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data/web/corefork.telegram.org/mtproto/auth_key.html
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@ -57,9 +57,8 @@
<h5><a class="anchor" href="#3-client-decomposes-pq-into-prime-factors-such-that-p--q" id="3-client-decomposes-pq-into-prime-factors-such-that-p--q" name="3-client-decomposes-pq-into-prime-factors-such-that-p--q"><i class="anchor-icon"></i></a>3) Client decomposes pq into prime factors such that p &lt; q.</h5>
<p>This starts a round of Diffie-Hellman key exchanges.</p>
<h4><a class="anchor" href="#presenting-proof-of-work-server-authentication" id="presenting-proof-of-work-server-authentication" name="presenting-proof-of-work-server-authentication"><i class="anchor-icon"></i></a>Presenting proof of work; Server authentication</h4>
<h5><a class="anchor" href="#4-client-sends-query-to-server" id="4-client-sends-query-to-server" name="4-client-sends-query-to-server"><i class="anchor-icon"></i></a>4) Client sends query to server</h5>
<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>
<p>Here, encrypted_data is obtained as follows:</p>
<h5><a class="anchor" href="#4-encrypted-data-payload-generation" id="4-encrypted-data-payload-generation" name="4-encrypted-data-payload-generation"><i class="anchor-icon"></i></a>4) <code>encrypted_data</code> payload generation</h5>
<p>First of all, generate an <code>encrypted_data</code> payload as follows:</p>
<ul>
<li>
<p>new_nonce := another (good) random number generated by the client; after this query, it is known to both client and server;</p>
@ -89,7 +88,9 @@
<li>The value of key_aes_encrypted is compared with the RSA-modulus of server_pubkey as a big-endian 2048-bit (256-byte) unsigned integer. If key_aes_encrypted turns out to be greater than or equal to the RSA modulus, the previous steps starting from the generation of new random temp_key are repeated. Otherwise the final step is performed:</li>
<li>encrypted_data := RSA(key_aes_encrypted, server_pubkey); -- 256-byte big-endian integer is elevated to the requisite power from the RSA public key modulo the RSA modulus, and the result is stored as a big-endian integer consisting of exactly 256 bytes (with leading zero bytes if required).</li>
</ul>
<h5><a class="anchor" href="#5-server-responds-with" id="5-server-responds-with" name="5-server-responds-with"><i class="anchor-icon"></i></a>5) Server responds with:</h5>
<h5><a class="anchor" href="#5-send-req-dh-params-query-with-generated-encrypted-data" id="5-send-req-dh-params-query-with-generated-encrypted-data" name="5-send-req-dh-params-query-with-generated-encrypted-data"><i class="anchor-icon"></i></a>5) Send req_DH_params query with generated <code>encrypted_data</code></h5>
<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>
<h5><a class="anchor" href="#6-server-responds-with" id="6-server-responds-with" name="6-server-responds-with"><i class="anchor-icon"></i></a>6) Server responds with:</h5>
<pre><code>server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:string = Server_DH_Params;</code></pre>
<blockquote>
<p>If the query is incorrect, the server returns a <code>-404</code> error and the handshake must be restarted (any subsequent request also returns <code>-404</code>, even if it is correct).<br>
@ -110,7 +111,7 @@ A <code>-444</code> error may also be returned if a test DC ID is passed in <cod
<p>If the verification takes too long time (which is the case for older mobile devices), one might initially run only 15 Miller--Rabin iterations for verifying primeness of <strong>p</strong> and <strong>(p - 1)/2</strong> with error probability not exceeding one billionth, and do more iterations later in the background.</p>
<p>Another optimization is to embed into the client application code a small table with some known "good" couples <strong>(g,p)</strong> (or just known safe primes <strong>p</strong>, since the condition on <strong>g</strong> is easily verified during execution), checked during code generation phase, so as to avoid doing such verification during runtime altogether. Server changes these values rarely, thus one usually has to put the current value of server's <strong>dh_prime</strong> into such a table. For example, current value of <strong>dh_prime</strong> equals (in big-endian byte order)</p>
<pre><code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code></pre>
<h5><a class="anchor" href="#6-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message" id="6-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message" name="6-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message"><i class="anchor-icon"></i></a>6) Client computes random 2048-bit number <em>b</em> (using a sufficient amount of entropy) and sends the server a message</h5>
<h5><a class="anchor" href="#7-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message" id="7-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message" name="7-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message"><i class="anchor-icon"></i></a>7) Client computes random 2048-bit number <em>b</em> (using a sufficient amount of entropy) and sends the server a message</h5>
<pre><code>set_client_DH_params#f5045f1f nonce:int128 server_nonce:int128 encrypted_data:string = Set_client_DH_params_answer;</code></pre>
<p>Here, encrypted_data is obtained thus:</p>
<ul>
@ -121,8 +122,8 @@ A <code>-444</code> error may also be returned if a test DC ID is passed in <cod
<li>encrypted_data := AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv);</li>
</ul>
<p>The retry_id field is equal to zero at the time of the first attempt; otherwise, it is equal to auth_key_aux_hash from the previous failed attempt (see <a href="#9-server-responds-in-one-of-three-ways">Item 9</a>).</p>
<h5><a class="anchor" href="#7-thereafter-auth-key-equals-powg-ab-mod-dh-prime-on-the-server-it-is-computed-as-powg-b-a-mod-dh-prime-and-on-the-client-as-g-ab-mod-dh-prime" id="7-thereafter-auth-key-equals-powg-ab-mod-dh-prime-on-the-server-it-is-computed-as-powg-b-a-mod-dh-prime-and-on-the-client-as-g-ab-mod-dh-prime" name="7-thereafter-auth-key-equals-powg-ab-mod-dh-prime-on-the-server-it-is-computed-as-powg-b-a-mod-dh-prime-and-on-the-client-as-g-ab-mod-dh-prime"><i class="anchor-icon"></i></a>7) Thereafter, auth_key equals <code>pow(g, {ab}) mod dh_prime</code>; on the server, it is computed as <code>pow(g_b, a) mod dh_prime</code>, and on the client as <code>(g_a)^b mod dh_prime</code>.</h5>
<h5><a class="anchor" href="#8-auth-key-hash-is-computed--64-lower-order-bits-of-sha1-auth-key-the-server-checks-whether-there-already-is-another-key-with-the-same-auth-key-hash-and-responds-in-one-of-the-following-ways" id="8-auth-key-hash-is-computed--64-lower-order-bits-of-sha1-auth-key-the-server-checks-whether-there-already-is-another-key-with-the-same-auth-key-hash-and-responds-in-one-of-the-following-ways" name="8-auth-key-hash-is-computed--64-lower-order-bits-of-sha1-auth-key-the-server-checks-whether-there-already-is-another-key-with-the-same-auth-key-hash-and-responds-in-one-of-the-following-ways"><i class="anchor-icon"></i></a>8) auth_key_hash is computed := 64 lower-order bits of SHA1 (auth_key). The server checks whether there already is another key with the same auth_key_hash and responds in one of the following ways.</h5>
<h5><a class="anchor" href="#8-thereafter-auth-key-equals-powg-ab-mod-dh-prime-on-the-server-it-is-computed-as-powg-b-a-mod-dh-prime-and-on-the-client-as-g-ab-mod-dh-prime" id="8-thereafter-auth-key-equals-powg-ab-mod-dh-prime-on-the-server-it-is-computed-as-powg-b-a-mod-dh-prime-and-on-the-client-as-g-ab-mod-dh-prime" name="8-thereafter-auth-key-equals-powg-ab-mod-dh-prime-on-the-server-it-is-computed-as-powg-b-a-mod-dh-prime-and-on-the-client-as-g-ab-mod-dh-prime"><i class="anchor-icon"></i></a>8) Thereafter, auth_key equals <code>pow(g, {ab}) mod dh_prime</code>; on the server, it is computed as <code>pow(g_b, a) mod dh_prime</code>, and on the client as <code>(g_a)^b mod dh_prime</code>.</h5>
<p>Auth_key_hash is computed := 64 lower-order bits of SHA1 (auth_key). The server checks whether there already is another key with the same auth_key_hash and responds in one of the following ways.</p>
<h4><a class="anchor" href="#dh-key-exchange-complete" id="dh-key-exchange-complete" name="dh-key-exchange-complete"><i class="anchor-icon"></i></a>DH key exchange complete</h4>
<h5><a class="anchor" href="#9-server-responds-in-one-of-three-ways" id="9-server-responds-in-one-of-three-ways" name="9-server-responds-in-one-of-three-ways"><i class="anchor-icon"></i></a>9) Server responds in one of three ways:</h5>
<pre><code>dh_gen_ok#3bcbf734 nonce:int128 server_nonce:int128 new_nonce_hash1:int128 = Set_client_DH_params_answer;

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data/web/corefork.telegram.org/mtproto/samples-auth_key.html
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@ -42,17 +42,21 @@
<div class="dev_page_bread_crumbs"><ul class="breadcrumb clearfix"><li><a href="/mtproto" >Mobile Protocol</a></li><i class="icon icon-breadcrumb-divider"></i><li><a href="/mtproto/samples-auth_key" >Auth key generation example</a></li></ul></div>
<h1 id="dev_page_title">Auth key generation example</h1>
<div id="dev_page_content"><p>In the examples below, the <a href="/mtproto#transport">transport</a> headers are omitted:</p>
<div id="dev_page_content"><!-- scroll_nav -->
<h1><a class="anchor" href="#" id="" name=""><i class="anchor-icon"></i></a></h1>
<p>In the examples below, the <a href="/mtproto#transport">transport</a> headers are omitted:</p>
<blockquote>
<p>For example, for the <a href="/mtproto/mtproto-transports#abridged">abridged version of the transport »</a>, the client sends <code>0xef</code> as the first byte (<strong>important:</strong> only prior to the very first data packet), then the packet length is encoded with a single byte (<code>0x01-0x7e</code> = data length divided by 4; or <code>0x7f</code> followed by 3 bytes (little endian) divided by 4) followed by the data itself. In this case, server responses have the same structure (although the server does not send <code>0xef</code>as the first byte).</p>
</blockquote>
<p>Detailed documentation on creating authorization keys is available <a href="/mtproto/auth_key">here »</a>.</p>
<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>
<h4><a class="anchor" href="#dh-exchange-initiation" id="dh-exchange-initiation" name="dh-exchange-initiation"><i class="anchor-icon"></i></a>DH exchange initiation</h4>
<h5><a class="anchor" href="#1-client-sends-query-to-server" id="1-client-sends-query-to-server" name="1-client-sends-query-to-server"><i class="anchor-icon"></i></a>1) Client sends query to server</h5>
<!-- 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 DC 9D 9C 64
0010 | 14 00 00 00 F1 8E 7E BE 36 5B 3A 12 7C 5B 59 09
0020 | 49 0E 6C 3A EC EC 01 26</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 00 00 00 00 87 A8 9C 64
0010 | 14 00 00 00 F1 8E 7E BE FA DA 40 F3 24 30 86 3C
0020 | 25 83 58 32 EF 2E CF 48</code></pre>
<p>Payload (de)serialization:</p>
<pre><code>req_pq_multi#be7e8ef1 nonce:int128 = ResPQ;</code></pre>
<table class="table">
@ -74,7 +78,7 @@
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>00000000DC9D9C64</code></td>
<td><code>0000000087A89C64</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>
@ -92,20 +96,20 @@
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Random number</td>
</tr>
</tbody>
</table>
<!-- end req_pq_multi -->
<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>
<h5><a class="anchor" href="#2-server-sends-response-of-the-form" id="2-server-sends-response-of-the-form" name="2-server-sends-response-of-the-form"><i class="anchor-icon"></i></a>2) Server sends response of the form</h5>
<!-- start resPQ -->
<p>Received payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 90 2F 78 DC 9D 9C 64
0010 | 54 00 00 00 63 24 16 05 36 5B 3A 12 7C 5B 59 09
0020 | 49 0E 6C 3A EC EC 01 26 C2 18 4E 38 BA C1 64 9C
0030 | 35 FD 28 FC 20 E9 A7 EA 08 25 35 F6 04 92 13 80
0040 | 5B 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 B8 BB 7E 87 A8 9C 64
0010 | 50 00 00 00 63 24 16 05 FA DA 40 F3 24 30 86 3C
0020 | 25 83 58 32 EF 2E CF 48 82 93 B0 B5 EF 95 58 C3
0030 | 28 89 A6 F6 05 CA C3 C6 08 16 2C D4 B9 32 B1 0F
0040 | F1 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 (de)serialization:</p>
@ -129,13 +133,13 @@
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>01902F78DC9D9C64</code></td>
<td><code>01B8BB7E87A89C64</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>54000000</code> (84 in decimal)</td>
<td><code>50000000</code> (80 in decimal)</td>
<td>Message body length</td>
</tr>
<tr>
@ -147,19 +151,19 @@
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Server-generated random number</td>
</tr>
<tr>
<td>pq</td>
<td>56, 12</td>
<td><code>082535F6049213805B000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 2681319652660052059</td>
<td><code>08162CD4B932B10FF1000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1597885859694186481</td>
<td>Single-byte prefix denoting length, an 8-byte string, and three bytes of padding</td>
</tr>
<tr>
@ -202,22 +206,25 @@
</ul>
<p>Let's choose the only matching key, the one with fingerprint equal to <code>85FD64DE851D9DD0</code>.</p>
<!-- 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>
<h4><a class="anchor" href="#proof-of-work" id="proof-of-work" name="proof-of-work"><i class="anchor-icon"></i></a>Proof of work</h4>
<h5><a class="anchor" href="#3-client-decomposes-pq-into-prime-factors-such-that-p--q" id="3-client-decomposes-pq-into-prime-factors-such-that-p--q" name="3-client-decomposes-pq-into-prime-factors-such-that-p--q"><i class="anchor-icon"></i></a>3) Client decomposes pq into prime factors such that p &lt; q.</h5>
<!-- start pq -->
<pre><code>pq = 2681319652660052059</code></pre>
<p>Decompose into 2 prime cofactors: <code>2681319652660052059 = 1608915439 * 1666538581</code></p>
<pre><code>p = 1608915439
q = 1666538581</code></pre>
<pre><code>pq = 1597885859694186481</code></pre>
<p>Decompose into 2 prime cofactors: <code>1597885859694186481 = 1058029501 * 1510246981</code></p>
<pre><code>p = 1058029501
q = 1510246981</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>
<h4><a class="anchor" href="#presenting-proof-of-work-server-authentication" id="presenting-proof-of-work-server-authentication" name="presenting-proof-of-work-server-authentication"><i class="anchor-icon"></i></a>Presenting proof of work; Server authentication</h4>
<h5><a class="anchor" href="#4-encrypted-data-payload-generation" id="4-encrypted-data-payload-generation" name="4-encrypted-data-payload-generation"><i class="anchor-icon"></i></a>4) <code>encrypted_data</code> payload generation</h5>
<p>First of all, generate an <code>encrypted_data</code> payload as follows:</p>
<!-- start p_q_inner_data_dc -->
<p>Generated payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 95 5F F5 A9 08 25 35 F6 04 92 13 80 5B 00 00 00
0010 | 04 5F E6 19 EF 00 00 00 04 63 55 5C 55 00 00 00
0020 | 36 5B 3A 12 7C 5B 59 09 49 0E 6C 3A EC EC 01 26
0030 | C2 18 4E 38 BA C1 64 9C 35 FD 28 FC 20 E9 A7 EA
0040 | AA BB EA 0C 77 25 B4 A6 27 D8 E4 05 7B C3 BD A4
0050 | DF B4 30 72 30 91 E0 E2 0F BD 94 FC D0 F2 6F 24
<pre><code>0000 | 95 5F F5 A9 08 16 2C D4 B9 32 B1 0F F1 00 00 00
0010 | 04 3F 10 3F BD 00 00 00 04 5A 04 8A 45 00 00 00
0020 | FA DA 40 F3 24 30 86 3C 25 83 58 32 EF 2E CF 48
0030 | 82 93 B0 B5 EF 95 58 C3 28 89 A6 F6 05 CA C3 C6
0040 | E5 6A F7 39 8C 71 42 86 86 98 E5 F5 8F 89 A1 8B
0050 | AA 43 00 AE 87 A7 B9 6B 0D 01 B1 DC E9 9B 07 21
0060 | 02 00 00 00</code></pre>
<p>Payload (de)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;</code></pre>
@ -240,37 +247,37 @@ q = 1666538581</code></pre>
<tr>
<td>pq</td>
<td>4, 12</td>
<td><code>082535F6049213805B000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 2681319652660052059</td>
<td><code>08162CD4B932B10FF1000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1597885859694186481</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>045FE619EF000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1608915439</td>
<td><code>043F103FBD000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1058029501</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>0463555C55000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1666538581</td>
<td><code>045A048A45000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1510246981</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>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>48, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>new_nonce</td>
<td>64, 32</td>
<td><code>AABBEA0C7725B4A627D8E4057BC3BDA4</code> <code>DFB430723091E0E20FBD94FCD0F26F24</code></td>
<td><code>E56AF7398C7142868698E5F58F89A18B</code> <code>AA4300AE87A7B96B0D01B1DCE99B0721</code></td>
<td>Client-generated random number</td>
</tr>
<tr>
@ -285,39 +292,39 @@ q = 1666538581</code></pre>
<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 = 955FF5A9082535F6049213805B000000045FE619EF0000000463555C55000000365B3A127C5B5909490E6C3AECEC0126C2184E38BAC1649C35FD28FC20E9A7EAAABBEA0C7725B4A627D8E4057BC3BDA4DFB430723091E0E20FBD94FCD0F26F2402000000
random_padding_bytes = 216450FD2A974A81475A90261BAE56428354F18BEE55BFB415135941FFA2607DA534FB9099CB6B7A33FBF9E40ADCD43CB29C14B8E4C16DC2E0471A1E92D21966398AF8FF1EFEEF787DEB0D5AB1AA674D154799D1C9E9DBECA2682FD5</code></pre>
<pre><code>data = 955FF5A908162CD4B932B10FF1000000043F103FBD000000045A048A45000000FADA40F32430863C25835832EF2ECF488293B0B5EF9558C32889A6F605CAC3C6E56AF7398C7142868698E5F58F89A18BAA4300AE87A7B96B0D01B1DCE99B072102000000
random_padding_bytes = 534E43A33047EE7E3881F92F669DC5A6159FED723D7D2A7DD86A1AB4AE22AF3263AB39822511EF8CF2DD65C4B1D6B48FAA4ECC8E4621ED0DDC27D473F80DDD996BEB457BF8A486E0B024EC86C7A77D531087F944712FEDD47EBE03F0</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>
<h5><a class="anchor" href="#5-send-req-dh-params-query-with-generated-encrypted-data" id="5-send-req-dh-params-query-with-generated-encrypted-data" name="5-send-req-dh-params-query-with-generated-encrypted-data"><i class="anchor-icon"></i></a>5) Send req_DH_params query with generated <code>encrypted_data</code></h5>
<!-- 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 DC 9D 9C 64
0010 | 40 01 00 00 BE E4 12 D7 36 5B 3A 12 7C 5B 59 09
0020 | 49 0E 6C 3A EC EC 01 26 C2 18 4E 38 BA C1 64 9C
0030 | 35 FD 28 FC 20 E9 A7 EA 04 5F E6 19 EF 00 00 00
0040 | 04 63 55 5C 55 00 00 00 85 FD 64 DE 85 1D 9D D0
0050 | FE 00 01 00 27 23 90 AE 7D 9B D6 42 31 0E 05 D7
0060 | 7A 4C 34 AE 44 CA 37 90 AA 81 FA A4 D1 8D E3 27
0070 | DF 7D F5 75 10 5F DD 87 44 16 F2 E9 07 C9 7A A9
0080 | 7A 06 97 D4 60 E3 82 4C 51 39 76 75 E5 31 41 96
0090 | EB F6 E1 E7 71 43 68 30 84 44 17 67 1E 29 58 22
00A0 | E1 FB 89 2D C8 30 CE FC 75 6E BB F5 92 67 03 93
00B0 | 09 18 FC 0F A3 79 B3 50 D5 C4 F7 4C 82 21 62 2C
00C0 | 58 BD 05 61 E8 98 DD C1 F6 14 AE 73 A6 D6 E7 27
00D0 | D1 85 73 61 E7 94 0A 23 3D B2 06 A2 3F 7B 02 A1
00E0 | 09 C0 D6 94 DF 29 CC 9C 63 08 5A 98 F6 C4 78 A7
00F0 | 26 C7 D0 18 89 DB 00 9A 47 1C 2C 47 15 30 AD 95
0100 | FD D7 98 9B 13 D6 21 63 45 31 4B EF 01 E8 4C 8D
0110 | 67 37 86 86 13 43 A9 97 9C 54 DD 93 7B FA 1A 1B
0120 | 12 C0 2B 30 3E AF C9 F6 9F 16 DB BE D0 AD 56 89
0130 | 49 5B 90 DD 2F 40 62 56 2D CF 79 34 B7 5F 5F 00
0140 | C9 05 90 05 CE 58 1D C2 EE 70 45 48 70 3E 74 C9
0150 | 75 EE D2 E4</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 04 00 00 00 87 A8 9C 64
0010 | 40 01 00 00 BE E4 12 D7 FA DA 40 F3 24 30 86 3C
0020 | 25 83 58 32 EF 2E CF 48 82 93 B0 B5 EF 95 58 C3
0030 | 28 89 A6 F6 05 CA C3 C6 04 3F 10 3F BD 00 00 00
0040 | 04 5A 04 8A 45 00 00 00 85 FD 64 DE 85 1D 9D D0
0050 | FE 00 01 00 5E 84 6B B8 56 F5 9D 77 3E FC A5 96
0060 | F0 18 40 0A 57 48 CE 6A 6D C8 B5 C7 91 EC A7 F5
0070 | 70 A0 04 FE 95 52 4B 92 7B 6E D7 36 87 B8 65 14
0080 | B9 D2 7D 19 BA 06 D5 9B CF 00 23 99 45 C9 0B D3
0090 | 1E 3D 96 EE 36 46 76 80 3F FB 9B A6 56 AF F8 F3
00A0 | 9D B6 96 A5 05 BF 14 27 46 29 5C C0 3F 61 58 9E
00B0 | 86 35 9D 91 B5 88 A1 FD 8B 8A D5 FA 25 E4 92 FF
00C0 | 64 C6 A8 CF 45 53 D3 8E DF B3 03 C5 F3 11 29 DF
00D0 | 80 8B A5 9F AA 3D FA E2 7C 4E 66 D4 A2 A2 BC 9C
00E0 | 7C 7B 61 5C 76 5C 15 DA B6 71 1E 69 05 12 6F F5
00F0 | F0 CF CC E4 3C 5B 61 87 DD FC F4 88 1A 00 80 02
0100 | CC DE 82 2F 38 CE C9 35 FD 35 64 A7 81 2F E0 E3
0110 | 5F 83 A0 29 1C 6B D8 53 A4 67 AF 9D 75 B0 25 79
0120 | FA D2 0D 19 BC 49 DD A2 1E 6D 57 34 C3 E2 23 BF
0130 | 55 D8 26 1E 2E D4 16 46 B7 00 43 DC 9C DC 1D EF
0140 | B8 12 3E 95 24 59 C8 11 E2 F1 74 04 B8 E9 98 02
0150 | 84 78 51 BF</code></pre>
<p>Payload (de)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">
@ -339,7 +346,7 @@ random_padding_bytes = 216450FD2A974A81475A90261BAE56428354F18BEE55BFB415135941F
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>04000000DC9D9C64</code></td>
<td><code>0400000087A89C64</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>
@ -357,25 +364,25 @@ random_padding_bytes = 216450FD2A974A81475A90261BAE56428354F18BEE55BFB415135941F
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>p</td>
<td>56, 8</td>
<td><code>045FE619EF000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1608915439</td>
<td><code>043F103FBD000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1058029501</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>0463555C55000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1666538581</td>
<td><code>045A048A45000000</code><br>TL byte deserialization <br>=&gt; bigendian conversion to decimal<br>=&gt; 1510246981</td>
<td>Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding</td>
</tr>
<tr>
@ -387,56 +394,56 @@ random_padding_bytes = 216450FD2A974A81475A90261BAE56428354F18BEE55BFB415135941F
<tr>
<td>encrypted_data</td>
<td>80, 260</td>
<td><code>FE000100272390AE7D9BD642310E05D7</code> <code>7A4C34AE44CA3790AA81FAA4D18DE327</code> <code>DF7DF575105FDD874416F2E907C97AA9</code> <code>7A0697D460E3824C51397675E5314196</code> <code>EBF6E1E771436830844417671E295822</code> <code>E1FB892DC830CEFC756EBBF592670393</code> <code>0918FC0FA379B350D5C4F74C8221622C</code> <code>58BD0561E898DDC1F614AE73A6D6E727</code> <code>D1857361E7940A233DB206A23F7B02A1</code> <code>09C0D694DF29CC9C63085A98F6C478A7</code> <code>26C7D01889DB009A471C2C471530AD95</code> <code>FDD7989B13D6216345314BEF01E84C8D</code> <code>673786861343A9979C54DD937BFA1A1B</code> <code>12C02B303EAFC9F69F16DBBED0AD5689</code> <code>495B90DD2F4062562DCF7934B75F5F00</code> <code>C9059005CE581DC2EE704548703E74C9</code><br> <code>75EED2E4</code></td>
<td><code>FE0001005E846BB856F59D773EFCA596</code> <code>F018400A5748CE6A6DC8B5C791ECA7F5</code> <code>70A004FE95524B927B6ED73687B86514</code> <code>B9D27D19BA06D59BCF00239945C90BD3</code> <code>1E3D96EE364676803FFB9BA656AFF8F3</code> <code>9DB696A505BF142746295CC03F61589E</code> <code>86359D91B588A1FD8B8AD5FA25E492FF</code> <code>64C6A8CF4553D38EDFB303C5F31129DF</code> <code>808BA59FAA3DFAE27C4E66D4A2A2BC9C</code> <code>7C7B615C765C15DAB6711E6905126FF5</code> <code>F0CFCCE43C5B6187DDFCF4881A008002</code> <code>CCDE822F38CEC935FD3564A7812FE0E3</code> <code>5F83A0291C6BD853A467AF9D75B02579</code> <code>FAD20D19BC49DDA21E6D5734C3E223BF</code> <code>55D8261E2ED41646B70043DC9CDC1DEF</code> <code>B8123E952459C811E2F17404B8E99802</code><br> <code>847851BF</code></td>
<td>See <a href="#generation-of-encrypted-data">Generation of encrypted_data »</a></td>
</tr>
</tbody>
</table>
<!-- end req_DH_params -->
<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>
<h5><a class="anchor" href="#6-server-responds-with" id="6-server-responds-with" name="6-server-responds-with"><i class="anchor-icon"></i></a>6) Server responds with:</h5>
<!-- 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 F4 AA 18 DD 9D 9C 64
0010 | 84 02 00 00 5C 07 E8 D0 36 5B 3A 12 7C 5B 59 09
0020 | 49 0E 6C 3A EC EC 01 26 C2 18 4E 38 BA C1 64 9C
0030 | 35 FD 28 FC 20 E9 A7 EA FE 50 02 00 70 2F F1 03
0040 | 2B 5B A7 26 4B 04 CD 20 AA 98 0F B8 21 79 D0 16
0050 | 27 46 00 12 8E C8 6B 8E 70 5D 09 B6 C9 23 9A A6
0060 | 97 A9 9D 0D 6B 9F 39 7B 58 12 2C 49 20 5C 60 62
0070 | 90 C6 4B 67 FD 47 AA 12 5E BC 78 20 89 1E 11 7C
0080 | 99 10 98 4D 5F 82 4F 3B 51 3E 11 2E 73 3D 3A 79
0090 | 5C 0C 82 F1 59 36 4B 35 9F ED 51 E0 65 AE 46 4E
00A0 | 0A DF F0 5E 65 75 95 EF 0D DE 7D 28 D7 3A 86 42
00B0 | 04 85 48 3C BD 77 AD EE 1B AF CB 00 02 07 4D 76
00C0 | 6A C6 B7 C3 0D 4B 41 2F E2 DE 9B C7 0E FD 5D C2
00D0 | E7 BA A4 D5 2E 96 AF E6 8A FB 4D E4 C1 8E 16 03
00E0 | 4E 1F 0D 1E D8 93 07 B7 32 45 95 BF 8F DF 83 4C
00F0 | 10 9E A1 E0 B9 D9 D0 B6 56 A3 B3 BB B1 C3 FC 36
0100 | 27 FF F3 DE 47 0D 22 C8 37 5B 6C 76 99 AD 67 EF
0110 | 0F 72 0B 16 F9 EA 69 5C 53 0D 13 E5 85 A7 E6 12
0120 | 90 99 58 17 CB 21 ED 22 CD 74 BB 94 21 8C 39 CB
0130 | A8 60 F6 65 3E 43 BB C7 2C 02 A0 47 B8 11 CD 4D
0140 | 6A 48 46 EF A8 D3 F9 19 06 D9 05 6A AF 89 0E 0E
0150 | F5 1E A3 A7 2D FC 7F B6 CE 81 74 6F 1E A0 45 CF
0160 | B5 71 4D 2A E0 4E C0 12 CF 9A 44 24 CC B2 3C CC
0170 | BB 4C 84 82 CE BF 06 4B EE 18 EE AF 2A 43 85 01
0180 | 99 C7 44 31 ED BB 10 5C 63 CA 66 BA 31 37 84 40
0190 | 5D B0 E7 4F DD 70 D0 D5 E2 2E FD 16 57 2B 79 0F
01A0 | 9C E2 03 5E 51 E6 8B 82 7B 1B 7C 8E 36 48 E2 C3
01B0 | 7F BE F2 4A D2 5D 7E 97 95 B9 18 3D B2 C8 6E 30
01C0 | 8B 31 04 6E E2 92 3C C6 58 12 2F C9 02 40 95 C2
01D0 | 93 F7 E7 F7 E9 59 6C C0 75 0F 55 86 F2 0F 85 6A
01E0 | 56 1F A6 E2 FE 66 06 7C C7 5B A0 F1 A9 ED 76 C9
01F0 | FE DC 8B 13 77 FB DB 9C CC D0 29 37 DD 8E EA 22
0200 | 58 54 5A AA AB 6C BC 77 D9 1D 3F 22 87 41 DE 65
0210 | AB 49 26 4B 36 1B 93 6D 7B E2 06 AA D1 90 4C A5
0220 | 3D 29 14 48 DA D1 98 8B B2 77 9F 15 F6 F9 E8 26
0230 | 2A 7E C2 69 0D 8A 19 4F 0A 66 E8 0C 2C 18 90 1C
0240 | FD 81 1B 7C 2A 6A 07 DE 5A 62 AC 53 E6 BC F0 67
0250 | 9B A3 00 C4 E3 50 1D DF C5 0B 2E 5E 64 69 5A 2F
0260 | 38 C8 97 AD 6C DF 59 6B EB C7 5F 57 AB C5 F2 92
0270 | 8D 7C AE E7 9C 23 66 BA 19 72 FE 1D 98 95 04 1D
0280 | 4D 7F C8 48 3C 96 46 BB 1E BE FB 4D</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 78 4F 2B 88 A8 9C 64
0010 | 78 02 00 00 5C 07 E8 D0 FA DA 40 F3 24 30 86 3C
0020 | 25 83 58 32 EF 2E CF 48 82 93 B0 B5 EF 95 58 C3
0030 | 28 89 A6 F6 05 CA C3 C6 FE 50 02 00 AE 97 57 53
0040 | 05 3F 28 E4 CB 74 11 62 70 70 21 D3 46 28 97 C6
0050 | F2 49 46 98 10 6F 2D 4A 6A 8C CB E8 AE 5D 35 54
0060 | 79 91 F3 81 0C EC E3 3E 14 60 B6 BB 6A 3A C9 B9
0070 | 98 47 F9 5E 3C 47 08 82 E2 1C 9D 2D 0A BD 8D 91
0080 | 71 03 4C EE 99 1F 90 7C 5F 13 1E DE 6E B7 33 0C
0090 | 6E AD 5D 60 60 82 08 BF 40 DB 3D 20 F7 48 0B 34
00A0 | 9B C5 F4 7B 67 F8 15 3F 3C 90 C1 88 68 22 8B 8D
00B0 | A7 35 96 B7 7E 63 55 F9 17 81 B8 A8 42 51 79 EB
00C0 | 05 A7 CE B9 04 0B 3B 25 17 1B E8 2B 17 A4 85 F2
00D0 | 10 90 03 1E 12 26 74 79 8F B0 A8 19 EC 1D 71 53
00E0 | 71 14 29 3B 82 1B 07 67 21 A5 C8 75 E4 F7 8B 1F
00F0 | 2A 9D 1D F1 B3 0D 0A 13 36 7A 00 CD A3 6E EC E6
0100 | 5C 6D 4A 91 D7 59 D6 53 1A 4D E4 AF 02 80 1C 52
0110 | 7E 20 B3 07 D3 27 C5 D0 E3 91 61 59 44 9D 9E C2
0120 | 4E E0 EF CD AA F7 8F 7D 8B F6 47 24 FB 62 FF 0E
0130 | 7D AE D5 66 97 6A FA BC 34 86 A3 26 FB C2 F0 24
0140 | 04 67 F5 D1 D1 CD 7E DF 33 9F F1 1F BE 4D 3F 83
0150 | F4 33 CF 09 03 77 FE 20 47 CA 4B 35 7C 5F 75 4A
0160 | F5 45 F4 3A 8C 09 F8 EE CF 7B 16 0B 31 F8 02 4D
0170 | 5A 7F D8 45 D7 41 83 8A E8 9D 8C 09 B1 97 DB 51
0180 | 29 E1 E1 06 06 51 54 12 97 04 F0 B9 23 74 9F 9B
0190 | 65 D7 E6 B9 3C E4 96 5E 2A 76 EE A2 AE 18 44 4C
01A0 | 5B 41 6E 08 62 C0 7F 83 AD C7 7D 35 02 22 5E 47
01B0 | 5C B1 28 2B 25 1B F0 69 24 D5 ED F6 F1 98 7D 50
01C0 | 1C 27 95 56 F0 FD 1B 4E 78 DC A0 72 A4 22 EE B6
01D0 | 6A 80 73 A9 5E 93 92 8F 0D 40 FF AC E7 ED CB 49
01E0 | C5 85 11 0E 66 A0 C4 B3 47 BC 44 7B 8E 3D 78 03
01F0 | 49 26 BE 45 58 19 AA CC D4 DE 2F 16 D4 3D 4D FC
0200 | B0 36 E0 41 88 2D A8 30 C1 28 3E AB 16 B7 04 0A
0210 | 67 56 EC EA DD 88 9A 5E E7 57 B7 75 F5 B9 21 8F
0220 | 3A CB A2 C3 90 E4 FA 7E AD 1D 05 4F E4 B9 8D 4C
0230 | 31 04 6F 4D 3F AA E0 97 8E 8A 73 C2 32 38 8E 11
0240 | B7 F1 FC C8 86 78 73 BD FC 99 74 FC 89 1A 95 7D
0250 | 09 56 05 11 82 D7 B5 C6 3E FA 4E C3 3D 55 54 88
0260 | 17 10 B2 41 1A 20 1C 5C 00 FF 19 4B DD 50 6F 7B
0270 | D2 B4 6B E0 DE D0 9A 68 13 14 8B 03 6D 50 E1 5B
0280 | 9C 1A 7D F2 75 C1 73 40 FC C4 E9 03</code></pre>
<p>Payload (de)serialization:</p>
<pre><code>server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:string = Server_DH_Params;</code></pre>
<table class="table">
@ -458,13 +465,13 @@ random_padding_bytes = 216450FD2A974A81475A90261BAE56428354F18BEE55BFB415135941F
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>01F4AA18DD9D9C64</code></td>
<td><code>01784F2B88A89C64</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>84020000</code> (644 in decimal)</td>
<td><code>78020000</code> (632 in decimal)</td>
<td>Message body length</td>
</tr>
<tr>
@ -476,41 +483,40 @@ random_padding_bytes = 216450FD2A974A81475A90261BAE56428354F18BEE55BFB415135941F
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>encrypted_answer</td>
<td>56, 596</td>
<td><code>FE500200702FF1032B5BA7264B04CD20</code> <code>AA980FB82179D016274600128EC86B8E</code> <code>705D09B6C9239AA697A99D0D6B9F397B</code> <code>58122C49205C606290C64B67FD47AA12</code> <code>5EBC7820891E117C9910984D5F824F3B</code> <code>513E112E733D3A795C0C82F159364B35</code> <code>9FED51E065AE464E0ADFF05E657595EF</code> <code>0DDE7D28D73A86420485483CBD77ADEE</code> <code>1BAFCB0002074D766AC6B7C30D4B412F</code> <code>E2DE9BC70EFD5DC2E7BAA4D52E96AFE6</code> <code>8AFB4DE4C18E16034E1F0D1ED89307B7</code> <code>324595BF8FDF834C109EA1E0B9D9D0B6</code> <code>56A3B3BBB1C3FC3627FFF3DE470D22C8</code> <code>375B6C7699AD67EF0F720B16F9EA695C</code> <code>530D13E585A7E61290995817CB21ED22</code> <code>CD74BB94218C39CBA860F6653E43BBC7</code> <code>2C02A047B811CD4D6A4846EFA8D3F919</code> <code>06D9056AAF890E0EF51EA3A72DFC7FB6</code> <code>CE81746F1EA045CFB5714D2AE04EC012</code> <code>CF9A4424CCB23CCCBB4C8482CEBF064B</code> <code>EE18EEAF2A43850199C74431EDBB105C</code> <code>63CA66BA313784405DB0E74FDD70D0D5</code> <code>E22EFD16572B790F9CE2035E51E68B82</code> <code>7B1B7C8E3648E2C37FBEF24AD25D7E97</code> <code>95B9183DB2C86E308B31046EE2923CC6</code> <code>58122FC9024095C293F7E7F7E9596CC0</code> <code>750F5586F20F856A561FA6E2FE66067C</code> <code>C75BA0F1A9ED76C9FEDC8B1377FBDB9C</code> <code>CCD02937DD8EEA2258545AAAAB6CBC77</code> <code>D91D3F228741DE65AB49264B361B936D</code> <code>7BE206AAD1904CA53D291448DAD1988B</code> <code>B2779F15F6F9E8262A7EC2690D8A194F</code> <code>0A66E80C2C18901CFD811B7C2A6A07DE</code> <code>5A62AC53E6BCF0679BA300C4E3501DDF</code> <code>C50B2E5E64695A2F38C897AD6CDF596B</code> <code>EBC75F57ABC5F2928D7CAEE79C2366BA</code> <code>1972FE1D9895041D4D7FC8483C9646BB</code><br> <code>1EBEFB4D</code></td>
<td><code>FE500200AE975753053F28E4CB741162</code> <code>707021D3462897C6F2494698106F2D4A</code> <code>6A8CCBE8AE5D35547991F3810CECE33E</code> <code>1460B6BB6A3AC9B99847F95E3C470882</code> <code>E21C9D2D0ABD8D9171034CEE991F907C</code> <code>5F131EDE6EB7330C6EAD5D60608208BF</code> <code>40DB3D20F7480B349BC5F47B67F8153F</code> <code>3C90C18868228B8DA73596B77E6355F9</code> <code>1781B8A8425179EB05A7CEB9040B3B25</code> <code>171BE82B17A485F21090031E12267479</code> <code>8FB0A819EC1D71537114293B821B0767</code> <code>21A5C875E4F78B1F2A9D1DF1B30D0A13</code> <code>367A00CDA36EECE65C6D4A91D759D653</code> <code>1A4DE4AF02801C527E20B307D327C5D0</code> <code>E3916159449D9EC24EE0EFCDAAF78F7D</code> <code>8BF64724FB62FF0E7DAED566976AFABC</code> <code>3486A326FBC2F0240467F5D1D1CD7EDF</code> <code>339FF11FBE4D3F83F433CF090377FE20</code> <code>47CA4B357C5F754AF545F43A8C09F8EE</code> <code>CF7B160B31F8024D5A7FD845D741838A</code> <code>E89D8C09B197DB5129E1E10606515412</code> <code>9704F0B923749F9B65D7E6B93CE4965E</code> <code>2A76EEA2AE18444C5B416E0862C07F83</code> <code>ADC77D3502225E475CB1282B251BF069</code> <code>24D5EDF6F1987D501C279556F0FD1B4E</code> <code>78DCA072A422EEB66A8073A95E93928F</code> <code>0D40FFACE7EDCB49C585110E66A0C4B3</code> <code>47BC447B8E3D78034926BE455819AACC</code> <code>D4DE2F16D43D4DFCB036E041882DA830</code> <code>C1283EAB16B7040A6756ECEADD889A5E</code> <code>E757B775F5B9218F3ACBA2C390E4FA7E</code> <code>AD1D054FE4B98D4C31046F4D3FAAE097</code> <code>8E8A73C232388E11B7F1FCC8867873BD</code> <code>FC9974FC891A957D0956051182D7B5C6</code> <code>3EFA4EC33D5554881710B2411A201C5C</code> <code>00FF194BDD506F7BD2B46BE0DED09A68</code> <code>13148B036D50E15B9C1A7DF275C17340</code><br> <code>FCC4E903</code></td>
<td>See <a href="#conversion-of-encrypted-answer-into-answer">Decomposition of encrypted_answer »</a></td>
</tr>
</tbody>
</table>
<!-- end server_DH_params_ok -->
<h1><a class="anchor" href="#41-server-dh-inner-data-decryption-and-deserialization" id="41-server-dh-inner-data-decryption-and-deserialization" name="41-server-dh-inner-data-decryption-and-deserialization"><i class="anchor-icon"></i></a>4.1 server_dh_inner_data decryption and deserialization</h1>
<p>Decrypt <code>encrypted_answer</code> using the reverse of the process specified in <a href="/mtproto/auth_key#5-server-responds-with">step 5</a>:</p>
<p>Decrypt <code>encrypted_answer</code> using the reverse of the process specified in <a href="/mtproto/auth_key#5-server-responds-with">step 6</a>:</p>
<!-- start server_DH_inner_data_input -->
<pre><code>encrypted_answer = 702FF1032B5BA7264B04CD20AA980FB82179D016274600128EC86B8E705D09B6C9239AA697A99D0D6B9F397B58122C49205C606290C64B67FD47AA125EBC7820891E117C9910984D5F824F3B513E112E733D3A795C0C82F159364B359FED51E065AE464E0ADFF05E657595EF0DDE7D28D73A86420485483CBD77ADEE1BAFCB0002074D766AC6B7C30D4B412FE2DE9BC70EFD5DC2E7BAA4D52E96AFE68AFB4DE4C18E16034E1F0D1ED89307B7324595BF8FDF834C109EA1E0B9D9D0B656A3B3BBB1C3FC3627FFF3DE470D22C8375B6C7699AD67EF0F720B16F9EA695C530D13E585A7E61290995817CB21ED22CD74BB94218C39CBA860F6653E43BBC72C02A047B811CD4D6A4846EFA8D3F91906D9056AAF890E0EF51EA3A72DFC7FB6CE81746F1EA045CFB5714D2AE04EC012CF9A4424CCB23CCCBB4C8482CEBF064BEE18EEAF2A43850199C74431EDBB105C63CA66BA313784405DB0E74FDD70D0D5E22EFD16572B790F9CE2035E51E68B827B1B7C8E3648E2C37FBEF24AD25D7E9795B9183DB2C86E308B31046EE2923CC658122FC9024095C293F7E7F7E9596CC0750F5586F20F856A561FA6E2FE66067CC75BA0F1A9ED76C9FEDC8B1377FBDB9CCCD02937DD8EEA2258545AAAAB6CBC77D91D3F228741DE65AB49264B361B936D7BE206AAD1904CA53D291448DAD1988BB2779F15F6F9E8262A7EC2690D8A194F0A66E80C2C18901CFD811B7C2A6A07DE5A62AC53E6BCF0679BA300C4E3501DDFC50B2E5E64695A2F38C897AD6CDF596BEBC75F57ABC5F2928D7CAEE79C2366BA1972FE1D9895041D4D7FC8483C9646BB1EBEFB4D
tmp_aes_key = 81A769A19DC0ED0D3DABE397D479407674D72119F479C1425094F54AB0188100
tmp_aes_iv = 3C22B0B11A532C2778AEB3002E5331A7B5D59D62E0E72FA734EB7B62AABBEA0C</code></pre>
<pre><code>encrypted_answer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
tmp_aes_key = 5591331B9FCD7D6497E6CB4AA80ED849263CE0E54F29B93A527A6ED056DCCBC4
tmp_aes_iv = D18064B0BB84ACB797BD4CB2F01B4FDE19F32A390408CAE58C7DCE20E56AF739</code></pre>
<!-- end server_DH_inner_data_input -->
<p>Yielding:</p>
<!-- start server_DH_inner_data_output -->
<pre><code>answer_with_hash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
answer = BA0D89B5365B3A127C5B5909490E6C3AECEC0126C2184E38BAC1649C35FD28FC20E9A7EA03000000FE000100C71CAEB9C6B1C9048E6C522F70F13F73980D40238E3E21C14934D037563D930F48198A0AA7C14058229493D22530F4DBFA336F6E0AC925139543AED44CCE7C3720FD51F69458705AC68CD4FE6B6B13ABDC9746512969328454F18FAF8C595F642477FE96BB2A941D5BCD1D4AC8CC49880708FA9B378E3C4F3A9060BEE67CF9A4A4A695811051907E162753B56B0F6B410DBA74D8A84B2A14B3144E0EF1284754FD17ED950D5965B4B9DD46582DB1178D169C6BC465B0D6FF9CA3928FEF5B9AE4E418FC15E83EBEA0F87FA9FF5EED70050DED2849F47BF959D956850CE929851F0D8115F635B105EE2E4E15D04B2454BF6F4FADF034B10403119CD8E3B92FCC5BFE000100AA3BB529DC2EF3C74A49AB7F8C9A84BFE86F5CC3ACBBBB5EE047566E5AF06CE56F10627D75F886ECD2777D1679B87E81523BB585DC50F768C9A419C22C260B6924B17A8F153B9F260FC161ECE1D595380FC33CDBDF552F019FB829E0701C005A7B849A71F9EF8C5141E01F152466F41BB9F13B0FEF8E0EFC3091DAF7C4A9E4F65F77B4D3F15EC3977FFA6CB6BAB7F995E2CE25398E09DA9EAD7AAA4BF05A9133B954080F7B258F20C0FADE9E44A7B2AA73E51D91AC86720335CBB38A3DB90689D85233899F292228EFB6FD285923760A5E220ADC3F52B3E0265BFC5AB23E4DDC2D4E14E18B2811EE656B5A16586663289D02422C48F1B8D77017EFFCD276E5EDDD9D9C64A1FEA3302BD58173</code></pre>
<pre><code>answer_with_hash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
answer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code></pre>
<!-- end server_DH_inner_data_output -->
<!-- start server_DH_inner_data -->
<p>Generated payload (excluding transport headers/trailers):</p>
<pre><code>0000 | BA 0D 89 B5 36 5B 3A 12 7C 5B 59 09 49 0E 6C 3A
0010 | EC EC 01 26 C2 18 4E 38 BA C1 64 9C 35 FD 28 FC
0020 | 20 E9 A7 EA 03 00 00 00 FE 00 01 00 C7 1C AE B9
<pre><code>0000 | BA 0D 89 B5 FA DA 40 F3 24 30 86 3C 25 83 58 32
0010 | EF 2E CF 48 82 93 B0 B5 EF 95 58 C3 28 89 A6 F6
0020 | 05 CA C3 C6 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
@ -527,23 +533,23 @@ answer = BA0D89B5365B3A127C5B5909490E6C3AECEC0126C2184E38BAC1649C35FD28FC20E9A7E
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 | AA 3B B5 29 DC 2E F3 C7 4A 49 AB 7F 8C 9A 84 BF
0140 | E8 6F 5C C3 AC BB BB 5E E0 47 56 6E 5A F0 6C E5
0150 | 6F 10 62 7D 75 F8 86 EC D2 77 7D 16 79 B8 7E 81
0160 | 52 3B B5 85 DC 50 F7 68 C9 A4 19 C2 2C 26 0B 69
0170 | 24 B1 7A 8F 15 3B 9F 26 0F C1 61 EC E1 D5 95 38
0180 | 0F C3 3C DB DF 55 2F 01 9F B8 29 E0 70 1C 00 5A
0190 | 7B 84 9A 71 F9 EF 8C 51 41 E0 1F 15 24 66 F4 1B
01A0 | B9 F1 3B 0F EF 8E 0E FC 30 91 DA F7 C4 A9 E4 F6
01B0 | 5F 77 B4 D3 F1 5E C3 97 7F FA 6C B6 BA B7 F9 95
01C0 | E2 CE 25 39 8E 09 DA 9E AD 7A AA 4B F0 5A 91 33
01D0 | B9 54 08 0F 7B 25 8F 20 C0 FA DE 9E 44 A7 B2 AA
01E0 | 73 E5 1D 91 AC 86 72 03 35 CB B3 8A 3D B9 06 89
01F0 | D8 52 33 89 9F 29 22 28 EF B6 FD 28 59 23 76 0A
0200 | 5E 22 0A DC 3F 52 B3 E0 26 5B FC 5A B2 3E 4D DC
0210 | 2D 4E 14 E1 8B 28 11 EE 65 6B 5A 16 58 66 63 28
0220 | 9D 02 42 2C 48 F1 B8 D7 70 17 EF FC D2 76 E5 ED
0230 | DD 9D 9C 64</code></pre>
0130 | 16 FF 6E A3 81 CE BA C8 34 CD 02 D5 F6 1E 51 E8
0140 | 0F 7B B2 03 51 E4 69 26 C8 14 96 7E 6E A9 67 D6
0150 | CD 00 66 A5 A3 00 FF FD 94 67 03 6A A1 1D C0 B4
0160 | 71 1A 2A D0 BA 0A 91 E2 37 BD 29 0F 87 94 35 B4
0170 | 59 DE 03 2D 26 27 16 90 9E 6C 69 96 BC ED 43 46
0180 | 1D 53 60 BC D8 C0 03 95 09 F0 F5 7F D4 FD 9B 77
0190 | F9 A1 E8 4C 3D 37 76 3A 01 43 92 4F C1 01 C8 F1
01A0 | B0 4B 21 40 FF 36 8E DB A7 E9 EF 9E 58 E6 B8 6C
01B0 | 02 8B 46 FA 8B 1D 05 CE B6 DF 48 E5 76 AA 7C 08
01C0 | EC 53 51 3A CE F7 1E AB 76 ED 09 A1 79 14 B6 37
01D0 | 1D 4C 2F 86 EE A1 CB 56 52 43 3E 3C 3E A4 26 20
01E0 | 11 CB BE 35 55 44 3B B1 40 33 2E EB F9 C7 E6 D0
01F0 | 7C 75 9A E7 D1 A5 B5 73 8E 17 A7 DA 9E 5D BD EE
0200 | 2B C1 CC 90 35 65 95 CD 42 F3 8F DE CC DB 2A 1A
0210 | 3F C3 D9 00 9F 8B 73 73 D9 58 F5 E4 9B B4 5E 8D
0220 | B3 9A D9 DD CC C4 8A 47 5D 30 B3 BB 88 78 CA E5
0230 | 88 A8 9C 64</code></pre>
<p>Payload (de)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">
@ -565,13 +571,13 @@ answer = BA0D89B5365B3A127C5B5909490E6C3AECEC0126C2184E38BAC1649C35FD28FC20E9A7E
<tr>
<td>nonce</td>
<td>4, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>20, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
@ -589,49 +595,49 @@ answer = BA0D89B5365B3A127C5B5909490E6C3AECEC0126C2184E38BAC1649C35FD28FC20E9A7E
<tr>
<td>g_a</td>
<td>300, 260</td>
<td><code>FE000100AA3BB529DC2EF3C74A49AB7F</code> <code>8C9A84BFE86F5CC3ACBBBB5EE047566E</code> <code>5AF06CE56F10627D75F886ECD2777D16</code> <code>79B87E81523BB585DC50F768C9A419C2</code> <code>2C260B6924B17A8F153B9F260FC161EC</code> <code>E1D595380FC33CDBDF552F019FB829E0</code> <code>701C005A7B849A71F9EF8C5141E01F15</code> <code>2466F41BB9F13B0FEF8E0EFC3091DAF7</code> <code>C4A9E4F65F77B4D3F15EC3977FFA6CB6</code> <code>BAB7F995E2CE25398E09DA9EAD7AAA4B</code> <code>F05A9133B954080F7B258F20C0FADE9E</code> <code>44A7B2AA73E51D91AC86720335CBB38A</code> <code>3DB90689D85233899F292228EFB6FD28</code> <code>5923760A5E220ADC3F52B3E0265BFC5A</code> <code>B23E4DDC2D4E14E18B2811EE656B5A16</code> <code>586663289D02422C48F1B8D77017EFFC</code><br> <code>D276E5ED</code></td>
<td><code>FE00010016FF6EA381CEBAC834CD02D5</code> <code>F61E51E80F7BB20351E46926C814967E</code> <code>6EA967D6CD0066A5A300FFFD9467036A</code> <code>A11DC0B4711A2AD0BA0A91E237BD290F</code> <code>879435B459DE032D262716909E6C6996</code> <code>BCED43461D5360BCD8C0039509F0F57F</code> <code>D4FD9B77F9A1E84C3D37763A0143924F</code> <code>C101C8F1B04B2140FF368EDBA7E9EF9E</code> <code>58E6B86C028B46FA8B1D05CEB6DF48E5</code> <code>76AA7C08EC53513ACEF71EAB76ED09A1</code> <code>7914B6371D4C2F86EEA1CB5652433E3C</code> <code>3EA4262011CBBE3555443BB140332EEB</code> <code>F9C7E6D07C759AE7D1A5B5738E17A7DA</code> <code>9E5DBDEE2BC1CC90356595CD42F38FDE</code> <code>CCDB2A1A3FC3D9009F8B7373D958F5E4</code> <code>9BB45E8DB39AD9DDCCC48A475D30B3BB</code><br> <code>8878CAE5</code></td>
<td><code>g_a</code> diffie-hellman parameter</td>
</tr>
<tr>
<td>server_time</td>
<td>560, 4</td>
<td><code>DD9D9C64</code> (1687985629 in decimal)</td>
<td><code>88A89C64</code> (1687988360 in decimal)</td>
<td>Server time</td>
</tr>
</tbody>
</table>
<!-- end server_DH_inner_data -->
<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>
<h5><a class="anchor" href="#7-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message" id="7-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message" name="7-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message"><i class="anchor-icon"></i></a>7) Client computes random 2048-bit number <em>b</em> (using a sufficient amount of entropy) and sends the server a message</h5>
<p>First, generate a secure random 2048-bit number b:</p>
<!-- start b -->
<pre><code>b = 3333AB3DDBC89A3297AFD5C1FD314F9F6F90D3FDFB47EEC50B6710C2378B98D18EDDB06FD1977780D8B10A5DE2B5CBAD8FADD3F6526F3ECB8AF27ADF629915701287D23BC30EC426C4DCF8663DA2D700A98617E74EEFDDA53F4F6DEC2086406FC9FD1EBF423380E57C796B599978B6A028A70CA23D9D53318A9CD17C4AF652CA9119AFB6031EBD15293D1BFEA24183FE033113FF79BCC7C9A472CFC4CEFC800793CBC2366777525895056107937C7C52C34CD318F91F8B59D5DAA100AE11A2C4381D2FC16086C8C46BA641CF25036F52575688956773C91C734D7BF63FBC699795669B832A879A93B06238720B35A46B4C8878627D96C18577C978BFE9499157</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>
<h6>7.1) generation of encrypted_data</h6>
<!-- start client_DH_inner_data -->
<p>Generated payload (excluding transport headers/trailers):</p>
<pre><code>0000 | 54 B6 43 66 36 5B 3A 12 7C 5B 59 09 49 0E 6C 3A
0010 | EC EC 01 26 C2 18 4E 38 BA C1 64 9C 35 FD 28 FC
0020 | 20 E9 A7 EA 00 00 00 00 00 00 00 00 FE 00 01 00
0030 | 3D E7 53 B9 F0 98 5A 68 E1 4B D9 5E 3B 72 0F CB
0040 | 61 7E B5 89 9A A2 87 72 C8 B4 77 BA D4 FA 95 44
0050 | C6 71 AA 9D 4B 3E 2F 90 AB DC 55 B2 5A 61 AD 4F
0060 | E5 13 2A D3 CF ED C5 EA 19 61 10 F4 E4 F0 26 56
0070 | F5 7D 61 FC E0 5D 66 0F 12 9D D1 B8 17 A0 03 F7
0080 | 37 83 BA 04 11 03 A1 99 B0 AA B7 6A 13 FF FC 33
0090 | 9C 35 DB 8A 36 8F CB B4 B3 53 87 CB 82 A0 19 88
00A0 | 6F EF B1 72 27 61 6B BE 28 78 18 B5 55 3E 33 92
00B0 | 47 89 02 88 C2 DC 60 77 FE 72 1F 76 9F 92 75 1F
00C0 | 63 7E 17 31 D1 10 18 03 E5 22 F2 93 D4 BE B4 B1
00D0 | 7F DF 12 1F B5 C2 3B 8D 0E F2 B0 2A 07 06 63 8F
00E0 | D6 41 5B 5A 7E 90 B8 A5 5A E6 CA 13 E2 F2 38 BF
00F0 | 4C 78 56 D1 40 6E D5 46 D7 A6 A7 9C BC ED DB F2
0100 | 20 9C 0F 07 45 02 06 7B 7A 15 B2 AD 28 EE 13 9D
0110 | 22 50 00 6E CE 5A 24 49 C8 7F 2B 0E AA 0B 2C B7
0120 | 5C D9 7D 77 50 55 49 5D B0 3C 7E 03 F9 F6 14 DF</code></pre>
<pre><code>0000 | 54 B6 43 66 FA DA 40 F3 24 30 86 3C 25 83 58 32
0010 | EF 2E CF 48 82 93 B0 B5 EF 95 58 C3 28 89 A6 F6
0020 | 05 CA C3 C6 00 00 00 00 00 00 00 00 FE 00 01 00
0030 | 6C AC FC 73 0C 86 DE 7C F1 14 F5 68 5E C4 56 F4
0040 | 78 2B 25 4C 4D 34 0F 0D 7E 6D E5 68 9D 8D FB 2F
0050 | EC 55 39 50 F4 8D 6E 02 7F 98 2F 4A DE 4D 78 3D
0060 | 93 60 80 4B B6 DD 9A 81 C2 2A EC 69 C7 41 77 E7
0070 | EC CB 1D 5F 41 B4 23 1E BB 6C F6 AE 69 E7 15 77
0080 | 55 95 0A 42 A4 E2 71 71 90 0E 98 DA 31 4C F4 92
0090 | F1 D1 24 B6 9F AA 20 3A F0 7C 8C 61 5F C3 2F 9E
00A0 | A2 8C 78 6C 61 02 F7 B5 71 93 2F FA 1E 32 16 EB
00B0 | D8 F9 EA 47 09 D9 BF 12 12 DB 7D 9E B4 E0 81 B0
00C0 | 91 2C 94 A1 36 EF 66 D0 CD 70 65 FD B4 D9 AB 12
00D0 | 3F C9 2D 00 9A 00 FE 5E 06 B3 CC 1A 01 5F 56 1C
00E0 | A8 9C E9 F7 90 7A 5F 5D 95 F3 65 44 BF D9 B5 88
00F0 | CC 27 D8 D9 ED D1 31 3B 64 25 DA FF 97 EB 04 A9
0100 | BD 47 D4 DA 15 D6 E3 B9 51 C6 31 B3 51 59 82 E8
0110 | 6A 16 3F EE 16 1F F7 C7 04 85 C1 BC AA 67 5B F6
0120 | FD 1E C3 76 D3 83 E1 C1 77 07 BF 18 02 E5 12 91</code></pre>
<p>Payload (de)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">
@ -653,73 +659,73 @@ answer = BA0D89B5365B3A127C5B5909490E6C3AECEC0126C2184E38BAC1649C35FD28FC20E9A7E
<tr>
<td>nonce</td>
<td>4, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>20, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>g_b</td>
<td>36, 260</td>
<td><code>FE0001003DE753B9F0985A68E14BD95E</code> <code>3B720FCB617EB5899AA28772C8B477BA</code> <code>D4FA9544C671AA9D4B3E2F90ABDC55B2</code> <code>5A61AD4FE5132AD3CFEDC5EA196110F4</code> <code>E4F02656F57D61FCE05D660F129DD1B8</code> <code>17A003F73783BA041103A199B0AAB76A</code> <code>13FFFC339C35DB8A368FCBB4B35387CB</code> <code>82A019886FEFB17227616BBE287818B5</code> <code>553E339247890288C2DC6077FE721F76</code> <code>9F92751F637E1731D1101803E522F293</code> <code>D4BEB4B17FDF121FB5C23B8D0EF2B02A</code> <code>0706638FD6415B5A7E90B8A55AE6CA13</code> <code>E2F238BF4C7856D1406ED546D7A6A79C</code> <code>BCEDDBF2209C0F074502067B7A15B2AD</code> <code>28EE139D2250006ECE5A2449C87F2B0E</code> <code>AA0B2CB75CD97D775055495DB03C7E03</code><br> <code>F9F614DF</code></td>
<td><code>FE0001006CACFC730C86DE7CF114F568</code> <code>5EC456F4782B254C4D340F0D7E6DE568</code> <code>9D8DFB2FEC553950F48D6E027F982F4A</code> <code>DE4D783D9360804BB6DD9A81C22AEC69</code> <code>C74177E7ECCB1D5F41B4231EBB6CF6AE</code> <code>69E7157755950A42A4E27171900E98DA</code> <code>314CF492F1D124B69FAA203AF07C8C61</code> <code>5FC32F9EA28C786C6102F7B571932FFA</code> <code>1E3216EBD8F9EA4709D9BF1212DB7D9E</code> <code>B4E081B0912C94A136EF66D0CD7065FD</code> <code>B4D9AB123FC92D009A00FE5E06B3CC1A</code> <code>015F561CA89CE9F7907A5F5D95F36544</code> <code>BFD9B588CC27D8D9EDD1313B6425DAFF</code> <code>97EB04A9BD47D4DA15D6E3B951C631B3</code> <code>515982E86A163FEE161FF7C70485C1BC</code> <code>AA675BF6FD1EC376D383E1C17707BF18</code><br> <code>02E51291</code></td>
<td>Single-byte prefix denoting length, a 256-byte (2048-bit) string, and zero bytes of padding</td>
</tr>
<tr>
<td>retry_id</td>
<td>296, 8</td>
<td><code>0000000000000000</code></td>
<td>Equal to zero at the time of the first attempt; otherwise, it is equal to <code>auth_key_aux_hash</code> from the previous failed attempt (see <a href="/mtproto/auth_key#9-server-responds-in-one-of-three-ways">Item 9</a>).</td>
<td>Equal to zero at the time of the first attempt; otherwise, it is equal to <code>auth_key_aux_hash</code> from the previous failed attempt (see Item 7).</td>
</tr>
</tbody>
</table>
<!-- end client_DH_inner_data -->
<p>The serialization of <em>Client_DH_Inner_Data</em> produces a string <strong>data</strong>. This is used to generate <strong>encrypted_data</strong> as specified in <a href="#6-client-computes-random-2048-bit-number-b-using-a-sufficient-amount-of-entropy-and-sends-the-server-a-message">step 6</a>, using the following inputs:</p>
<!-- start client_DH_inner_data_input -->
<pre><code>data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
padding = 8FD908884FACC949D9DC73DE
tmp_aes_key = 81A769A19DC0ED0D3DABE397D479407674D72119F479C1425094F54AB0188100
tmp_aes_iv = 3C22B0B11A532C2778AEB3002E5331A7B5D59D62E0E72FA734EB7B62AABBEA0C</code></pre>
<pre><code>data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
padding = ADBCA793403652D954B1FC6C
tmp_aes_key = 5591331B9FCD7D6497E6CB4AA80ED849263CE0E54F29B93A527A6ED056DCCBC4
tmp_aes_iv = D18064B0BB84ACB797BD4CB2F01B4FDE19F32A390408CAE58C7DCE20E56AF739</code></pre>
<!-- end client_DH_inner_data_input -->
<p>Process:</p>
<pre><code>data_with_hash := SHA1(data) + data + padding (0-15 random bytes such that total length is divisible by 16)
encrypted_data := AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv);</code></pre>
<p>Output:</p>
<!-- start client_DH_inner_data_output -->
<pre><code>encrypted_data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code></pre>
<pre><code>encrypted_data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code></pre>
<!-- end client_DH_inner_data_output -->
<p>The length of the final string is 336 bytes.</p>
<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>
<h6>7.2) set_client_DH_params query</h6>
<!-- 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 DD 9D 9C 64
0010 | 78 01 00 00 1F 5F 04 F5 36 5B 3A 12 7C 5B 59 09
0020 | 49 0E 6C 3A EC EC 01 26 C2 18 4E 38 BA C1 64 9C
0030 | 35 FD 28 FC 20 E9 A7 EA FE 50 01 00 93 33 06 04
0040 | E4 4C 6F 99 33 49 C6 0F 05 C2 3E DC 56 B8 44 B5
0050 | 7C 65 4A ED F1 9B 44 F5 EF 8D B9 59 0F 7D 9A 9F
0060 | 8E 81 C5 0C 37 7E 34 81 D8 DF 9D D5 85 D4 5A E2
0070 | 5D 3B 9E 51 CE 4F F5 84 13 02 36 69 7C 14 C6 BB
0080 | FD 65 59 9D 53 13 2A B5 FB 31 FF 4A AC 92 EC 7F
0090 | 25 6B 5F 9C E8 FF B7 47 F7 7E 9F 81 58 8D 27 7E
00A0 | 3D FF B9 F1 4E 36 42 AC D2 A1 F9 BB E6 60 54 60
00B0 | 86 27 02 76 92 D2 A0 8D CC 66 71 A4 E6 A4 3E FF
00C0 | 37 05 3E 7F 57 DA 1E 04 D8 D6 39 5D 27 BD 09 D7
00D0 | D4 9F 46 71 3C F0 23 20 73 B3 42 A3 E2 F3 4D 23
00E0 | D9 D8 CD 70 E1 54 A7 13 B0 AF AC C2 79 10 AB C4
00F0 | 9D 99 EB A8 82 FE BC 22 F6 A5 E7 FD 5A E5 AB F4
0100 | 93 52 37 2F A6 4D 9D 11 BF 43 80 19 7C 59 AE DE
0110 | 23 D1 1D D7 E0 9F AB DD 85 A6 17 3C D0 CB 8F 1D
0120 | FD 7D 03 01 C6 DD 4E 40 FD DC 9C 3A 80 C1 E5 AB
0130 | DC 51 AD FE F3 57 75 3C 7B 7D 4D E4 E8 A4 CA F1
0140 | 0D F7 24 8B CD AC E1 25 A0 8A 35 CB F4 A0 21 CF
0150 | A1 D7 8F 60 6E E6 04 BA 14 F0 12 B1 3F 22 25 2C
0160 | 95 2F D5 2B 05 60 67 9C 63 16 81 88 B0 78 05 E4
0170 | 56 13 C7 EF EE 8C 54 95 E7 29 31 C2 55 3A 0F CA
0180 | 7B B1 1D 3E D4 8F 1A 50 43 DC 77 6D</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 00 00 00 00 88 A8 9C 64
0010 | 78 01 00 00 1F 5F 04 F5 FA DA 40 F3 24 30 86 3C
0020 | 25 83 58 32 EF 2E CF 48 82 93 B0 B5 EF 95 58 C3
0030 | 28 89 A6 F6 05 CA C3 C6 FE 50 01 00 38 F1 71 9D
0040 | 5B 8E F6 E2 AA B7 4F F2 FD 0B 2A 57 31 7F 19 71
0050 | CF 66 A6 8A D1 34 58 9D 66 FF B9 5C 11 52 B1 85
0060 | C5 54 21 B7 47 30 80 AE 93 78 75 46 16 60 19 B3
0070 | 91 20 7A BF A3 B1 10 C4 42 B0 F3 19 CB 73 8D B7
0080 | 30 36 41 DA 3E 21 65 23 19 23 A9 3D 11 36 92 0F
0090 | B4 76 46 14 BC 2F 9A 9A 13 27 38 19 AF 01 9D C3
00A0 | 33 32 FB 87 B1 F1 79 C1 A2 28 B4 4B B0 3E 36 73
00B0 | D6 64 97 9F 8F 50 38 5A 5F 97 79 C5 5C BD 9F DE
00C0 | 7B A9 4A F9 DB 9A ED F5 D3 0A F6 21 E3 8E 80 06
00D0 | B6 34 29 73 1E 4F D6 3E 52 4B F0 8D AE 17 B2 98
00E0 | E0 E7 22 1E B4 35 87 82 AB 7B 95 CD EC 66 B5 01
00F0 | 43 D4 15 CD 0C FC 4C BA 2C AB 26 D4 20 3B 37 BA
0100 | 4A B2 23 69 4B 51 87 EA 6F 3B 01 76 90 A5 CE 7A
0110 | 5B C6 AF E0 E4 9A A0 5C B9 0C EF 4B 6E 9B E6 47
0120 | 03 03 2A 49 A7 6E AC 8A B0 6F 2F 2C 23 BE 94 F9
0130 | 6D 9F 32 BE 36 91 85 28 85 CF 1A 69 13 94 C5 A0
0140 | B4 6C CB E6 6A 3B 96 74 63 E9 16 3A 19 41 4F CC
0150 | 67 03 01 82 3E 9F C1 E9 B3 DD BB 66 68 0E 97 C2
0160 | 67 A8 F7 43 CC 6D 20 CE 0C 4E 55 7B 7F 51 92 3A
0170 | 9F 3B EF 77 E7 19 0B 42 C1 BA CB 24 69 0C 47 6E
0180 | A6 BD D7 F7 C7 3A 99 AE 42 AF 8F D7</code></pre>
<p>Payload (de)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">
@ -741,7 +747,7 @@ encrypted_data := AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv);<
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>00000000DD9D9C64</code></td>
<td><code>0000000088A89C64</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>
@ -759,38 +765,38 @@ encrypted_data := AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv);<
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>encrypted_data</td>
<td>56, 340</td>
<td><code>FE50010093330604E44C6F993349C60F</code> <code>05C23EDC56B844B57C654AEDF19B44F5</code> <code>EF8DB9590F7D9A9F8E81C50C377E3481</code> <code>D8DF9DD585D45AE25D3B9E51CE4FF584</code> <code>130236697C14C6BBFD65599D53132AB5</code> <code>FB31FF4AAC92EC7F256B5F9CE8FFB747</code> <code>F77E9F81588D277E3DFFB9F14E3642AC</code> <code>D2A1F9BBE66054608627027692D2A08D</code> <code>CC6671A4E6A43EFF37053E7F57DA1E04</code> <code>D8D6395D27BD09D7D49F46713CF02320</code> <code>73B342A3E2F34D23D9D8CD70E154A713</code> <code>B0AFACC27910ABC49D99EBA882FEBC22</code> <code>F6A5E7FD5AE5ABF49352372FA64D9D11</code> <code>BF4380197C59AEDE23D11DD7E09FABDD</code> <code>85A6173CD0CB8F1DFD7D0301C6DD4E40</code> <code>FDDC9C3A80C1E5ABDC51ADFEF357753C</code> <code>7B7D4DE4E8A4CAF10DF7248BCDACE125</code> <code>A08A35CBF4A021CFA1D78F606EE604BA</code> <code>14F012B13F22252C952FD52B0560679C</code> <code>63168188B07805E45613C7EFEE8C5495</code> <code>E72931C2553A0FCA7BB11D3ED48F1A50</code><br> <code>43DC776D</code></td>
<td><code>FE50010038F1719D5B8EF6E2AAB74FF2</code> <code>FD0B2A57317F1971CF66A68AD134589D</code> <code>66FFB95C1152B185C55421B7473080AE</code> <code>93787546166019B391207ABFA3B110C4</code> <code>42B0F319CB738DB7303641DA3E216523</code> <code>1923A93D1136920FB4764614BC2F9A9A</code> <code>13273819AF019DC33332FB87B1F179C1</code> <code>A228B44BB03E3673D664979F8F50385A</code> <code>5F9779C55CBD9FDE7BA94AF9DB9AEDF5</code> <code>D30AF621E38E8006B63429731E4FD63E</code> <code>524BF08DAE17B298E0E7221EB4358782</code> <code>AB7B95CDEC66B50143D415CD0CFC4CBA</code> <code>2CAB26D4203B37BA4AB223694B5187EA</code> <code>6F3B017690A5CE7A5BC6AFE0E49AA05C</code> <code>B90CEF4B6E9BE64703032A49A76EAC8A</code> <code>B06F2F2C23BE94F96D9F32BE36918528</code> <code>85CF1A691394C5A0B46CCBE66A3B9674</code> <code>63E9163A19414FCC670301823E9FC1E9</code> <code>B3DDBB66680E97C267A8F743CC6D20CE</code> <code>0C4E557B7F51923A9F3BEF77E7190B42</code> <code>C1BACB24690C476EA6BDD7F7C73A99AE</code><br> <code>42AF8FD7</code></td>
<td>Encrypted client_DH_inner_data generated previously, serialized as a TL byte string</td>
</tr>
</tbody>
</table>
<!-- end set_client_DH_params -->
<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>
<h5><a class="anchor" href="#8-auth-key-generation" id="8-auth-key-generation" name="8-auth-key-generation"><i class="anchor-icon"></i></a>8) Auth key generation</h5>
<p>The client computes the auth_key using formula <code>g_a^b mod dh_prime</code>:</p>
<!-- start auth_key -->
<pre><code>auth_key = 05ACE659A2FCCFDE0B093E1FAC47A3FA50D252047AE565F40311FC448366518D7419AA9E1ACE2AAB527BAF62405988E30B8A604BA8FADFEDCB0E36A0C9DD11CEF496105F252996DDC7925D5BB0DDA956448F460AC373FAF99575CC8D477C77B90261092265F272DF7B82753DEBDC86831D36FFF971F05CD9D9E5A09088FE293F2E9BCF08A75B66A9FE01D91CD75707B8F91BEAFD541EA235CB831CCF7694DFAB9C7E1BECF60CCBF2A38C1CD413DCB9D2E109153F66693A54E5DECAB905BBF1D7434D6FCF6A7C8D5A9787DA866ACC25B9F1317D7DD34C185ADD5A90861CF592DD0B8C09F825D26FDE8F3E17AE16478BB5D7F95AE11D4F674D8D21EAF6CC67CF29</code></pre>
<pre><code>auth_key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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>
<h5><a class="anchor" href="#9-final-server-reply" id="9-final-server-reply" name="9-final-server-reply"><i class="anchor-icon"></i></a>9) Final server reply</h5>
<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 A8 E5 65 DD 9D 9C 64
0010 | A0 00 00 00 34 F7 CB 3B 36 5B 3A 12 7C 5B 59 09
0020 | 49 0E 6C 3A EC EC 01 26 C2 18 4E 38 BA C1 64 9C
0030 | 35 FD 28 FC 20 E9 A7 EA 20 6C 98 37 3F A1 E0 49
0040 | 14 C0 9B E1 57 2B 96 3C</code></pre>
<pre><code>0000 | 00 00 00 00 00 00 00 00 01 D0 27 78 88 A8 9C 64
0010 | 34 00 00 00 34 F7 CB 3B FA DA 40 F3 24 30 86 3C
0020 | 25 83 58 32 EF 2E CF 48 82 93 B0 B5 EF 95 58 C3
0030 | 28 89 A6 F6 05 CA C3 C6 50 DA F0 67 93 65 D2 53
0040 | 2F DE 18 A4 36 13 0C A2</code></pre>
<p>Payload (de)serialization:</p>
<pre><code>dh_gen_ok#3bcbf734 nonce:int128 server_nonce:int128 new_nonce_hash1:int128 = Set_client_DH_params_answer;</code></pre>
<table class="table">
@ -812,13 +818,13 @@ encrypted_data := AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv);<
<tr>
<td>message_id</td>
<td>8, 8</td>
<td><code>01A8E565DD9D9C64</code></td>
<td><code>01D0277888A89C64</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>A0000000</code> (160 in decimal)</td>
<td><code>34000000</code> (52 in decimal)</td>
<td>Message body length</td>
</tr>
<tr>
@ -830,19 +836,19 @@ encrypted_data := AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv);<
<tr>
<td>nonce</td>
<td>24, 16</td>
<td><code>365B3A127C5B5909490E6C3AECEC0126</code></td>
<td><code>FADA40F32430863C25835832EF2ECF48</code></td>
<td>Value generated by client in Step 1</td>
</tr>
<tr>
<td>server_nonce</td>
<td>40, 16</td>
<td><code>C2184E38BAC1649C35FD28FC20E9A7EA</code></td>
<td><code>8293B0B5EF9558C32889A6F605CAC3C6</code></td>
<td>Value received from server in Step 2</td>
</tr>
<tr>
<td>new_nonce_hash1</td>
<td>56, 16</td>
<td><code>206C98373FA1E04914C09BE1572B963C</code></td>
<td><code>50DAF0679365D2532FDE18A436130CA2</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>