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< title > Auth key generation example< / title >
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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 -->
< 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 >
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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 >
< pre > < code > 0000 | 00 00 00 00 00 00 00 00 84 8C 00 00 B1 AF 9C 64
0010 | 14 00 00 00 F1 8E 7E BE B0 BB 83 C2 68 49 38 B7
0020 | 6A C4 92 3A A5 45 C8 F0< / code > < / pre >
< 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 > 848C0000B1AF9C64< / code > < / td >
< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > < / 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 > B0BB83C2684938B76AC4923AA545C8F0< / 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 >
< pre > < code > 0000 | 00 00 00 00 00 00 00 00 01 9C 04 77 B1 AF 9C 64
0010 | 50 00 00 00 63 24 16 05 B0 BB 83 C2 68 49 38 B7
0020 | 6A C4 92 3A A5 45 C8 F0 59 2E 37 C5 BF 99 B8 DD
0030 | AE 33 E6 EE 39 4B 47 42 08 2E 07 1E 8F 6E F5 45
0040 | 63 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 >
< pre > < code > resPQ#05162463 nonce:int128 server_nonce:int128 pq:string server_public_key_fingerprints:Vector< long> = 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 > 019C0477B1AF9C64< / code > < / td >
< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > < / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > 50000000< / code > (80 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 > B0BB83C2684938B76AC4923AA545C8F0< / 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 > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 > 082E071E8F6EF54563000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 3316653251972384099< / td >
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< td > Single-byte prefix denoting length, an 8-byte string, and three bytes of padding< / td >
< / tr >
< tr >
< td > %(Vector long)< / td >
< 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 >
< 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 < q.< / h5 >
<!-- start pq -->
< pre > < code > pq = 3316653251972384099< / code > < / pre >
< p > Decompose into 2 prime cofactors: < code > 3316653251972384099 = 1704206131 * 1946157329< / code > < / p >
< pre > < code > p = 1704206131
q = 1946157329< / code > < / pre >
<!-- 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 >
< pre > < code > 0000 | 95 5F F5 A9 08 2E 07 1E 8F 6E F5 45 63 00 00 00
0010 | 04 65 94 1F 33 00 00 00 04 74 00 01 11 00 00 00
0020 | B0 BB 83 C2 68 49 38 B7 6A C4 92 3A A5 45 C8 F0
0030 | 59 2E 37 C5 BF 99 B8 DD AE 33 E6 EE 39 4B 47 42
0040 | FA 05 D4 1E 4C C4 D7 94 58 F8 26 B2 33 4B 26 67
0050 | 5C C6 64 8E 23 E7 62 6B 75 A1 B9 09 98 1A C9 55
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 > 082E071E8F6EF54563000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 3316653251972384099< / 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 > 0465941F33000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1704206131< / 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 > 0474000111000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1946157329< / 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 > B0BB83C2684938B76AC4923AA545C8F0< / 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 > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 > FA05D41E4CC4D79458F826B2334B2667< / code > < code > 5CC6648E23E7626B75A1B909981AC955< / 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 -->
< pre > < code > data = 955FF5A9082E071E8F6EF545630000000465941F330000000474000111000000B0BB83C2684938B76AC4923AA545C8F0592E37C5BF99B8DDAE33E6EE394B4742FA05D41E4CC4D79458F826B2334B26675CC6648E23E7626B75A1B909981AC95502000000
random_padding_bytes = 2F9E22AC78033569C4B3F7035D5FFAFC3EBF28ECD70A65926B2E64D9118B8AB14EB6A100AA469AACCB3B9961D5E588C19A4E0C17F8C5CEDC003442FD0AECC129BFD6EEA4AD293FF753A0B194AB005F24E74FA78A98E10EAA2F16AD98< / 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 >
<!-- 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 >
< pre > < code > 0000 | 00 00 00 00 00 00 00 00 74 07 01 00 B1 AF 9C 64
0010 | 40 01 00 00 BE E4 12 D7 B0 BB 83 C2 68 49 38 B7
0020 | 6A C4 92 3A A5 45 C8 F0 59 2E 37 C5 BF 99 B8 DD
0030 | AE 33 E6 EE 39 4B 47 42 04 65 94 1F 33 00 00 00
0040 | 04 74 00 01 11 00 00 00 85 FD 64 DE 85 1D 9D D0
0050 | FE 00 01 00 DF 92 28 7F 32 BB AE 22 04 9A 7D F8
0060 | 80 07 F9 FB E0 10 3D 8D F5 33 E4 ED 59 C0 A2 5B
0070 | 6D 99 FA 0A 9F 2C 83 A8 E4 5C 28 B2 C7 AB 6D 54
0080 | 1B 38 C6 25 4F DE 09 B7 73 B3 8E CD B9 4B 66 0D
0090 | 71 41 5C DF D4 B8 BA D8 B9 1D C6 0B 83 7B F4 20
00A0 | 5A 78 1A B7 78 85 D8 E0 EF 71 E3 29 D4 B9 35 63
00B0 | 02 C4 D2 BE 16 E3 4A 6A 93 95 59 BE 65 EC 2F 0E
00C0 | FE 2C D5 61 E9 B0 58 A1 3B 5C 8E EE B6 90 7D F8
00D0 | 97 AA 7E 48 BE 7F 7D E1 D1 30 58 47 6C 8E DF 60
00E0 | A7 93 30 D0 A9 17 8E 3F A0 64 EF 06 90 63 BC 37
00F0 | AA A3 CC 1B 5E 0E 34 72 90 E5 C1 19 7A 10 C0 19
0100 | 86 03 5E 20 C0 B1 06 07 4C 85 79 06 13 1A CE 5F
0110 | 75 90 00 37 E1 6F 66 FC 0D 0D 62 38 34 12 CE 7D
0120 | 7A 9D CC 45 AF C3 02 5A D9 97 62 68 66 4F 41 62
0130 | 58 11 75 13 9A 2F 09 10 C6 9C DF BE 9D A9 3C AC
0140 | 8C 3C A6 7A 42 78 E2 CD 2A 67 EF 9D 9F F5 D7 F8
0150 | 66 E2 45 96< / 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 >
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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 > 74070100B1AF9C64< / code > < / td >
< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > < / 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 > B0BB83C2684938B76AC4923AA545C8F0< / 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 > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 > 0465941F33000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1704206131< / 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 > 0474000111000000< / code > < br > TL byte deserialization < br > => bigendian conversion to decimal< br > => 1946157329< / 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 > FE000100DF92287F32BBAE22049A7DF8< / code > < code > 8007F9FBE0103D8DF533E4ED59C0A25B< / code > < code > 6D99FA0A9F2C83A8E45C28B2C7AB6D54< / code > < code > 1B38C6254FDE09B773B38ECDB94B660D< / code > < code > 71415CDFD4B8BAD8B91DC60B837BF420< / code > < code > 5A781AB77885D8E0EF71E329D4B93563< / code > < code > 02C4D2BE16E34A6A939559BE65EC2F0E< / code > < code > FE2CD561E9B058A13B5C8EEEB6907DF8< / code > < code > 97AA7E48BE7F7DE1D13058476C8EDF60< / code > < code > A79330D0A9178E3FA064EF069063BC37< / code > < code > AAA3CC1B5E0E347290E5C1197A10C019< / code > < code > 86035E20C0B106074C857906131ACE5F< / code > < code > 75900037E16F66FC0D0D62383412CE7D< / code > < code > 7A9DCC45AFC3025AD9976268664F4162< / code > < code > 581175139A2F0910C69CDFBE9DA93CAC< / code > < code > 8C3CA67A4278E2CD2A67EF9D9FF5D7F8< / code > < br > < code > 66E24596< / code > < / td >
< 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 >
< pre > < code > 0000 | 00 00 00 00 00 00 00 00 01 30 87 1E B2 AF 9C 64
0010 | 78 02 00 00 5C 07 E8 D0 B0 BB 83 C2 68 49 38 B7
0020 | 6A C4 92 3A A5 45 C8 F0 59 2E 37 C5 BF 99 B8 DD
0030 | AE 33 E6 EE 39 4B 47 42 FE 50 02 00 07 3F F0 CE
0040 | BA 1A 9E F8 80 F8 85 E4 D0 E9 C1 EF 93 F6 1A 18
0050 | BD 1B B7 8D 7A 36 D3 BF 1B 76 6E 28 13 91 02 C4
0060 | 85 BA 0D 47 D3 83 C8 E6 03 9D BB D3 78 BA A6 4D
0070 | C0 67 F1 60 43 96 DA A0 4D 72 1E 11 0D 23 08 F4
0080 | 95 A5 34 DE 44 30 06 DE 91 76 B4 B8 D9 27 24 84
0090 | 02 E1 6D 69 FC 8F 73 48 54 BA FB F8 06 00 4E 43
00A0 | 26 9C A8 C8 72 91 D4 F8 F4 36 84 3A 0C B3 FD 63
00B0 | 1F E4 D7 F4 1E 8F AC 2E 34 EF 84 0B DA C0 33 14
00C0 | 24 8A 4A F6 91 AD AB 7A 0C 6B DC CA 3D 85 FD 49
00D0 | E4 9A E6 E5 18 AF 6D DA 95 CF 03 4F 90 EB 1B 42
00E0 | 50 CD F6 03 F5 81 21 BC 3C 48 89 E0 C6 73 0C 89
00F0 | 77 3A 8D 77 C9 FC 7A F3 05 C9 F9 3B D8 35 10 FB
0100 | F1 B9 8E D7 08 49 61 5A D2 C9 49 7F 9C 8A 94 4C
0110 | B1 D3 A5 1A D1 01 44 B7 77 7A 4A 5E D9 59 FF E0
0120 | 3B 87 3D 4C F0 10 B3 61 C6 2F 7B 42 3E EC 02 CA
0130 | CE 0D 28 0A 6E 34 1E A5 BD AE 28 EF BA 69 D0 50
0140 | 58 10 56 35 6B 7B 6F 66 D9 A9 51 44 16 57 88 42
0150 | 24 0B ED 86 33 38 1F 0C 4A B0 06 C5 4B 60 29 E5
0160 | 8E AF A3 6F 87 2E E7 C9 5B 5D F5 91 C7 C2 68 6A
0170 | 3E 61 48 9F FB 06 F9 10 AC 03 C5 F4 56 B9 A3 C3
0180 | 4A 5C CA CE 67 6E 87 5C F3 E7 67 91 C4 AD 88 C3
0190 | 1F 9D 6F 43 EF 4E 9E F4 8E 0D BC 30 1E F2 9D 2E
01A0 | B3 80 30 70 5E 1A 0F 25 F2 00 7D 54 12 96 66 38
01B0 | DC 51 14 37 1A 63 08 2C 81 46 2C 3B 70 0E A5 35
01C0 | 6E 28 92 3F 50 87 AF 05 1C FD 81 59 B6 4B 2A DC
01D0 | 80 4E 66 CB 70 F6 AD 25 17 21 C6 B8 CA 2F 21 68
01E0 | 73 14 32 C9 67 BC 8B AE AD 02 96 40 E8 0C 2D C2
01F0 | 7A E0 3C FC 5F C1 17 39 65 F9 CD F8 C2 93 1B 6E
0200 | C5 D4 63 51 D7 E7 9D 33 AF BE 6C 58 66 3F 3E AD
0210 | A5 B2 A4 9D F6 CD E1 C9 90 78 61 08 11 65 11 DD
0220 | 9F C6 73 E0 55 9D 84 A5 51 36 C0 01 83 0F E6 2C
0230 | 49 5C 90 39 8E 96 05 49 4E 24 10 7C 02 67 BD A1
0240 | 29 79 7B 7B 1A CF 86 1C 04 F0 7D 6B BA 8B 11 1F
0250 | 88 86 11 E5 63 1E FF 97 16 C4 06 A7 AE 8B E2 DD
0260 | E1 D8 73 FB 57 1C 82 08 8A BD 18 FE 05 1F 6E 4A
0270 | EE 9B 90 94 C6 3F AC 38 CA 68 B4 EA 46 F1 2C D7
0280 | 09 DF DA C9 44 ED 46 AF 79 2F DB A2< / 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 >
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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 > 0130871EB2AF9C64< / code > < / td >
< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > < / td >
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< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
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< td > < code > 78020000< / code > (632 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 >
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< td > < code > B0BB83C2684938B76AC4923AA545C8F0< / 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 >
2023-06-29 09:45:26 +02:00
< td > < code > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 >
2023-06-29 09:45:26 +02:00
< td > < code > FE500200073FF0CEBA1A9EF880F885E4< / code > < code > D0E9C1EF93F61A18BD1BB78D7A36D3BF< / code > < code > 1B766E28139102C485BA0D47D383C8E6< / code > < code > 039DBBD378BAA64DC067F1604396DAA0< / code > < code > 4D721E110D2308F495A534DE443006DE< / code > < code > 9176B4B8D927248402E16D69FC8F7348< / code > < code > 54BAFBF806004E43269CA8C87291D4F8< / code > < code > F436843A0CB3FD631FE4D7F41E8FAC2E< / code > < code > 34EF840BDAC03314248A4AF691ADAB7A< / code > < code > 0C6BDCCA3D85FD49E49AE6E518AF6DDA< / code > < code > 95CF034F90EB1B4250CDF603F58121BC< / code > < code > 3C4889E0C6730C89773A8D77C9FC7AF3< / code > < code > 05C9F93BD83510FBF1B98ED70849615A< / code > < code > D2C9497F9C8A944CB1D3A51AD10144B7< / code > < code > 777A4A5ED959FFE03B873D4CF010B361< / code > < code > C62F7B423EEC02CACE0D280A6E341EA5< / code > < code > BDAE28EFBA69D050581056356B7B6F66< / code > < code > D9A9514416578842240BED8633381F0C< / code > < code > 4AB006C54B6029E58EAFA36F872EE7C9< / code > < code > 5B5DF591C7C2686A3E61489FFB06F910< / code > < code > AC03C5F456B9A3C34A5CCACE676E875C< / code > < code > F3E76791C4AD88C31F9D6F43EF4E9EF4< / code > < code > 8E0DBC301EF29D2EB38030705E1A0F25< / code > < code > F2007D5412966638DC5114371A63082C< / code > < code > 81462C3B700EA5356E28923F5087AF05< / code > < code > 1CFD8159B64B2ADC804E66CB70F6AD25< / code > < code > 1721C6B8CA2F2168731432C967BC8BAE< / code > < code > AD029640E80C2DC27AE03CFC5FC11739< / code > < code > 65F9CDF8C2931B6EC5D46351D7E79D33< / code > < code > AFBE6C58663F3EADA5B2A49DF6CDE1C9< / code > < code > 90786108116511DD9FC673E0559D84A5< / code > < code > 5136C001830FE62C495C90398E960549< / code > < code > 4E24107C0267BDA129797B7B1ACF861C< / code > < code > 04F07D6BBA8B111F888611E5631EFF97< / code > < code > 16C406A7AE8BE2DDE1D873FB571C8208< / code > < code > 8ABD18FE051F6E4AEE9B9094C63FAC38< / code > < code > CA68B4EA46F12CD709DFDAC944ED46AF< / code > < br > < code > 792FDBA2< / 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 -->
< pre > < code > encrypted_answer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
tmp_aes_key = 3826079A7BBD2CC9B9AE0E9D1BEEDA1A663CE630DC446D259DE256A1C953E8FA
tmp_aes_iv = 7A6748BA29AAC95EF75BD4588351617832FD34568EF1C4018F04F871FA05D41E< / 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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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 B0 BB 83 C2 68 49 38 B7 6A C4 92 3A
0010 | A5 45 C8 F0 59 2E 37 C5 BF 99 B8 DD AE 33 E6 EE
0020 | 39 4B 47 42 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
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
0130 | 2F DA B5 90 4B 04 F6 87 AF F2 E8 19 84 5C F3 BE
0140 | 57 A1 47 00 4C FF EF 1C 5D EA 25 74 EB 87 C7 A1
0150 | 46 2E AF 35 6C BA D7 B1 1B C1 AA F4 C6 49 24 55
0160 | 58 34 B4 E0 FE CB 94 11 8F 21 95 88 24 D8 E0 EB
0170 | 78 FD 33 BA 71 18 06 50 8E 1E FA 3B DB 45 20 DB
0180 | D4 45 9C A6 BA D3 A8 CD 59 87 4A E8 29 5D BD 0B
0190 | 6E C3 1C 2A 38 14 06 FC FB CA 40 31 ED B4 33 CD
01A0 | CF 43 55 1B ED AC 54 CB F8 20 95 42 C2 2B C0 D5
01B0 | 64 FC 85 85 94 58 69 AF 49 69 94 DE E5 E9 B1 E5
01C0 | 9C 96 02 07 13 B4 B3 AE 90 ED 7D C6 8F D1 DB 5B
01D0 | 81 C2 41 1E 7C 0E 70 89 3B C1 A5 80 45 63 D4 24
01E0 | AE 95 A4 53 41 9A FF EB 3B 8A 8A F7 C9 99 50 41
01F0 | DD BB 31 17 F1 05 39 7B 25 0C 2F F1 F5 65 92 60
0200 | 00 CC 06 E1 75 B9 A7 07 8A BF A6 38 3D 07 71 82
0210 | 22 91 D8 3B C8 2D CD 16 E9 91 B4 AC F7 F9 C1 78
0220 | 14 F6 71 5D 35 17 F4 E6 64 01 86 34 18 F1 6A AB
0230 | B2 AF 9C 64< / code > < / pre >
< 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 > B0BB83C2684938B76AC4923AA545C8F0< / 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 > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 > FE0001002FDAB5904B04F687AFF2E819< / code > < code > 845CF3BE57A147004CFFEF1C5DEA2574< / code > < code > EB87C7A1462EAF356CBAD7B11BC1AAF4< / code > < code > C64924555834B4E0FECB94118F219588< / code > < code > 24D8E0EB78FD33BA711806508E1EFA3B< / code > < code > DB4520DBD4459CA6BAD3A8CD59874AE8< / code > < code > 295DBD0B6EC31C2A381406FCFBCA4031< / code > < code > EDB433CDCF43551BEDAC54CBF8209542< / code > < code > C22BC0D564FC8585945869AF496994DE< / code > < code > E5E9B1E59C96020713B4B3AE90ED7DC6< / code > < code > 8FD1DB5B81C2411E7C0E70893BC1A580< / code > < code > 4563D424AE95A453419AFFEB3B8A8AF7< / code > < code > C9995041DDBB3117F105397B250C2FF1< / code > < code > F565926000CC06E175B9A7078ABFA638< / code > < code > 3D0771822291D83BC82DCD16E991B4AC< / code > < code > F7F9C17814F6715D3517F4E664018634< / code > < br > < code > 18F16AAB< / code > < / td >
< 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 > B2AF9C64< / code > (1687990194 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 -->
< 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 >
<!-- end g_b -->
< 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 B0 BB 83 C2 68 49 38 B7 6A C4 92 3A
0010 | A5 45 C8 F0 59 2E 37 C5 BF 99 B8 DD AE 33 E6 EE
0020 | 39 4B 47 42 00 00 00 00 00 00 00 00 FE 00 01 00
0030 | 69 A1 9D F1 CA 7E 2F 7E B2 D1 C4 FB 9B A2 85 6E
0040 | F2 AA 19 51 06 69 FF 99 17 57 F7 A3 A1 0A A1 76
0050 | A8 1C BD 99 3D C7 BD 79 4C 4E 16 90 56 60 1B AB
0060 | FF E5 C1 A8 DC 6B CB 70 5B B2 4B DB 5E 17 28 0D
0070 | 26 DA F0 A9 A8 01 55 8C B8 7A 11 E3 0D 6E 8D D2
0080 | 9C C0 39 D0 14 EA 81 9C D0 F8 14 8C BA 1B DB 21
0090 | 33 1F FC B6 06 3E D8 FB 66 A6 E9 0A 02 A8 0B 68
00A0 | CD E5 3C B4 5D 12 66 E8 C1 96 17 FD D5 AF D8 24
00B0 | 00 1F D1 6B F6 66 A1 94 6B 54 B4 5C 75 1C DD 53
00C0 | 5B 37 18 C6 BE 7A 2E BA D4 B3 5F 5C A6 1D 12 8B
00D0 | 5B 10 ED 42 23 C0 8D 72 94 FC E1 8C 8D 30 B5 CF
00E0 | C8 D7 3A 80 46 91 50 F7 18 0F 5F 76 F4 FE AA 01
00F0 | 56 EF A7 66 5B B3 7F 87 B5 F9 EE AA 65 45 50 55
0100 | 5C 05 F9 13 42 60 8B B7 6F 1E 39 4E A6 C5 1C E6
0110 | 45 89 54 0E 87 29 F9 F5 AE 1B 33 10 8E 8D 35 23
0120 | 3A BF EE 82 4A A2 B9 40 C5 F0 43 35 CA 59 E0 C4< / 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 >
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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 > B0BB83C2684938B76AC4923AA545C8F0< / 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 > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 >
< td > < code > FE00010069A19DF1CA7E2F7EB2D1C4FB< / code > < code > 9BA2856EF2AA19510669FF991757F7A3< / code > < code > A10AA176A81CBD993DC7BD794C4E1690< / code > < code > 56601BABFFE5C1A8DC6BCB705BB24BDB< / code > < code > 5E17280D26DAF0A9A801558CB87A11E3< / code > < code > 0D6E8DD29CC039D014EA819CD0F8148C< / code > < code > BA1BDB21331FFCB6063ED8FB66A6E90A< / code > < code > 02A80B68CDE53CB45D1266E8C19617FD< / code > < code > D5AFD824001FD16BF666A1946B54B45C< / code > < code > 751CDD535B3718C6BE7A2EBAD4B35F5C< / code > < code > A61D128B5B10ED4223C08D7294FCE18C< / code > < code > 8D30B5CFC8D73A80469150F7180F5F76< / code > < code > F4FEAA0156EFA7665BB37F87B5F9EEAA< / code > < code > 654550555C05F91342608BB76F1E394E< / code > < code > A6C51CE64589540E8729F9F5AE1B3310< / code > < code > 8E8D35233ABFEE824AA2B940C5F04335< / code > < br > < code > CA59E0C4< / code > < / td >
< 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 -->
< pre > < code > data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
padding = 4670CB59FFB7033A86C62AA9
tmp_aes_key = 3826079A7BBD2CC9B9AE0E9D1BEEDA1A663CE630DC446D259DE256A1C953E8FA
tmp_aes_iv = 7A6748BA29AAC95EF75BD4588351617832FD34568EF1C4018F04F871FA05D41E< / 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 = B157BF3596956D48DF20A9E10AB507971128D20530E7E3B6087FB1BA74DBE774DE8C5A1AC9D01F70868ED3681FC694F30CE358FC74B854DB48143196F4555CB22721DB87E83D14286CBFB54F4C18F51C9EB719C5924B4E546D6B073C68BA93198FB7A91FB4538E88F6DA2DCCF3734F7EA0112595DEDD6E69C38A5F70E1507069C26E847FB39EEF4BE96863A898FB521117DA5289CAD8F26F3D912D3314A3D4E54D81202AB36ED3625704730BCB495D3464433CB2CC51D1A355AD788C04084CFF69AEAA9AC6282785192BE1C7C1E4AC14E91358056E1A4BC2B0D5E9840F19F70257AD7975DAC3338C5B393835296E51D4845C07962A58F88EE2E2E67C46B1F44CBCA4624D6BD8CC3BA6B59B635CAFF706893E6368404F0475975F652D4C7C69C4E8FA88A9023BB89895823132B3408C0326A4FE9EE68ADEBC56768F0329C9DB79108F080FCEE326135F10E4F89E4C9EF5< / code > < / pre >
<!-- 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 >
< pre > < code > 0000 | 00 00 00 00 00 00 00 00 BC D6 09 00 B2 AF 9C 64
0010 | 78 01 00 00 1F 5F 04 F5 B0 BB 83 C2 68 49 38 B7
0020 | 6A C4 92 3A A5 45 C8 F0 59 2E 37 C5 BF 99 B8 DD
0030 | AE 33 E6 EE 39 4B 47 42 FE 50 01 00 B1 57 BF 35
0040 | 96 95 6D 48 DF 20 A9 E1 0A B5 07 97 11 28 D2 05
0050 | 30 E7 E3 B6 08 7F B1 BA 74 DB E7 74 DE 8C 5A 1A
0060 | C9 D0 1F 70 86 8E D3 68 1F C6 94 F3 0C E3 58 FC
0070 | 74 B8 54 DB 48 14 31 96 F4 55 5C B2 27 21 DB 87
0080 | E8 3D 14 28 6C BF B5 4F 4C 18 F5 1C 9E B7 19 C5
0090 | 92 4B 4E 54 6D 6B 07 3C 68 BA 93 19 8F B7 A9 1F
00A0 | B4 53 8E 88 F6 DA 2D CC F3 73 4F 7E A0 11 25 95
00B0 | DE DD 6E 69 C3 8A 5F 70 E1 50 70 69 C2 6E 84 7F
00C0 | B3 9E EF 4B E9 68 63 A8 98 FB 52 11 17 DA 52 89
00D0 | CA D8 F2 6F 3D 91 2D 33 14 A3 D4 E5 4D 81 20 2A
00E0 | B3 6E D3 62 57 04 73 0B CB 49 5D 34 64 43 3C B2
00F0 | CC 51 D1 A3 55 AD 78 8C 04 08 4C FF 69 AE AA 9A
0100 | C6 28 27 85 19 2B E1 C7 C1 E4 AC 14 E9 13 58 05
0110 | 6E 1A 4B C2 B0 D5 E9 84 0F 19 F7 02 57 AD 79 75
0120 | DA C3 33 8C 5B 39 38 35 29 6E 51 D4 84 5C 07 96
0130 | 2A 58 F8 8E E2 E2 E6 7C 46 B1 F4 4C BC A4 62 4D
0140 | 6B D8 CC 3B A6 B5 9B 63 5C AF F7 06 89 3E 63 68
0150 | 40 4F 04 75 97 5F 65 2D 4C 7C 69 C4 E8 FA 88 A9
0160 | 02 3B B8 98 95 82 31 32 B3 40 8C 03 26 A4 FE 9E
0170 | E6 8A DE BC 56 76 8F 03 29 C9 DB 79 10 8F 08 0F
0180 | CE E3 26 13 5F 10 E4 F8 9E 4C 9E F5< / code > < / pre >
< 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 > BCD60900B2AF9C64< / code > < / td >
< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > < / 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 > B0BB83C2684938B76AC4923AA545C8F0< / 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 > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 > FE500100B157BF3596956D48DF20A9E1< / code > < code > 0AB507971128D20530E7E3B6087FB1BA< / code > < code > 74DBE774DE8C5A1AC9D01F70868ED368< / code > < code > 1FC694F30CE358FC74B854DB48143196< / code > < code > F4555CB22721DB87E83D14286CBFB54F< / code > < code > 4C18F51C9EB719C5924B4E546D6B073C< / code > < code > 68BA93198FB7A91FB4538E88F6DA2DCC< / code > < code > F3734F7EA0112595DEDD6E69C38A5F70< / code > < code > E1507069C26E847FB39EEF4BE96863A8< / code > < code > 98FB521117DA5289CAD8F26F3D912D33< / code > < code > 14A3D4E54D81202AB36ED3625704730B< / code > < code > CB495D3464433CB2CC51D1A355AD788C< / code > < code > 04084CFF69AEAA9AC6282785192BE1C7< / code > < code > C1E4AC14E91358056E1A4BC2B0D5E984< / code > < code > 0F19F70257AD7975DAC3338C5B393835< / code > < code > 296E51D4845C07962A58F88EE2E2E67C< / code > < code > 46B1F44CBCA4624D6BD8CC3BA6B59B63< / code > < code > 5CAFF706893E6368404F0475975F652D< / code > < code > 4C7C69C4E8FA88A9023BB89895823132< / code > < code > B3408C0326A4FE9EE68ADEBC56768F03< / code > < code > 29C9DB79108F080FCEE326135F10E4F8< / code > < br > < code > 9E4C9EF5< / code > < / td >
< 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 -->
< pre > < code > auth_key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code > < / pre >
<!-- 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 >
< pre > < code > 0000 | 00 00 00 00 00 00 00 00 01 60 9B 67 B2 AF 9C 64
0010 | 34 00 00 00 34 F7 CB 3B B0 BB 83 C2 68 49 38 B7
0020 | 6A C4 92 3A A5 45 C8 F0 59 2E 37 C5 BF 99 B8 DD
0030 | AE 33 E6 EE 39 4B 47 42 6A F1 5D D5 EA 4A 58 6A
0040 | 27 E0 A1 DC 7E 26 D2 C4< / 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 >
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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 >
< td > < code > 01609B67B2AF9C64< / code > < / td >
< td > Message ID generated as specified < a href = "/mtproto/description#message-identifier-msg-id" > here »< / a > < / td >
< / tr >
< tr >
< td > message_length< / td >
< td > 16, 4< / td >
< td > < code > 34000000< / code > (52 in decimal)< / td >
< 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 >
< td > < code > B0BB83C2684938B76AC4923AA545C8F0< / 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 >
< td > < code > 592E37C5BF99B8DDAE33E6EE394B4742< / 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 >
< td > < code > 6AF15DD5EA4A586A27E0A1DC7E26D2C4< / 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 >
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< / tr >
< / tbody >
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< / table >
<!-- end dh_gen_ok --> < / div >
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