7 24 55
0020 | 20 11 1F B7 30 1C 95 C0 70 EA 28 24 B9 2F 73 9F
0030 | 4C 26 45 7B 02 94 8D CA FE 50 01 00 3E CB CE 83
0040 | 97 30 9D A1 84 5B 93 88 3B 11 99 21 90 FF B9 C5
0050 | 52 26 5C 26 2C 62 77 A3 0E 61 86 2B C5 45 0D 67
0060 | 21 78 1F 07 CE AD 81 67 FE E4 BE 78 4E 4A AF F5
0070 | 73 D9 DD 31 ED 4C 76 48 DB D5 A9 3C F2 90 6E BB
0080 | DE 0C E8 F2 F5 2F D6 81 3C C3 F8 63 46 9C F0 BE
0090 | C7 7A F8 A7 2B 10 1A D6 BB 93 00 1A 20 C9 E8 F0
00A0 | EF A0 AA 45 8E 84 A0 F2 BC 74 D1 BE 4D 7A BB BB
00B0 | EC 9A B6 9B DA C5 7E B7 83 91 51 17 16 83 53 78
00C0 | 7B B6 B6 73 B4 3C BC 33 FC 0B 28 0A CF E7 2E 1B
00D0 | EA 4D B7 EC F6 D6 30 7C CC FB 0F 0C 06 68 68 A3
00E0 | 82 AC EA C6 8E A4 AB 0B 31 3A 16 EF DE 55 C3 4B
00F0 | F4 F1 19 E7 F0 EE 5B D7 79 2F C8 52 23 C1 99 AA
0100 | 79 44 EC 88 11 94 0D CE 47 0C F6 A1 52 23 35 EB
0110 | BA 78 ED F2 59 75 FE 0E BD 06 33 E0 1D EB 6C 87
0120 | 01 A6 BF F1 9A AB 13 BB 3E 1E 4C 17 43 78 04 12
0130 | 45 6E 01 33 B3 70 DC 70 85 20 63 82 20 02 DE 00
0140 | 50 08 9E 37 49 E5 E6 2F D3 B9 8C C0 40 A1 60 45
0150 | 4A 81 56 E6 76 5B 1C 7B 22 D3 67 03 A3 AC D4 6B
0160 | C5 0A F3 73 C2 F0 CC 4A 1C 31 45 30 25 D9 A8 70
0170 | 45 52 BA 9F E5 E7 F3 19 85 B0 54 8A B3 93 33 F9
0180 | DB E9 3C C0 83 FF BD 09 BA 66 DA 06</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 00 00 00 00 C5 90 9C 64
0010 | 78 01 00 00 1F 5F 04 F5 DF D6 01 C3 D4 AD 9E 9F
0020 | 59 2A 9E 0E 97 B3 E6 03 74 8B 67 63 BB E5 93 96
0030 | D6 24 9A 28 79 1F F0 70 FE 50 01 00 61 90 D4 3D
0040 | 96 79 4A F6 81 C7 36 6F A0 50 7F 35 CB E5 0F D0
0050 | 1E D9 BF 27 49 B1 D4 DB B9 17 C7 73 B6 05 B5 37
0060 | 0C F1 01 A2 0C F8 A6 E3 5E C8 C7 F0 7F A2 B4 C3
0070 | CF F9 7D 11 55 FD 90 37 9B A3 D5 87 53 10 1A D4
0080 | FA 36 8F 0C 56 B9 C5 7D 50 1C 14 AF F8 5C 97 65
0090 | 73 40 A6 F3 45 87 13 F5 F7 D7 4B 2B 79 45 52 03
00A0 | 22 4F 42 5D E4 65 2D 05 A4 4A FF A4 E7 70 B6 CF
00B0 | A8 BD D2 2C 01 B6 4C 3F 0D 32 09 D8 4C 64 FF C7
00C0 | EB C9 B3 C8 5D 8C 02 F9 D2 7E F7 20 EE A4 DC 78
00D0 | 71 A7 C9 F1 4C 0A B1 31 35 5E EB 80 EE C9 16 8F
00E0 | 86 83 26 4D FF F9 48 75 41 F9 B5 2D C6 92 15 7A
00F0 | 71 6F A0 CC 9E 45 0F 44 CF F4 19 BB 0E B8 7C 52
0100 | 1D F8 1C 9D 24 F3 4D 47 77 2A 63 87 B9 3D 4C 5F
0110 | E0 CA E8 44 4B 29 BE 25 38 C4 E0 CA 5E E6 9A 20
0120 | 49 F8 C9 2B 09 FE 52 BE 48 E9 E6 5C 76 7D D2 6C
0130 | 5D 52 36 42 A6 11 04 D1 B6 81 9C 88 D9 A9 77 5A
0140 | E8 56 4A 72 21 8B 38 DC 53 48 7E 91 95 9E 5A EC
0150 | 7C E8 DB 02 04 4D 2D D1 C8 26 2A F6 50 75 E3 0F
0160 | 2C EA 99 73 60 CF 1F EF B7 A3 46 4E 1C 69 24 61
0170 | 7B CE D6 B3 AD 89 A5 87 42 20 4D A0 76 0E EB E5
0180 | 8D A2 81 B4 C1 0D 97 32 99 E0 58 67</code></pre>
<p>Payload serialization:</p>
<pre><code>set_client_DH_params#f5045f1f nonce:int128 server_nonce:int128 encrypted_data:string = Set_client_DH_params_answer;</code></pre>
<table class="table">
@ -727,7 +727,7 @@ AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv) = 928A4957D0463B525
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>0000000014909C64</code></td>
<td><code>00000000C5909C64</code></td>
<td>Exact <code>unixtime*2^32</code>, <code>+(4*N)</code> if N messages with the same message ID were already generated</td>
</tr>
<tr>
@ -745,19 +745,19 @@ AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv) = 928A4957D0463B525
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>encrypted_data</td>
<td>56, 340</td>
<td><code>FE5001003ECBCE8397309DA1845B9388</code> <code>3B11992190FFB9C552265C262C6277A3</code> <code>0E61862BC5450D6721781F07CEAD8167</code> <code>FEE4BE784E4AAFF573D9DD31ED4C7648</code> <code>DBD5A93CF2906EBBDE0CE8F2F52FD681</code> <code>3CC3F863469CF0BEC77AF8A72B101AD6</code> <code>BB93001A20C9E8F0EFA0AA458E84A0F2</code> <code>BC74D1BE4D7ABBBBEC9AB69BDAC57EB7</code> <code>83915117168353787BB6B673B43CBC33</code> <code>FC0B280ACFE72E1BEA4DB7ECF6D6307C</code> <code>CCFB0F0C066868A382ACEAC68EA4AB0B</code> <code>313A16EFDE55C34BF4F119E7F0EE5BD7</code> <code>792FC85223C199AA7944EC8811940DCE</code> <code>470CF6A1522335EBBA78EDF25975FE0E</code> <code>BD0633E01DEB6C8701A6BFF19AAB13BB</code> <code>3E1E4C1743780412456E0133B370DC70</code> <code>852063822002DE0050089E3749E5E62F</code> <code>D3B98CC040A160454A8156E6765B1C7B</code> <code>22D36703A3ACD46BC50AF373C2F0CC4A</code> <code>1C31453025D9A8704552BA9FE5E7F319</code> <code>85B0548AB39333F9DBE93CC083FFBD09BA66DA06</code></td>
<td><code>FE5001006190D43D96794AF681C7366F</code> <code>A0507F35CBE50FD01ED9BF2749B1D4DB</code> <code>B917C773B605B5370CF101A20CF8A6E3</code> <code>5EC8C7F07FA2B4C3CFF97D1155FD9037</code> <code>9BA3D58753101AD4FA368F0C56B9C57D</code> <code>501C14AFF85C97657340A6F3458713F5</code> <code>F7D74B2B79455203224F425DE4652D05</code> <code>A44AFFA4E770B6CFA8BDD22C01B64C3F</code> <code>0D3209D84C64FFC7EBC9B3C85D8C02F9</code> <code>D27EF720EEA4DC7871A7C9F14C0AB131</code> <code>355EEB80EEC9168F8683264DFFF94875</code> <code>41F9B52DC692157A716FA0CC9E450F44</code> <code>CFF419BB0EB87C521DF81C9D24F34D47</code> <code>772A6387B93D4C5FE0CAE8444B29BE25</code> <code>38C4E0CA5EE69A2049F8C92B09FE52BE</code> <code>48E9E65C767DD26C5D523642A61104D1</code> <code>B6819C88D9A9775AE8564A72218B38DC</code> <code>53487E91959E5AEC7CE8DB02044D2DD1</code> <code>C8262AF65075E30F2CEA997360CF1FEF</code> <code>B7A3464E1C6924617BCED6B3AD89A587</code> <code>42204DA0760EEBE58DA281B4C10D9732</code><br> <code>99E05867</code></td>
<td>Encrypted client_DH_inner_data, generated as follows</td>
</tr>
</tbody>
@ -766,17 +766,17 @@ AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv) = 928A4957D0463B525
<h1><a class="anchor" href="#6-auth-key-generation" id="6-auth-key-generation" name="6-auth-key-generation"><i class="anchor-icon"></i></a>6. auth key generation</h1>
<p>The clients computes the auth_key using formula <code>g^{ab} mod dh_prime</code>:</p>
<!-- start auth_key -->
<pre><code>auth_key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code></pre>
<pre><code>auth_key = 7AB41163F9DADC0E7AD17B0ED9C960B23436B0925E8D875C14AE2CB171D3B37F5E98A186E6C447641AD963FB63D99B31DEF206F55D522A41D120D04C4D5ACA12CEBF1130A4BF09C7A430CF5ACF550BA166CAE2AD842ECD94E26B4DC57460F537B2CB1DEEB8F681ABFF0C416757BAE47C4B1E2BFEE3EEB994D653D9794633A5C8BE0EEAEE35E1DFA271BE94140F39FCDAE9DD51330C7F46761744F4B79CBFB89A82891567A4AB8924C84F2024049F3E2DB86E6008454A0D3E5353E44E72CB2E1A24CFF0573F8EC4FE420EF0F4D15DE37749D2907DDB960C9BA0A8C89EA6AFAD8E8B0862D231329DEC391C793D067F4459587A5D6374B188126A949852133013A6</code></pre>
<!-- end auth_key -->
<h1><a class="anchor" href="#7-reply-set-client-dh-params-answer" id="7-reply-set-client-dh-params-answer" name="7-reply-set-client-dh-params-answer"><i class="anchor-icon"></i></a>7. reply set_client_dh_params_answer</h1>
<p>The server verifies and confirms that auth_key_hash is unique: since it's unique, it replies with the following:</p>
<!-- start dh_gen_ok -->
<p>Received payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 04 20 8A 14 90 9C 64
0010 | 74 00 00 00 34 F7 CB 3B A1 F9 B9 D5 B1 C7 24 55
0020 | 20 11 1F B7 30 1C 95 C0 70 EA 28 24 B9 2F 73 9F
0030 | 4C 26 45 7B 02 94 8D CA 87 FA CB 12 63 11 10 7E
0040 | CB 62 4A C0 8D 59 55 B4</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 94 13 B1 C5 90 9C 64
0010 | 38 00 00 00 34 F7 CB 3B DF D6 01 C3 D4 AD 9E 9F
0020 | 59 2A 9E 0E 97 B3 E6 03 74 8B 67 63 BB E5 93 96
0030 | D6 24 9A 28 79 1F F0 70 61 A9 07 63 0C 8B FD 9E
0040 | 2E D7 28 5B 0B 4C C8 26</code></pre>
<p>Payload serialization:</p>
<pre><code>dh_gen_ok#3bcbf734 nonce:int128 server_nonce:int128 new_nonce_hash1:int128 = Set_client_DH_params_answer;
dh_gen_retry#46dc1fb9 nonce:int128 server_nonce:int128 new_nonce_hash2:int128 = Set_client_DH_params_answer;
@ -800,13 +800,13 @@ dh_gen_fail#a69dae02 nonce:int128 server_nonce:int128 new_nonce_hash3:int128 = S
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>0104208A14909C64</code></td>
<td><code>019413B1C5909C64</code></td>
<td>Exact <code>unixtime*2^32</code>, <code>+(4*N)</code> if N messages with the same message ID were already generated</td>
</tr>
<tr>
<td>message_length</td>
<td>16, 4</td>
<td><code>74000000</code> (116 in decimal)</td>
<td><code>38000000</code> (56 in decimal)</td>
<td>Message body length</td>
</tr>
<tr>
@ -818,19 +818,19 @@ dh_gen_fail#a69dae02 nonce:int128 server_nonce:int128 new_nonce_hash3:int128 = S
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>A1F9B9D5B1C7245520111FB7301C95C0</code></td>
<td><code>DFD601C3D4AD9E9F592A9E0E97B3E603</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>70EA2824B92F739F4C26457B02948DCA</code></td>
<td><code>748B6763BBE59396D6249A28791FF070</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>new_nonce_hash1</td>
<td>56, 16</td>
<td><code>87FACB126311107ECB624AC08D5955B4</code></td>
<td><code>61A907630C8BFD9E2ED7285B0B4CC826</code></td>
<td>The 128 lower-order bits of SHA1 of the byte string derived from the <code>new_nonce</code> string by adding a single byte with the value of 1, 2, or 3, and followed by another 8 bytes with <code>auth_key_aux_hash</code>. Different values are required to prevent an intruder from changing server response dh_gen_ok into dh_gen_retry.</td>
</tr>
</tbody>