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< li class = "" > < a href = "/api" > API< / a > < / li >
< li class = "active" > < a href = "/mtproto" > Protocol< / a > < / li >
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< 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 >
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< div id = "dev_page_content" > <!-- scroll_nav -->
< p > In the examples below, the < a href = "/mtproto#transport" > transport< / a > headers are omitted:< / p >
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< blockquote >
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< 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 >
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< / blockquote >
< p > Detailed documentation on creating authorization keys is available < a href = "/mtproto/auth_key" > here »< / a > .< / p >
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< 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 >
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< pre > < code > 0000 | 00 00 00 00 00 00 00 00 2C A3 0D 00 0D 0D C3 66
0010 | 14 00 00 00 F1 8E 7E BE AC 7E C6 49 66 2E CF 3C
0020 | F3 BA 99 1B 9D 8D AB D5< / code > < / pre >
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< p > Payload (de)serialization:< / p >
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< pre > < code > req_pq_multi#be7e8ef1 nonce:int128 = ResPQ;< / code > < / pre >
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< table class = "table" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > auth_key_id< / td >
< td > 0, 8< / td >
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< td > < code > 0000000000000000< / code > < / td >
< td > 0 since the message is in plain text< / td >
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< / tr >
< tr >
< td > message_id< / td >
< td > 8, 8< / td >
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< td > < code > 2CA30D000D0DC366< / code > < / td >
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< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > (unixtime() < < 32) + (N*4)< / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > 14000000< / code > (20 in decimal)< / td >
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< td > Message body length< / td >
< / tr >
< tr >
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< td > %(req_pq_multi)< / td >
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< td > 20, 4< / td >
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< td > < code > f18e7ebe< / code > < / td >
< td > < em > req_pq_multi< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
< td > 24, 16< / td >
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< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Random number< / td >
< / tr >
< / tbody >
< / table >
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<!-- end req_pq_multi -->
< 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 >
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< pre > < code > 0000 | 00 00 00 00 00 00 00 00 01 74 FF E0 0D 0D C3 66
0010 | 90 00 00 00 63 24 16 05 AC 7E C6 49 66 2E CF 3C
0020 | F3 BA 99 1B 9D 8D AB D5 6C 8D 9C F5 77 54 AE 5A
0030 | 5C B3 05 75 9A 60 50 D0 08 1B E3 63 A4 6F 8E DF
0040 | C1 00 00 00 15 C4 B5 1C 03 00 00 00 A5 B7 F7 09
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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 >
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< pre > < code > resPQ#05162463 nonce:int128 server_nonce:int128 pq:string server_public_key_fingerprints:Vector< strlong> = ResPQ;< / code > < / pre >
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< table class = "table" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > auth_key_id< / td >
< td > 0, 8< / td >
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< td > < code > 0000000000000000< / code > < / td >
< td > 0 since the message is in plain text< / td >
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< / tr >
< tr >
< td > message_id< / td >
< td > 8, 8< / td >
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< td > < code > 0174FFE00D0DC366< / code > < / td >
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< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > (unixtime() < < 32) + (N*4)< / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > 90000000< / code > (144 in decimal)< / td >
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< td > Message body length< / td >
< / tr >
< tr >
< td > %(resPQ)< / td >
< td > 20, 4< / td >
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< td > < code > 63241605< / code > < / td >
< td > < em > resPQ< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
< td > 24, 16< / td >
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< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
< td > 40, 16< / td >
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< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Server-generated random number< / td >
< / tr >
< tr >
< td > pq< / td >
< td > 56, 12< / td >
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< td > < code > 081BE363A46F8EDFC1000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 2009559416634793921< / td >
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< td > Single-byte prefix denoting length, an 8-byte string, and three bytes of padding< / td >
< / tr >
< tr >
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< td > %(Vector strlong)< / td >
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< td > 68, 4< / td >
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< td > < code > 15c4b51c< / code > < / td >
< td > < em > Vector t< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > count< / td >
< td > 72, 4< / td >
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< td > < code > 03000000< / code > < / td >
< td > Number of elements in server_public_key_fingerprints< / td >
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< / tr >
< tr >
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< td > server_public_key_fingerprints[0]< / td >
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< td > 76, 8< / td >
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< td > < code > A5B7F709355FC30B< / code > < / td >
< td > 64 lower-order bits of < code > SHA1(server_public_key)< / code > < / td >
< / tr >
< tr >
< td > server_public_key_fingerprints[1]< / td >
< td > 84, 8< / td >
< td > < code > 216BE86C022BB4C3< / code > < / td >
< td > 64 lower-order bits of < code > SHA1(server_public_key)< / code > < / td >
< / tr >
< tr >
< td > server_public_key_fingerprints[2]< / td >
< td > 92, 8< / td >
< td > < code > 85FD64DE851D9DD0< / code > < / td >
< td > 64 lower-order bits of < code > SHA1(server_public_key)< / code > < / td >
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< / tr >
< / tbody >
< / table >
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<!-- end resPQ -->
< p > In our case, the client only has the following public keys, with the following fingerprints:< / p >
<!-- start fingerprints -->
< ul >
< li > < code > 85FD64DE851D9DD0< / code > < / li >
< / ul >
< p > Let's choose the only matching key, the one with fingerprint equal to < code > 85FD64DE851D9DD0< / code > .< / p >
<!-- end fingerprints -->
< 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 >
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< h5 > < a class = "anchor" href = "#3-client-decomposes-pq-into-prime-factors-such-that-p-lt-q" id = "3-client-decomposes-pq-into-prime-factors-such-that-p-lt-q" name = "3-client-decomposes-pq-into-prime-factors-such-that-p-lt-q" > < i class = "anchor-icon" > < / i > < / a > 3) Client decomposes pq into prime factors such that p < q.< / h5 >
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<!-- start pq -->
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< pre > < code > pq = 2009559416634793921< / code > < / pre >
< p > Decompose into 2 prime cofactors < code > p < q< / code > : < code > 2009559416634793921 = 1090123583 * 1843423487< / code > < / p >
< pre > < code > p = 1090123583
q = 1843423487< / code > < / pre >
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<!-- end pq -->
< 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 >
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< pre > < code > 0000 | 95 5F F5 A9 08 1B E3 63 A4 6F 8E DF C1 00 00 00
0010 | 04 40 F9 F7 3F 00 00 00 04 6D E0 68 FF 00 00 00
0020 | AC 7E C6 49 66 2E CF 3C F3 BA 99 1B 9D 8D AB D5
0030 | 6C 8D 9C F5 77 54 AE 5A 5C B3 05 75 9A 60 50 D0
0040 | DB 3F 7E 5E 2E E1 CF 4C 86 05 74 57 84 5C 5C 5B
0050 | 4F 2A 99 51 F0 38 E4 31 B2 94 33 4E 12 C6 C4 19
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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 >
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< table class = "table" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td > %(p_q_inner_data_dc)< / td >
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< td > 0, 4< / td >
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< td > < code > 955ff5a9< / code > < / td >
< td > < em > p_q_inner_data_dc< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > pq< / td >
< td > 4, 12< / td >
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< td > < code > 081BE363A46F8EDFC1000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 2009559416634793921< / td >
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< td > Single-byte prefix denoting length, 8-byte string, and three bytes of padding< / td >
< / tr >
< tr >
< td > p< / td >
< td > 16, 8< / td >
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< td > < code > 0440F9F73F000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1090123583< / td >
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< 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 >
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< td > < code > 046DE068FF000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1843423487< / td >
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< 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 >
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< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
< td > 48, 16< / td >
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< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
< td > new_nonce< / td >
< td > 64, 32< / td >
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< td > < code > DB3F7E5E2EE1CF4C86057457845C5C5B< / code > < code > 4F2A9951F038E431B294334E12C6C419< / code > < / td >
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< td > Client-generated random number< / td >
< / tr >
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< tr >
< td > dc< / td >
< td > 96, 4< / td >
< td > < code > 02000000< / code > (2 in decimal)< / td >
< td > DC ID: < code > 10000< / code > (decimal) has to be added to the DC ID to connect to the test servers; it has to be made negative if the DC we're connecting to is a media (not CDN) DC.< / td >
< / tr >
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< / tbody >
< / table >
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<!-- end p_q_inner_data_dc -->
< 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 -->
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< pre > < code > data = 955FF5A9081BE363A46F8EDFC10000000440F9F73F000000046DE068FF000000AC7EC649662ECF3CF3BA991B9D8DABD56C8D9CF57754AE5A5CB305759A6050D0DB3F7E5E2EE1CF4C86057457845C5C5B4F2A9951F038E431B294334E12C6C41902000000
random_padding_bytes = 82EF77A67CA950176B3C8A6AED8C49B22B5B8338E93D9A8077219C1F643736C7ADE8802882B4E6667914AA15469B2AAC5111CA5F9D52D0C5949AAB0B8F9D894DCDA3ECD755440EBBC1A5FD15EB5486870DA7BA006C53D35B1C76B0B4< / code > < / pre >
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<!-- end p_q_inner_data_input -->
< p > And this is the output:< / p >
<!-- start p_q_inner_data_output -->
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< pre > < code > encrypted_data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code > < / pre >
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<!-- end p_q_inner_data_output -->
< p > The length of the final string is 256 bytes.< / p >
< 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 >
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< pre > < code > 0000 | 00 00 00 00 00 00 00 00 94 C9 0E 00 0E 0D C3 66
0010 | 40 01 00 00 BE E4 12 D7 AC 7E C6 49 66 2E CF 3C
0020 | F3 BA 99 1B 9D 8D AB D5 6C 8D 9C F5 77 54 AE 5A
0030 | 5C B3 05 75 9A 60 50 D0 04 40 F9 F7 3F 00 00 00
0040 | 04 6D E0 68 FF 00 00 00 85 FD 64 DE 85 1D 9D D0
0050 | FE 00 01 00 C7 10 92 A1 87 94 98 AD 33 CC AF 6B
0060 | F2 F4 81 45 F0 F6 24 E2 0B 99 A8 43 9C FC 4D 59
0070 | 97 4E D6 29 93 99 FE 92 C8 0D 06 DF 95 1C DA 75
0080 | 7A AB 30 14 EC 0B 33 B7 D9 B1 F9 AB 6B FF 3C FB
0090 | 72 84 55 2A 27 BB C4 2F BC E1 D5 D2 2B B0 5E 9D
00A0 | 90 F0 46 91 F5 0C 99 0B F4 F3 15 D2 04 F1 20 8F
00B0 | CC 93 8C 59 F0 4B 7F 8E 61 2D AA 6F 65 BD 76 8A
00C0 | 08 5D 42 63 F0 24 49 64 47 83 3F 73 1D B4 C9 96
00D0 | 0B E5 26 3F 98 F4 48 C3 2F 89 43 25 8C 68 7D C7
00E0 | CD 6C 35 81 FD 37 1B 21 14 65 4F 3A 5C D9 2B C0
00F0 | 32 E8 C6 B6 44 D8 59 D5 61 57 12 BA 52 8C F8 EC
0100 | 73 E1 B0 88 7E 20 4C A8 18 47 30 4A 2F B3 C4 AA
0110 | AA 8A 45 C3 64 D6 CC 6F E0 70 91 3B 7B 19 C2 04
0120 | 5B E3 42 6D 2C FE C5 53 3A 0C A2 8D 5B 47 D6 97
0130 | 52 D6 8F 74 0C B1 BC 9C 23 CD 15 59 C2 05 4B AF
0140 | 7E B8 62 2C 39 34 8A 2B 95 A7 D7 9F D4 F8 A3 90
0150 | 1B 15 01 C5< / code > < / pre >
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< 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 >
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< table class = "table" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > auth_key_id< / td >
< td > 0, 8< / td >
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< td > < code > 0000000000000000< / code > < / td >
< td > 0 since the message is in plain text< / td >
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< / tr >
< tr >
< td > message_id< / td >
< td > 8, 8< / td >
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< td > < code > 94C90E000E0DC366< / code > < / td >
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< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > (unixtime() < < 32) + (N*4)< / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > 40010000< / code > (320 in decimal)< / td >
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< td > Message body length< / td >
< / tr >
< tr >
< td > %(req_DH_params)< / td >
< td > 20, 4< / td >
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< td > < code > bee412d7< / code > < / td >
< td > < em > req_DH_params< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
< td > 24, 16< / td >
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< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
< td > 40, 16< / td >
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< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
< td > p< / td >
< td > 56, 8< / td >
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< td > < code > 0440F9F73F000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1090123583< / td >
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< 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 >
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< td > < code > 046DE068FF000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1843423487< / td >
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< td > Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding< / td >
< / tr >
< tr >
< td > public_key_fingerprint< / td >
< td > 72, 8< / td >
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< td > < code > 85FD64DE851D9DD0< / code > < / td >
< td > < code > fingerprint< / code > of public key used< / td >
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< / tr >
< tr >
< td > encrypted_data< / td >
< td > 80, 260< / td >
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< td > < code > FE000100C71092A1879498AD33CCAF6B< / code > < code > F2F48145F0F624E20B99A8439CFC4D59< / code > < code > 974ED6299399FE92C80D06DF951CDA75< / code > < code > 7AAB3014EC0B33B7D9B1F9AB6BFF3CFB< / code > < code > 7284552A27BBC42FBCE1D5D22BB05E9D< / code > < code > 90F04691F50C990BF4F315D204F1208F< / code > < code > CC938C59F04B7F8E612DAA6F65BD768A< / code > < code > 085D4263F024496447833F731DB4C996< / code > < code > 0BE5263F98F448C32F8943258C687DC7< / code > < code > CD6C3581FD371B2114654F3A5CD92BC0< / code > < code > 32E8C6B644D859D5615712BA528CF8EC< / code > < code > 73E1B0887E204CA81847304A2FB3C4AA< / code > < code > AA8A45C364D6CC6FE070913B7B19C204< / code > < code > 5BE3426D2CFEC5533A0CA28D5B47D697< / code > < code > 52D68F740CB1BC9C23CD1559C2054BAF< / code > < code > 7EB8622C39348A2B95A7D79FD4F8A390< / code > < br > < code > 1B1501C5< / code > < / td >
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< td > Value generated above< / td >
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< / tr >
< / tbody >
< / table >
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<!-- end req_DH_params -->
< 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 >
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< pre > < code > 0000 | 00 00 00 00 00 00 00 00 01 3C 42 AF 0E 0D C3 66
0010 | F0 02 00 00 5C 07 E8 D0 AC 7E C6 49 66 2E CF 3C
0020 | F3 BA 99 1B 9D 8D AB D5 6C 8D 9C F5 77 54 AE 5A
0030 | 5C B3 05 75 9A 60 50 D0 FE 50 02 00 28 D0 E4 6D
0040 | 08 A4 80 08 9A 50 37 02 51 A2 2F 16 07 0A 5D 0F
0050 | C7 51 4D BB 6D F2 BE 81 A6 48 9E 9B 53 66 A1 DD
0060 | 30 C4 DD 51 E9 98 54 E0 FA 9A A1 A2 3F 97 F4 A2
0070 | E6 80 59 DF 84 AE C5 5C 3F 81 06 55 51 F3 A0 66
0080 | B1 17 8F 4C F2 82 C6 34 A6 07 87 3F 42 10 87 C0
0090 | 73 99 FE EC 09 07 36 B9 7C 5D 2E FD 71 DB 7D C0
00A0 | B7 2B F3 B6 36 C6 D6 3E 20 FE DE 5D 86 5A 71 8E
00B0 | 85 84 DE 49 9E 8C 94 54 38 03 B4 40 30 54 C8 FE
00C0 | DE C8 1C AF F5 C7 56 6B 65 6B 4D 85 EF 92 7A 7C
00D0 | 06 A3 CF ED 2E 45 19 A6 22 EE 63 D5 FE 5D 51 1F
00E0 | 3A 01 9B 63 FC 11 F9 5B BC E7 FD E9 B0 58 C9 A7
00F0 | 12 02 09 C8 0C 57 38 08 43 59 8B 62 3B 94 FC D7
0100 | 16 96 04 7F 2A E1 07 69 0E 2F CD 61 EB 05 DA 5A
0110 | 6E 0F 13 FA 1E E1 4C 7B E1 E5 5D 47 D0 96 A7 87
0120 | 6F 2E 27 A3 C3 62 44 A9 86 E6 17 D9 1A 36 44 D7
0130 | DE 98 96 8B FD 09 A4 2C EB 3B 66 14 7A 0F C7 76
0140 | 92 2A F1 2D A3 37 7C 8F 33 AA C5 CF C8 75 0C 2F
0150 | 4C F9 89 48 09 EF E9 81 F2 88 63 64 FA 81 C7 59
0160 | 0A 12 24 4D 00 66 B8 62 D4 2D 78 86 5D DE 8F 2C
0170 | 8C 3E 1E ED FA ED 40 1A E2 36 23 D9 19 23 AA CC
0180 | A0 71 EE 9D D6 E3 F8 F6 C4 25 A6 06 AF 0B FE F1
0190 | 75 A5 17 B6 D4 F7 5C 56 BE 51 F6 DC 45 95 D7 45
01A0 | 4D A1 B5 DA D0 5D 59 69 F8 3F E8 DA F2 1C E6 CD
01B0 | 4A 57 95 12 CA FF 5F 58 D9 BC 9A 8E 45 92 95 D1
01C0 | 35 45 DD 4A C9 B8 37 7B 7A EC 68 2C F3 D7 7E FB
01D0 | D4 6B 46 5D 74 40 1F DA C1 7A 6A E4 C3 2F 1A 80
01E0 | 53 23 DC 9B 87 DB 38 21 05 38 E1 5D B5 B9 DE DA
01F0 | 6A 83 92 E0 1C 4C C4 02 27 16 36 FE BE 42 FE 7A
0200 | 2C 81 35 C4 85 A1 A1 04 F4 9B 1F 48 4F B1 8A 80
0210 | C8 C0 97 D3 D0 C2 0A 9B 4D 93 09 86 33 8E 2D F5
0220 | 56 59 CD F5 0C DE 50 E4 5E 05 CA 09 A3 94 8B BE
0230 | 2F 3D 68 E3 EA 5F 3B BF 3E 2E 9F F2 1B B4 5B 18
0240 | AF B4 44 F6 75 41 6C 27 C5 5F 3F 52 DA 11 B6 10
0250 | D6 C0 D7 07 90 1B 5A 39 3F 81 51 80 1A 3E 2E 38
0260 | 75 37 DC 21 DA EF 83 D1 44 1C 47 48 86 60 C0 07
0270 | 5F FE 01 D0 E2 0F 65 57 8F FB 6C F2 B3 98 25 38
0280 | 4B 29 5F BD 83 9B 46 FA 64 16 C0 A4< / code > < / pre >
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< 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 >
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< table class = "table" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > auth_key_id< / td >
< td > 0, 8< / td >
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< td > < code > 0000000000000000< / code > < / td >
< td > 0 since the message is in plain text< / td >
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< / tr >
< tr >
< td > message_id< / td >
< td > 8, 8< / td >
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< td > < code > 013C42AF0E0DC366< / code > < / td >
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< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > (unixtime() < < 32) + (N*4)< / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > F0020000< / code > (752 in decimal)< / td >
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< td > Message body length< / td >
< / tr >
< tr >
< td > %(server_DH_params_ok)< / td >
< td > 20, 4< / td >
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< td > < code > 5c07e8d0< / code > < / td >
< td > < em > server_DH_params_ok< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
< td > 24, 16< / td >
2024-09-18 00:21:45 +02:00
< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
< td > 40, 16< / td >
2024-09-18 00:21:45 +02:00
< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
< td > encrypted_answer< / td >
< td > 56, 596< / td >
2024-09-18 00:21:45 +02:00
< td > < code > FE50020028D0E46D08A480089A503702< / code > < code > 51A22F16070A5D0FC7514DBB6DF2BE81< / code > < code > A6489E9B5366A1DD30C4DD51E99854E0< / code > < code > FA9AA1A23F97F4A2E68059DF84AEC55C< / code > < code > 3F81065551F3A066B1178F4CF282C634< / code > < code > A607873F421087C07399FEEC090736B9< / code > < code > 7C5D2EFD71DB7DC0B72BF3B636C6D63E< / code > < code > 20FEDE5D865A718E8584DE499E8C9454< / code > < code > 3803B4403054C8FEDEC81CAFF5C7566B< / code > < code > 656B4D85EF927A7C06A3CFED2E4519A6< / code > < code > 22EE63D5FE5D511F3A019B63FC11F95B< / code > < code > BCE7FDE9B058C9A7120209C80C573808< / code > < code > 43598B623B94FCD71696047F2AE10769< / code > < code > 0E2FCD61EB05DA5A6E0F13FA1EE14C7B< / code > < code > E1E55D47D096A7876F2E27A3C36244A9< / code > < code > 86E617D91A3644D7DE98968BFD09A42C< / code > < code > EB3B66147A0FC776922AF12DA3377C8F< / code > < code > 33AAC5CFC8750C2F4CF9894809EFE981< / code > < code > F2886364FA81C7590A12244D0066B862< / code > < code > D42D78865DDE8F2C8C3E1EEDFAED401A< / code > < code > E23623D91923AACCA071EE9DD6E3F8F6< / code > < code > C425A606AF0BFEF175A517B6D4F75C56< / code > < code > BE51F6DC4595D7454DA1B5DAD05D5969< / code > < code > F83FE8DAF21CE6CD4A579512CAFF5F58< / code > < code > D9BC9A8E459295D13545DD4AC9B8377B< / code > < code > 7AEC682CF3D77EFBD46B465D74401FDA< / code > < code > C17A6AE4C32F1A805323DC9B87DB3821< / code > < code > 0538E15DB5B9DEDA6A8392E01C4CC402< / code > < code > 271636FEBE42FE7A2C8135C485A1A104< / code > < code > F49B1F484FB18A80C8C097D3D0C20A9B< / code > < code > 4D930986338E2DF55659CDF50CDE50E4< / code > < code > 5E05CA09A3948BBE2F3D68E3EA5F3BBF< / code > < code > 3E2E9FF21BB45B18AFB444F675416C27< / code > < code > C55F3F52DA11B610D6C0D707901B5A39< / code > < code > 3F8151801A3E2E387537DC21DAEF83D1< / code > < code > 441C47488660C0075FFE01D0E20F6557< / code > < code > 8FFB6CF2B39825384B295FBD839B46FA< / code > < br > < code > 6416C0A4< / code > < / td >
2022-05-14 00:37:40 +02:00
< td > See below< / td >
< / tr >
< / tbody >
< / table >
2023-06-29 09:45:26 +02:00
<!-- end server_DH_params_ok -->
< p > Decrypt < code > encrypted_answer< / code > using the reverse of the process specified in < a href = "/mtproto/auth_key#6-server-responds-with" > step 6< / a > :< / p >
<!-- start server_DH_inner_data_input -->
2024-09-18 00:21:45 +02:00
< pre > < code > encrypted_answer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
tmp_aes_key = F9AC244019A3D256B2D0B2A57CCBCB837A05D4A70685F26C926FBAAED69F4148
tmp_aes_iv = 1F5D43DF6BEE2B294A86F4F1DCE4E0A30C97CECB011C15F2E09241A4DB3F7E5E< / code > < / pre >
2023-06-29 09:45:26 +02:00
<!-- end server_DH_inner_data_input -->
< p > Yielding:< / p >
<!-- start server_DH_inner_data_output -->
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< pre > < code > answer_with_hash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
answer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code > < / pre >
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<!-- end server_DH_inner_data_output -->
<!-- start server_DH_inner_data -->
< p > Generated payload (excluding transport headers/trailers):< / p >
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< pre > < code > 0000 | BA 0D 89 B5 AC 7E C6 49 66 2E CF 3C F3 BA 99 1B
0010 | 9D 8D AB D5 6C 8D 9C F5 77 54 AE 5A 5C B3 05 75
0020 | 9A 60 50 D0 03 00 00 00 FE 00 01 00 C7 1C AE B9
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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
0060 | 0A C9 25 13 95 43 AE D4 4C CE 7C 37 20 FD 51 F6
0070 | 94 58 70 5A C6 8C D4 FE 6B 6B 13 AB DC 97 46 51
0080 | 29 69 32 84 54 F1 8F AF 8C 59 5F 64 24 77 FE 96
0090 | BB 2A 94 1D 5B CD 1D 4A C8 CC 49 88 07 08 FA 9B
00A0 | 37 8E 3C 4F 3A 90 60 BE E6 7C F9 A4 A4 A6 95 81
00B0 | 10 51 90 7E 16 27 53 B5 6B 0F 6B 41 0D BA 74 D8
00C0 | A8 4B 2A 14 B3 14 4E 0E F1 28 47 54 FD 17 ED 95
00D0 | 0D 59 65 B4 B9 DD 46 58 2D B1 17 8D 16 9C 6B C4
00E0 | 65 B0 D6 FF 9C A3 92 8F EF 5B 9A E4 E4 18 FC 15
00F0 | E8 3E BE A0 F8 7F A9 FF 5E ED 70 05 0D ED 28 49
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
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0130 | 7B 42 B2 99 03 9F BD E3 A5 89 69 36 83 98 69 7A
0140 | C9 52 27 1D C4 3A 54 38 E7 78 2B B6 52 91 F6 94
0150 | 83 57 5A 6E D2 C3 63 0E 91 75 C7 D4 23 17 43 05
0160 | FF 38 2C E1 DE D0 89 5A 9C EA FA 2E E9 22 D6 AB
0170 | F3 09 66 65 98 8A 10 F8 6D 45 8A 96 7E 13 28 15
0180 | 4A 8B 6D EF A5 7C 04 43 27 6A AA AF C9 BF 7E BE
0190 | FD FD 6B 1A 51 2B 7A 7D A6 04 2C 75 AD 9A 1D A9
01A0 | 9C 1B 8D A5 29 1E 61 4F 94 2F E5 1F D4 FC 13 4D
01B0 | 8C 8E 4A 20 20 21 5F D8 03 45 5E 0D 1C F1 2A 48
01C0 | B0 3E 77 FE 29 42 4D 18 4D 09 5B 54 55 39 18 3A
01D0 | EA C1 C5 DA 98 0A DA 7E F3 BC 20 49 3A 00 BB EA
01E0 | D8 19 93 39 81 E9 18 4B ED 92 21 1B 76 C0 2B 66
01F0 | DC 1A 54 91 86 34 A1 AE B3 16 71 78 B8 46 46 5F
0200 | B1 72 CD 52 5C 2A C7 DE A4 C7 C3 42 06 8E EC ED
0210 | 72 40 98 1B 35 3F 47 60 1F 45 B5 2E 83 B7 AD 97
0220 | D4 00 CF 5F D3 1F 81 08 08 D8 D8 57 EB 89 24 93
0230 | 0E 0D C3 66< / code > < / pre >
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< p > Payload (de)serialization:< / p >
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< 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" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > %(server_DH_inner_data)< / td >
< td > 0, 4< / td >
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< td > < code > ba0d89b5< / code > < / td >
< td > < em > server_DH_inner_data< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
< td > 4, 16< / td >
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< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
< td > 20, 16< / td >
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< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
< td > g< / td >
< td > 36, 4< / td >
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< td > < code > 03000000< / code > (3 in decimal)< / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
< td > dh_prime< / td >
< td > 40, 260< / td >
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< 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 >
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< / tr >
< tr >
< td > g_a< / td >
< td > 300, 260< / td >
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< td > < code > FE0001007B42B299039FBDE3A5896936< / code > < code > 8398697AC952271DC43A5438E7782BB6< / code > < code > 5291F69483575A6ED2C3630E9175C7D4< / code > < code > 23174305FF382CE1DED0895A9CEAFA2E< / code > < code > E922D6ABF3096665988A10F86D458A96< / code > < code > 7E1328154A8B6DEFA57C0443276AAAAF< / code > < code > C9BF7EBEFDFD6B1A512B7A7DA6042C75< / code > < code > AD9A1DA99C1B8DA5291E614F942FE51F< / code > < code > D4FC134D8C8E4A2020215FD803455E0D< / code > < code > 1CF12A48B03E77FE29424D184D095B54< / code > < code > 5539183AEAC1C5DA980ADA7EF3BC2049< / code > < code > 3A00BBEAD819933981E9184BED92211B< / code > < code > 76C02B66DC1A54918634A1AEB3167178< / code > < code > B846465FB172CD525C2AC7DEA4C7C342< / code > < code > 068EECED7240981B353F47601F45B52E< / code > < code > 83B7AD97D400CF5FD31F810808D8D857< / code > < br > < code > EB892493< / code > < / td >
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< td > < code > g_a< / code > diffie-hellman parameter< / td >
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< / tr >
< tr >
< td > server_time< / td >
< td > 560, 4< / td >
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< td > < code > 0E0DC366< / code > (1724058894 in decimal)< / td >
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< td > Server time< / td >
< / tr >
< / tbody >
< / table >
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<!-- end server_DH_inner_data -->
< 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 -->
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< pre > < code > b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code > < / pre >
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<!-- end b -->
< p > Then compute < code > g_b = pow(g, b) mod dh_prime< / code > < / p >
<!-- start g_b -->
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< pre > < code > g_b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code > < / pre >
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<!-- end g_b -->
< h6 > 7.1) generation of encrypted_data< / h6 >
<!-- start client_DH_inner_data -->
< p > Generated payload (excluding transport headers/trailers):< / p >
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< pre > < code > 0000 | 54 B6 43 66 AC 7E C6 49 66 2E CF 3C F3 BA 99 1B
0010 | 9D 8D AB D5 6C 8D 9C F5 77 54 AE 5A 5C B3 05 75
0020 | 9A 60 50 D0 00 00 00 00 00 00 00 00 FE 00 01 00
0030 | 8D 12 78 EB 55 A8 9D 36 7A 6E 59 DA 3E DE 2F B1
0040 | 97 71 9F ED B8 D0 26 7A E1 5A 60 9E 6E 63 13 52
0050 | A2 BA F8 C2 87 7A D5 60 10 AF 1A 7C 28 C5 8F 67
0060 | C8 2E 7F 16 36 0B 40 51 9F E7 5E 16 99 30 B9 6F
0070 | 55 D6 77 B3 F2 48 E0 14 72 A7 68 00 BC 08 CE 8D
0080 | AA 89 19 E4 90 2D 5E 9C 5B 34 4A D4 D7 5D FA 75
0090 | 00 70 1C 0B 6E 43 BC B2 7D D1 03 8B 77 DA 5B E1
00A0 | 5E 04 78 C9 7F 71 65 0D 65 6D 87 88 14 46 73 59
00B0 | 7A A6 65 ED DD C4 85 F7 03 AB 0A 32 6B CC B8 C1
00C0 | 1D 2C B7 48 67 3D 4D D5 BD 21 C2 79 F3 1F 89 30
00D0 | 36 93 0D C7 4D D5 64 CB C2 DE 3F B2 43 03 29 79
00E0 | A4 1C FD B7 FD 06 46 3F 43 72 1E 79 D0 C2 FD 44
00F0 | F4 BE 37 1C 73 85 D4 8C C7 1D 7A 10 4C F1 BB 8C
0100 | C2 1A C3 FC 7E 64 FD 64 70 21 F7 78 64 DD 28 A6
0110 | 17 F2 38 61 60 A7 DC D7 BA 7E A7 1C 1D E7 D2 1B
0120 | 30 4B EE 61 4B 3F 24 03 1F 70 E2 CE 02 36 8B C7< / code > < / pre >
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< 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 >
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< table class = "table" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > %(client_DH_inner_data)< / td >
< td > 0, 4< / td >
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< td > < code > 54b64366< / code > < / td >
< td > < em > client_DH_inner_data< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
< td > 4, 16< / td >
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< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
< td > 20, 16< / td >
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< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
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< td > g_b< / td >
< td > 36, 260< / td >
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< td > < code > FE0001008D1278EB55A89D367A6E59DA< / code > < code > 3EDE2FB197719FEDB8D0267AE15A609E< / code > < code > 6E631352A2BAF8C2877AD56010AF1A7C< / code > < code > 28C58F67C82E7F16360B40519FE75E16< / code > < code > 9930B96F55D677B3F248E01472A76800< / code > < code > BC08CE8DAA8919E4902D5E9C5B344AD4< / code > < code > D75DFA7500701C0B6E43BCB27DD1038B< / code > < code > 77DA5BE15E0478C97F71650D656D8788< / code > < code > 144673597AA665EDDDC485F703AB0A32< / code > < code > 6BCCB8C11D2CB748673D4DD5BD21C279< / code > < code > F31F893036930DC74DD564CBC2DE3FB2< / code > < code > 43032979A41CFDB7FD06463F43721E79< / code > < code > D0C2FD44F4BE371C7385D48CC71D7A10< / code > < code > 4CF1BB8CC21AC3FC7E64FD647021F778< / code > < code > 64DD28A617F2386160A7DCD7BA7EA71C< / code > < code > 1DE7D21B304BEE614B3F24031F70E2CE< / code > < br > < code > 02368BC7< / code > < / td >
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< td > Single-byte prefix denoting length, a 256-byte (2048-bit) string, and zero bytes of padding< / td >
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< / tr >
< tr >
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< 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 Item 7).< / td >
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< / tr >
< / tbody >
< / table >
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<!-- 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 = "#7-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 -->
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< pre > < code > data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
padding = FE5409530AA9DA24EA778019
tmp_aes_key = F9AC244019A3D256B2D0B2A57CCBCB837A05D4A70685F26C926FBAAED69F4148
tmp_aes_iv = 1F5D43DF6BEE2B294A86F4F1DCE4E0A30C97CECB011C15F2E09241A4DB3F7E5E< / code > < / pre >
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<!-- 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 -->
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< pre > < code > encrypted_data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code > < / pre >
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<!-- end client_DH_inner_data_output -->
< p > The length of the final string is 336 bytes.< / p >
< h6 > 7.2) set_client_DH_params query< / h6 >
<!-- start set_client_DH_params -->
< p > Sent payload (excluding transport headers/trailers):< / p >
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< pre > < code > 0000 | 00 00 00 00 00 00 00 00 98 C9 0E 00 0E 0D C3 66
0010 | 78 01 00 00 1F 5F 04 F5 AC 7E C6 49 66 2E CF 3C
0020 | F3 BA 99 1B 9D 8D AB D5 6C 8D 9C F5 77 54 AE 5A
0030 | 5C B3 05 75 9A 60 50 D0 FE 50 01 00 6D B2 19 EC
0040 | BF 7D 9D 7F 82 C7 4E D3 A0 F9 4C 6B 2D D8 EF D9
0050 | D0 13 CE 3C 83 71 11 87 BC DF AF 7A 7D 64 22 CC
0060 | 35 63 BF 79 7C F4 9D 6B 01 98 99 E8 B0 A9 F6 BF
0070 | F7 34 3A 2F 7B 25 7E 37 C5 AF 8B BE C9 B1 07 A8
0080 | 4D 17 BD 11 56 78 46 C8 04 C2 5C F1 D6 4A 66 94
0090 | 10 EF CF 2D 6F DC E3 46 EC D3 43 1A FA B0 B7 C0
00A0 | A4 B5 14 CC 50 2B 6A A6 6D 3F FF BB 24 0B 09 26
00B0 | E2 74 7E 68 79 10 C2 BA 53 CA FA C8 F7 F6 78 D6
00C0 | 78 89 61 69 CB D6 17 87 33 F0 69 AD 85 B2 3C A0
00D0 | A8 4B F7 6A 52 AA 47 0F DA 80 4A 1F 9F BF 34 A6
00E0 | C9 44 E4 19 69 7A E7 D2 B9 A4 FD 2D 28 BD 44 20
00F0 | 4E 66 FF 5E 6E 71 78 66 91 28 D6 8E DE 1D 03 B2
0100 | 60 20 A1 E9 E2 F3 87 80 FE A6 8A EB 62 97 F7 A2
0110 | 82 E1 64 C9 BA 2D C5 31 7A 75 41 B2 6F 72 6A B2
0120 | B1 3E 81 92 AF CE 8A 66 4F CF C7 1F CD 0B 6A 7F
0130 | 1A 82 9E D7 0C B7 F0 12 6E 0E 15 FC AF E0 7E 10
0140 | 3C A9 09 92 E0 00 71 C9 96 A2 25 7B 25 FA 51 EE
0150 | 5F 2F 97 25 5C 15 FA DC E6 48 D9 05 1C 03 F0 F5
0160 | F5 AB A5 32 CA 7A 53 40 E5 42 4E 48 31 B2 96 F3
0170 | 61 FE 4C 47 AC EC 49 F0 F0 0E 8D A4 34 A5 FC 4C
0180 | FA B5 D0 04 D9 86 7C 9C A9 19 5E C6< / code > < / pre >
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< p > Payload (de)serialization:< / p >
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< 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" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > auth_key_id< / td >
< td > 0, 8< / td >
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< td > < code > 0000000000000000< / code > < / td >
< td > 0 since the message is in plain text< / td >
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< / tr >
< tr >
< td > message_id< / td >
< td > 8, 8< / td >
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< td > < code > 98C90E000E0DC366< / code > < / td >
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< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > (unixtime() < < 32) + (N*4)< / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > 78010000< / code > (376 in decimal)< / td >
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< td > Message body length< / td >
< / tr >
< tr >
< td > %(set_client_DH_params)< / td >
< td > 20, 4< / td >
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< td > < code > 1f5f04f5< / code > < / td >
< td > < em > set_client_DH_params< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
< td > 24, 16< / td >
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< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
< td > 40, 16< / td >
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< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
< td > encrypted_data< / td >
< td > 56, 340< / td >
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< td > < code > FE5001006DB219ECBF7D9D7F82C74ED3< / code > < code > A0F94C6B2DD8EFD9D013CE3C83711187< / code > < code > BCDFAF7A7D6422CC3563BF797CF49D6B< / code > < code > 019899E8B0A9F6BFF7343A2F7B257E37< / code > < code > C5AF8BBEC9B107A84D17BD11567846C8< / code > < code > 04C25CF1D64A669410EFCF2D6FDCE346< / code > < code > ECD3431AFAB0B7C0A4B514CC502B6AA6< / code > < code > 6D3FFFBB240B0926E2747E687910C2BA< / code > < code > 53CAFAC8F7F678D678896169CBD61787< / code > < code > 33F069AD85B23CA0A84BF76A52AA470F< / code > < code > DA804A1F9FBF34A6C944E419697AE7D2< / code > < code > B9A4FD2D28BD44204E66FF5E6E717866< / code > < code > 9128D68EDE1D03B26020A1E9E2F38780< / code > < code > FEA68AEB6297F7A282E164C9BA2DC531< / code > < code > 7A7541B26F726AB2B13E8192AFCE8A66< / code > < code > 4FCFC71FCD0B6A7F1A829ED70CB7F012< / code > < code > 6E0E15FCAFE07E103CA90992E00071C9< / code > < code > 96A2257B25FA51EE5F2F97255C15FADC< / code > < code > E648D9051C03F0F5F5ABA532CA7A5340< / code > < code > E5424E4831B296F361FE4C47ACEC49F0< / code > < code > F00E8DA434A5FC4CFAB5D004D9867C9C< / code > < br > < code > A9195EC6< / code > < / td >
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< td > Encrypted client_DH_inner_data generated previously, serialized as a TL byte string< / td >
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< / tr >
< / tbody >
< / table >
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<!-- end set_client_DH_params -->
< 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 -->
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< pre > < code > auth_key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code > < / pre >
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<!-- end auth_key -->
< 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 >
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< pre > < code > 0000 | 00 00 00 00 00 00 00 00 01 74 0C 9C 0F 0D C3 66
0010 | 60 00 00 00 34 F7 CB 3B AC 7E C6 49 66 2E CF 3C
0020 | F3 BA 99 1B 9D 8D AB D5 6C 8D 9C F5 77 54 AE 5A
0030 | 5C B3 05 75 9A 60 50 D0 A1 20 67 1F 5B 7A 78 E9
0040 | DB D0 18 6D 6D B6 73 54< / code > < / pre >
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< 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 >
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< table class = "table" >
< thead >
< tr >
< th > Parameter< / th >
< th > Offset, Length in bytes< / th >
< th > Value< / th >
< th > Description< / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td > auth_key_id< / td >
< td > 0, 8< / td >
< td > < code > 0000000000000000< / code > < / td >
< td > 0 since the message is in plain text< / td >
< / tr >
< tr >
< td > message_id< / td >
< td > 8, 8< / td >
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< td > < code > 01740C9C0F0DC366< / code > < / td >
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< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > (unixtime() < < 32) + (N*4)< / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > 60000000< / code > (96 in decimal)< / td >
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< td > Message body length< / td >
< / tr >
< tr >
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< td > %(dh_gen_ok)< / td >
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< td > 20, 4< / td >
< td > < code > 34f7cb3b< / code > < / td >
< td > < em > dh_gen_ok< / em > constructor number from TL schema< / td >
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< / tr >
< tr >
< td > nonce< / td >
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< td > 24, 16< / td >
2024-09-18 00:21:45 +02:00
< td > < code > AC7EC649662ECF3CF3BA991B9D8DABD5< / code > < / td >
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< td > Value generated by client in Step 1< / td >
< / tr >
< tr >
< td > server_nonce< / td >
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< td > 40, 16< / td >
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< td > < code > 6C8D9CF57754AE5A5CB305759A6050D0< / code > < / td >
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< td > Value received from server in Step 2< / td >
< / tr >
< tr >
< td > new_nonce_hash1< / td >
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< td > 56, 16< / td >
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< td > < code > A120671F5B7A78E9DBD0186D6DB67354< / code > < / td >
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< 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 >
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< / tr >
< / tbody >
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< / table >
<!-- end dh_gen_ok --> < / div >
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