Auth key generation example

In the examples below, the transport headers are omitted:

For example, for the abridged version of the transport », the client sends 0xef as the first byte (important: only prior to the very first data packet), then the packet length is encoded with a single byte (0x01-0x7e = data length divided by 4; or 0x7f 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 0xefas the first byte). Detailed documentation on creating authorization keys is available here ».

DH exchange initiation

1) Client sends query to server

Sent payload (excluding transport headers/trailers):

0000 | 00 00 00 00 00 00 00 00 74 FE 09 00 A5 76 42 6A
0010 | 14 00 00 00 F1 8E 7E BE 7A 85 B8 E2 13 B2 DD BB
0020 | 21 68 85 19 D4 DC FD 57

Payload (de)serialization:

req_pq_multi#00000000 nonce:int128 = ResPQ;

Parameter	Offset, Length in bytes	Value	Description
auth_key_id	0, 8	`0000000000000000`	0 since the message is in plain text
message_id	8, 8	`74FE0900A576426A`	Message ID generated as specified here » (unixtime() << 32) + (N*4)
message_length	16, 4	`14000000` (20 in decimal)	Message body length
%(req_pq_multi)	20, 4	`f18e7ebe`	req_pq_multi constructor number from TL schema
nonce	24, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Random number

2) Server sends response of the form

Received payload (excluding transport headers/trailers):

0000 | 00 00 00 00 00 00 00 00 01 A4 61 E2 A5 76 42 6A
0010 | 50 00 00 00 63 24 16 05 7A 85 B8 E2 13 B2 DD BB
0020 | 21 68 85 19 D4 DC FD 57 12 92 3F 9A 3D 0F 00 CF
0030 | 2F 2B 96 C7 55 6A 7F 1C 08 25 C2 C7 48 EC A0 22
0040 | E1 00 00 00 15 C4 B5 1C 03 00 00 00 85 FD 64 DE
0050 | 85 1D 9D D0 A5 B7 F7 09 35 5F C3 0B 21 6B E8 6C
0060 | 02 2B B4 C3

Payload (de)serialization:

resPQ#00000000 nonce:int128 server_nonce:int128 pq:string server_public_key_fingerprints:Vector<strlong> = ResPQ;

Parameter	Offset, Length in bytes	Value	Description
auth_key_id	0, 8	`0000000000000000`	0 since the message is in plain text
message_id	8, 8	`01A461E2A576426A`	Message ID generated as specified here » (unixtime() << 32) + (N*4)
message_length	16, 4	`50000000` (80 in decimal)	Message body length
%(resPQ)	20, 4	`63241605`	resPQ constructor number from TL schema
nonce	24, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	40, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Server-generated random number
pq	56, 12	`0825C2C748ECA022E1000000` TL byte deserialization => bigendian conversion to decimal => 2720956240906691297	Single-byte prefix denoting length, an 8-byte string, and three bytes of padding
%(Vector strlong)	68, 4	`15c4b51c`	Vector t constructor number from TL schema
count	72, 4	`03000000`	Number of elements in server_public_key_fingerprints
server_public_key_fingerprints[0]	76, 8	`85FD64DE851D9DD0`	64 lower-order bits of `SHA1(server_public_key)`
server_public_key_fingerprints[1]	84, 8	`A5B7F709355FC30B`	64 lower-order bits of `SHA1(server_public_key)`
server_public_key_fingerprints[2]	92, 8	`216BE86C022BB4C3`	64 lower-order bits of `SHA1(server_public_key)`

In our case, the client only has the following public keys, with the following fingerprints:

85FD64DE851D9DD0

Let's choose the only matching key, the one with fingerprint equal to 85FD64DE851D9DD0.

Proof of work

3) Client decomposes pq into prime factors such that p < q.

pq = 2720956240906691297

Decompose into 2 prime cofactors p < q: 2720956240906691297 = 1487202733 * 1829579909

p = 1487202733
q = 1829579909

Presenting proof of work; Server authentication

4) `encrypted_data` payload generation

First of all, generate an encrypted_data payload as follows:

Generated payload (excluding transport headers/trailers):

0000 | 95 5F F5 A9 08 25 C2 C7 48 EC A0 22 E1 00 00 00
0010 | 04 58 A4 E9 AD 00 00 00 04 6D 0D 2C 85 00 00 00
0020 | 7A 85 B8 E2 13 B2 DD BB 21 68 85 19 D4 DC FD 57
0030 | 12 92 3F 9A 3D 0F 00 CF 2F 2B 96 C7 55 6A 7F 1C
0040 | 89 7F D7 EE 23 5D 5E AC 74 86 3A 73 B4 12 39 4E
0050 | 32 DF 7D 98 28 B2 4E 3A A9 F6 71 B6 32 A4 19 E9
0060 | 02 00 00 00

Payload (de)serialization:

p_q_inner_data_dc#00000000 pq:string p:string q:string nonce:int128 server_nonce:int128 new_nonce:int256 dc:int = P_Q_inner_data;

Parameter	Offset, Length in bytes	Value	Description
%(p_q_inner_data_dc)	0, 4	`955ff5a9`	p_q_inner_data_dc constructor number from TL schema
pq	4, 12	`0825C2C748ECA022E1000000` TL byte deserialization => bigendian conversion to decimal => 2720956240906691297	Single-byte prefix denoting length, 8-byte string, and three bytes of padding
p	16, 8	`0458A4E9AD000000` TL byte deserialization => bigendian conversion to decimal => 1487202733	First prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
q	24, 8	`046D0D2C85000000` TL byte deserialization => bigendian conversion to decimal => 1829579909	Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
nonce	32, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	48, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Value received from server in Step 2
new_nonce	64, 32	`897FD7EE235D5EAC74863A73B412394E` `32DF7D9828B24E3AA9F671B632A419E9`	Client-generated random number
dc	96, 4	`02000000` (2 in decimal)	DC ID: `10000` (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.

The serialization of P_Q_inner_data produces data, which is used to generate encrypted_data as specified in step 4.1.
These are the inputs to the algorithm specified in step 4.1:

data = 955FF5A90825C2C748ECA022E10000000458A4E9AD000000046D0D2C850000007A85B8E213B2DDBB21688519D4DCFD5712923F9A3D0F00CF2F2B96C7556A7F1C897FD7EE235D5EAC74863A73B412394E32DF7D9828B24E3AA9F671B632A419E902000000
random_padding_bytes = 3A32BC307BF75ABD3DA7D976AE390197F833C5211801BAF4DE7CE9E3F46787B30E81F7948114944AA6D534E66E45C88980E6E406E6CE206BD99E1A55455B2927E3D15F3AC56E4DF4A69FDD9B1B8A43966265DD4C4BCB8972DAABC4DE

And this is the output:

encrypted_data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

The length of the final string is 256 bytes.

5) Send req_DH_params query with generated `encrypted_data`

Sent payload (excluding transport headers/trailers):

0000 | 00 00 00 00 00 00 00 00 78 FE 09 00 A5 76 42 6A
0010 | 40 01 00 00 BE E4 12 D7 7A 85 B8 E2 13 B2 DD BB
0020 | 21 68 85 19 D4 DC FD 57 12 92 3F 9A 3D 0F 00 CF
0030 | 2F 2B 96 C7 55 6A 7F 1C 04 58 A4 E9 AD 00 00 00
0040 | 04 6D 0D 2C 85 00 00 00 85 FD 64 DE 85 1D 9D D0
0050 | FE 00 01 00 6F 2D 25 9C 0C 7F F5 99 70 5D 6C 19
0060 | 56 74 EF 6D 4F 2A BE E8 25 90 3F 44 B9 F5 B1 D5
0070 | 14 A2 2D 89 94 E5 26 2D E5 2E 0F 5E DD 07 4C 15
0080 | AE 23 A5 D5 8D C4 19 8E C9 51 D5 10 43 A9 F7 B8
0090 | 26 75 99 30 1F D0 27 93 C7 C4 BC 2B 0B 98 E5 4A
00A0 | CB 2F D5 9B 3F CD F2 46 DD A5 CE D2 76 89 53 D1
00B0 | F5 52 D7 50 0F C4 39 EB 47 D7 AE 4F 6D 28 D1 A0
00C0 | EB 9C BB FD DD 86 03 03 C1 1C 53 FD C3 5D 2E 1E
00D0 | 78 D0 48 F6 AB F0 37 8E 05 68 8D C1 39 CC 2E E0
00E0 | FC A3 35 FE 43 69 E6 9F 30 23 A1 79 FC 76 07 C0
00F0 | EB C0 60 CF 9E 6F 43 35 5F 48 9C 4F DF 58 FC 1D
0100 | 75 64 FC 19 6E DB DC 86 FE 5D F5 43 0A B4 4B A5
0110 | 77 9B CB 3A 33 B5 63 67 06 D0 E3 53 89 47 9D 53
0120 | A0 D4 33 C2 B4 03 0A 4E 2F 0E 59 10 33 6A CB 59
0130 | E0 80 17 DB 5F B1 5F C7 C9 53 D9 67 D6 63 24 5A
0140 | 3E 6F 2C ED 3C 3F DA D9 03 26 BE 82 B9 6D 7F 3F
0150 | FA D5 D4 4C

Payload (de)serialization:

req_DH_params#00000000 nonce:int128 server_nonce:int128 p:string q:string public_key_fingerprint:long encrypted_data:string = Server_DH_Params;

Parameter	Offset, Length in bytes	Value	Description
auth_key_id	0, 8	`0000000000000000`	0 since the message is in plain text
message_id	8, 8	`78FE0900A576426A`	Message ID generated as specified here » (unixtime() << 32) + (N*4)
message_length	16, 4	`40010000` (320 in decimal)	Message body length
%(req_DH_params)	20, 4	`bee412d7`	req_DH_params constructor number from TL schema
nonce	24, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	40, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Value received from server in Step 2
p	56, 8	`0458A4E9AD000000` TL byte deserialization => bigendian conversion to decimal => 1487202733	First prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
q	64, 8	`046D0D2C85000000` TL byte deserialization => bigendian conversion to decimal => 1829579909	Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
public_key_fingerprint	72, 8	`85FD64DE851D9DD0`	`fingerprint` of public key used
encrypted_data	80, 260	`FE0001006F2D259C0C7FF599705D6C19` `5674EF6D4F2ABEE825903F44B9F5B1D5` `14A22D8994E5262DE52E0F5EDD074C15` `AE23A5D58DC4198EC951D51043A9F7B8` `267599301FD02793C7C4BC2B0B98E54A` `CB2FD59B3FCDF246DDA5CED2768953D1` `F552D7500FC439EB47D7AE4F6D28D1A0` `EB9CBBFDDD860303C11C53FDC35D2E1E` `78D048F6ABF0378E05688DC139CC2EE0` `FCA335FE4369E69F3023A179FC7607C0` `EBC060CF9E6F43355F489C4FDF58FC1D` `7564FC196EDBDC86FE5DF5430AB44BA5` `779BCB3A33B5636706D0E35389479D53` `A0D433C2B4030A4E2F0E5910336ACB59` `E08017DB5FB15FC7C953D967D663245A` `3E6F2CED3C3FDAD90326BE82B96D7F3F` `FAD5D44C`	Value generated above

6) Server responds with:

Received payload (excluding transport headers/trailers):

0000 | 00 00 00 00 00 00 00 00 01 E0 3E 27 A6 76 42 6A
0010 | 78 02 00 00 5C 07 E8 D0 7A 85 B8 E2 13 B2 DD BB
0020 | 21 68 85 19 D4 DC FD 57 12 92 3F 9A 3D 0F 00 CF
0030 | 2F 2B 96 C7 55 6A 7F 1C FE 50 02 00 92 F1 64 55
0040 | 84 45 55 59 B3 D6 F7 06 33 82 E4 01 4B A7 06 5C
0050 | 22 28 5A 6D F8 80 08 04 28 7A C3 BE 57 B0 17 08
0060 | 7D B7 DB C6 D2 FA 9E 7D 5D 5E 58 75 86 B1 33 A7
0070 | 8A 87 A3 17 0A DC 7D D9 62 04 8E D0 D6 FC 0C 4C
0080 | 95 E3 6B BA 5B F2 40 9B 3D 14 0F E2 D9 A0 FE 54
0090 | EA E5 CA 4A 68 81 F2 C2 E5 8A DE F7 53 B3 99 07
00A0 | 50 84 2C 06 9E 18 2F A2 A9 D9 D0 CC DF 01 FF 42
00B0 | 0D 2A 80 56 BF 80 71 31 1F AF 6B 87 C4 80 6A 83
00C0 | 15 51 05 3F 87 17 67 D2 3D B3 B5 5C 70 F7 73 AC
00D0 | 80 98 36 FE 50 5D 60 EE 34 31 10 80 97 CC 43 BA
00E0 | 2E AB A3 D8 CD A8 5E F0 45 88 18 53 BB 13 5E 17
00F0 | D5 F7 44 66 C9 12 6F BD 34 D7 EF 2B 77 6D 46 FA
0100 | C1 21 E1 2E 13 DF EC AB 1A 34 BE 76 5A 52 20 8B
0110 | 3D 2B 99 95 41 DA 3A AC 19 D4 B1 E4 88 CC BD 3C
0120 | A8 DD EB B9 E3 E9 32 18 55 33 DD 99 70 68 74 17
0130 | CF D7 E1 65 0E E9 1C 82 D4 76 3C 74 59 1E 68 77
0140 | BA ED 2C 71 12 65 0C 4A 76 33 CB 56 A9 85 34 C7
0150 | 95 E9 2C BF BC EC C1 43 B8 23 91 50 FC 67 C5 2E
0160 | 82 35 2E 92 05 AC BA 4C 9B 83 DD 69 E2 2D BE 16
0170 | D5 B5 0E 86 C7 4C EC C4 9C 47 86 A6 24 2D 3F 18
0180 | 98 B4 AE 5B 20 29 5A 7C C2 75 11 37 2C 48 52 4B
0190 | 6A B9 4A 09 17 AE 01 01 CB 49 D0 B2 49 38 11 29
01A0 | DB 42 AD CA 1F 69 A5 A1 11 94 52 B0 E7 C7 CA 2E
01B0 | 7E 0C EE C4 A8 C9 7E D7 37 B6 31 3A 97 1E D0 0E
01C0 | B4 30 56 B6 0F 66 78 A4 4F 5F 8F 20 F6 A2 6B AF
01D0 | DC DD 93 BA 83 8C 92 24 14 D3 4A DB 20 60 AF 99
01E0 | A0 87 52 F3 99 7E 4A 70 69 E6 57 2E E0 47 53 98
01F0 | 6C 21 A0 E1 87 58 DE CB 90 C0 2A ED C2 92 92 8D
0200 | 5D A0 F0 4A CD AE 09 D6 53 6E 1A 4C 67 97 B7 40
0210 | 91 84 12 F4 3E 4B 1A F8 18 88 F5 D8 13 C9 E8 63
0220 | 1A 79 BA A1 8D CD 6F 52 20 E3 C6 06 87 3D D3 C1
0230 | 7D 6A 13 F7 29 67 77 BA 99 EB 21 4A E6 AA 69 91
0240 | 3A 94 B4 41 49 C0 7F C6 BB D9 A8 7E 69 09 BC 89
0250 | 92 6F 1B CF DB E0 34 B4 E4 34 94 BB BF 05 F5 68
0260 | 9E F7 FC B0 C8 55 F6 53 E5 41 27 7B CC B5 9C 0D
0270 | 75 74 9C AC C6 03 02 AC 1E C4 0B E4 5B DD 8F 0B
0280 | 77 F1 A1 5C 61 D3 74 68 9D 5C F9 89

Payload (de)serialization:

server_DH_params_ok#00000000 nonce:int128 server_nonce:int128 encrypted_answer:string = Server_DH_Params;

Parameter	Offset, Length in bytes	Value	Description
auth_key_id	0, 8	`0000000000000000`	0 since the message is in plain text
message_id	8, 8	`01E03E27A676426A`	Message ID generated as specified here » (unixtime() << 32) + (N*4)
message_length	16, 4	`78020000` (632 in decimal)	Message body length
%(server_DH_params_ok)	20, 4	`5c07e8d0`	server_DH_params_ok constructor number from TL schema
nonce	24, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	40, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Value received from server in Step 2
encrypted_answer	56, 596	`FE50020092F1645584455559B3D6F706` `3382E4014BA7065C22285A6DF8800804` `287AC3BE57B017087DB7DBC6D2FA9E7D` `5D5E587586B133A78A87A3170ADC7DD9` `62048ED0D6FC0C4C95E36BBA5BF2409B` `3D140FE2D9A0FE54EAE5CA4A6881F2C2` `E58ADEF753B3990750842C069E182FA2` `A9D9D0CCDF01FF420D2A8056BF807131` `1FAF6B87C4806A831551053F871767D2` `3DB3B55C70F773AC809836FE505D60EE` `3431108097CC43BA2EABA3D8CDA85EF0` `45881853BB135E17D5F74466C9126FBD` `34D7EF2B776D46FAC121E12E13DFECAB` `1A34BE765A52208B3D2B999541DA3AAC` `19D4B1E488CCBD3CA8DDEBB9E3E93218` `5533DD9970687417CFD7E1650EE91C82` `D4763C74591E6877BAED2C7112650C4A` `7633CB56A98534C795E92CBFBCECC143` `B8239150FC67C52E82352E9205ACBA4C` `9B83DD69E22DBE16D5B50E86C74CECC4` `9C4786A6242D3F1898B4AE5B20295A7C` `C27511372C48524B6AB94A0917AE0101` `CB49D0B249381129DB42ADCA1F69A5A1` `119452B0E7C7CA2E7E0CEEC4A8C97ED7` `37B6313A971ED00EB43056B60F6678A4` `4F5F8F20F6A26BAFDCDD93BA838C9224` `14D34ADB2060AF99A08752F3997E4A70` `69E6572EE04753986C21A0E18758DECB` `90C02AEDC292928D5DA0F04ACDAE09D6` `536E1A4C6797B740918412F43E4B1AF8` `1888F5D813C9E8631A79BAA18DCD6F52` `20E3C606873DD3C17D6A13F7296777BA` `99EB214AE6AA69913A94B44149C07FC6` `BBD9A87E6909BC89926F1BCFDBE034B4` `E43494BBBF05F5689EF7FCB0C855F653` `E541277BCCB59C0D75749CACC60302AC` `1EC40BE45BDD8F0B77F1A15C61D37468` `9D5CF989`	See below

Decrypt encrypted_answer using the reverse of the process specified in step 6:

encrypted_answer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
tmp_aes_key = 52421310325A031F2DE67C0D4915516112C47E730C4D4FB8D7CCA7E68BE3887D
tmp_aes_iv = AA5E08E9E35C4B500509C7D4964D398A86B9EF57E3F890D8B6E6E635897FD7EE

Yielding:

answer_with_hash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
answer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

Generated payload (excluding transport headers/trailers):

0000 | BA 0D 89 B5 7A 85 B8 E2 13 B2 DD BB 21 68 85 19
0010 | D4 DC FD 57 12 92 3F 9A 3D 0F 00 CF 2F 2B 96 C7
0020 | 55 6A 7F 1C 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 | 4C 74 D5 7A 16 18 61 D6 7C 37 83 D3 9E 07 E7 29
0140 | 6C 8B E2 8D 0C 02 99 82 16 8E 16 09 B0 F4 37 EF
0150 | 54 1D 30 B0 5F AE 23 C6 C8 3A 45 DA 56 F7 C5 A4
0160 | B6 D4 F4 8E 95 4E C8 10 4E 8B 1D 90 04 6A E6 87
0170 | DB 76 45 0A 72 41 02 36 80 9F C0 D3 E1 3A BC C4
0180 | B6 6B 60 D8 C2 4B CE A5 D1 38 C4 68 9C 7A C3 E3
0190 | CF 01 A1 B6 F8 E0 86 A9 83 C3 74 44 2E 7B 8E C4
01A0 | F4 83 A9 C7 D5 CB 19 B3 64 21 A4 37 4B E1 48 3A
01B0 | A6 6B B5 49 BB 1D 5E 5D FE 02 13 F1 99 92 50 B2
01C0 | 78 5D 42 CC F2 59 36 35 BF 7F A8 4D 70 5B E9 18
01D0 | 71 D6 25 8E 3E 58 03 56 57 D8 56 D6 58 7D 38 B2
01E0 | 17 EF 73 AC D5 B1 E6 34 88 28 52 B5 58 AF 9D 92
01F0 | 58 B7 36 A2 B1 A0 23 D0 56 B1 4F 44 D6 B9 4B 25
0200 | 81 5E FC 79 1C 51 98 FB 57 6D 7D 20 75 A9 15 EF
0210 | 4E EF FF E4 1C 72 B1 DB 4C 7B 72 84 68 61 E6 6D
0220 | 60 1A 19 F2 DF D0 90 C6 61 C6 F2 24 9C A4 FB 23
0230 | A6 76 42 6A

Payload (de)serialization:

server_DH_inner_data#00000000 nonce:int128 server_nonce:int128 g:int dh_prime:string g_a:string server_time:int = Server_DH_inner_data;

Parameter	Offset, Length in bytes	Value	Description
%(server_DH_inner_data)	0, 4	`ba0d89b5`	server_DH_inner_data constructor number from TL schema
nonce	4, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	20, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Value received from server in Step 2
g	36, 4	`03000000` (3 in decimal)	Value received from server in Step 2
dh_prime	40, 260	`FE000100C71CAEB9C6B1C9048E6C522F` `70F13F73980D40238E3E21C14934D037` `563D930F48198A0AA7C14058229493D2` `2530F4DBFA336F6E0AC925139543AED4` `4CCE7C3720FD51F69458705AC68CD4FE` `6B6B13ABDC9746512969328454F18FAF` `8C595F642477FE96BB2A941D5BCD1D4A` `C8CC49880708FA9B378E3C4F3A9060BE` `E67CF9A4A4A695811051907E162753B5` `6B0F6B410DBA74D8A84B2A14B3144E0E` `F1284754FD17ED950D5965B4B9DD4658` `2DB1178D169C6BC465B0D6FF9CA3928F` `EF5B9AE4E418FC15E83EBEA0F87FA9FF` `5EED70050DED2849F47BF959D956850C` `E929851F0D8115F635B105EE2E4E15D0` `4B2454BF6F4FADF034B10403119CD8E3` `B92FCC5B`	2048-bit prime, in big-endian byte order, to be checked as specified in the auth key docs
g_a	300, 260	`FE0001004C74D57A161861D67C3783D3` `9E07E7296C8BE28D0C029982168E1609` `B0F437EF541D30B05FAE23C6C83A45DA` `56F7C5A4B6D4F48E954EC8104E8B1D90` `046AE687DB76450A72410236809FC0D3` `E13ABCC4B66B60D8C24BCEA5D138C468` `9C7AC3E3CF01A1B6F8E086A983C37444` `2E7B8EC4F483A9C7D5CB19B36421A437` `4BE1483AA66BB549BB1D5E5DFE0213F1` `999250B2785D42CCF2593635BF7FA84D` `705BE91871D6258E3E58035657D856D6` `587D38B217EF73ACD5B1E634882852B5` `58AF9D9258B736A2B1A023D056B14F44` `D6B94B25815EFC791C5198FB576D7D20` `75A915EF4EEFFFE41C72B1DB4C7B7284` `6861E66D601A19F2DFD090C661C6F224` `9CA4FB23`	`g_a` diffie-hellman parameter
server_time	560, 4	`A676426A` (1782740646 in decimal)	Server time

7) Client computes random 2048-bit number b (using a sufficient amount of entropy) and sends the server a message

First, generate a secure random 2048-bit number b:

b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

Then compute g_b = pow(g, b) mod dh_prime

g_b = AB6C4F34A08B8101F336B66783FE2A80F6B859C4687D86192AC36BE256AC53D8583E97386F3420419F4016CA3CCC38978CC2F9A7E65266847C745F80FD76802DD0167EF858CAFDAB910FBCD640ECD34A771F2BCC53A26E319D490380B1745E9A1A00EDB04B6EE2AD5DC3A925C5BBF5B47B2FF0A80FC03F811FAD2B223A445A47D0E635F0D30B9CF8BF307C111D5054D94D8AB43DCBA675E1EE446A11BBE4ED70A30AFAFFA62041BABA13C54F71F5E10AF1C8F1A7DE576372F94B48D19A5400B310ED1368A4C574FE018C7AB8D901FC22100FBCE565302D92315877940F6729DEE08EE9CF799AEE514A43B93612C03C0545EF68EBDB406CAC9411316D64B3BF56

7.1) generation of encrypted_data

Generated payload (excluding transport headers/trailers):

0000 | 54 B6 43 66 7A 85 B8 E2 13 B2 DD BB 21 68 85 19
0010 | D4 DC FD 57 12 92 3F 9A 3D 0F 00 CF 2F 2B 96 C7
0020 | 55 6A 7F 1C 00 00 00 00 00 00 00 00 FE 00 01 00
0030 | AB 6C 4F 34 A0 8B 81 01 F3 36 B6 67 83 FE 2A 80
0040 | F6 B8 59 C4 68 7D 86 19 2A C3 6B E2 56 AC 53 D8
0050 | 58 3E 97 38 6F 34 20 41 9F 40 16 CA 3C CC 38 97
0060 | 8C C2 F9 A7 E6 52 66 84 7C 74 5F 80 FD 76 80 2D
0070 | D0 16 7E F8 58 CA FD AB 91 0F BC D6 40 EC D3 4A
0080 | 77 1F 2B CC 53 A2 6E 31 9D 49 03 80 B1 74 5E 9A
0090 | 1A 00 ED B0 4B 6E E2 AD 5D C3 A9 25 C5 BB F5 B4
00A0 | 7B 2F F0 A8 0F C0 3F 81 1F AD 2B 22 3A 44 5A 47
00B0 | D0 E6 35 F0 D3 0B 9C F8 BF 30 7C 11 1D 50 54 D9
00C0 | 4D 8A B4 3D CB A6 75 E1 EE 44 6A 11 BB E4 ED 70
00D0 | A3 0A FA FF A6 20 41 BA BA 13 C5 4F 71 F5 E1 0A
00E0 | F1 C8 F1 A7 DE 57 63 72 F9 4B 48 D1 9A 54 00 B3
00F0 | 10 ED 13 68 A4 C5 74 FE 01 8C 7A B8 D9 01 FC 22
0100 | 10 0F BC E5 65 30 2D 92 31 58 77 94 0F 67 29 DE
0110 | E0 8E E9 CF 79 9A EE 51 4A 43 B9 36 12 C0 3C 05
0120 | 45 EF 68 EB DB 40 6C AC 94 11 31 6D 64 B3 BF 56

Payload (de)serialization:

client_DH_inner_data#00000000 nonce:int128 server_nonce:int128 retry_id:long g_b:string = Client_DH_Inner_Data;

Parameter	Offset, Length in bytes	Value	Description
%(client_DH_inner_data)	0, 4	`54b64366`	client_DH_inner_data constructor number from TL schema
nonce	4, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	20, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Value received from server in Step 2
g_b	36, 260	`FE000100AB6C4F34A08B8101F336B667` `83FE2A80F6B859C4687D86192AC36BE2` `56AC53D8583E97386F3420419F4016CA` `3CCC38978CC2F9A7E65266847C745F80` `FD76802DD0167EF858CAFDAB910FBCD6` `40ECD34A771F2BCC53A26E319D490380` `B1745E9A1A00EDB04B6EE2AD5DC3A925` `C5BBF5B47B2FF0A80FC03F811FAD2B22` `3A445A47D0E635F0D30B9CF8BF307C11` `1D5054D94D8AB43DCBA675E1EE446A11` `BBE4ED70A30AFAFFA62041BABA13C54F` `71F5E10AF1C8F1A7DE576372F94B48D1` `9A5400B310ED1368A4C574FE018C7AB8` `D901FC22100FBCE565302D9231587794` `0F6729DEE08EE9CF799AEE514A43B936` `12C03C0545EF68EBDB406CAC9411316D` `64B3BF56`	Single-byte prefix denoting length, a 256-byte (2048-bit) string, and zero bytes of padding
retry_id	296, 8	`0000000000000000`	Equal to zero at the time of the first attempt; otherwise, it is equal to `auth_key_aux_hash` from the previous failed attempt (see Item 7).

The serialization of Client_DH_Inner_Data produces a string data. This is used to generate encrypted_data as specified in step 6, using the following inputs:

data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
padding = FDF526346BD1A6348DF5B586
tmp_aes_key = 52421310325A031F2DE67C0D4915516112C47E730C4D4FB8D7CCA7E68BE3887D
tmp_aes_iv = AA5E08E9E35C4B500509C7D4964D398A86B9EF57E3F890D8B6E6E635897FD7EE

Process:

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);

Output:

encrypted_data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

The length of the final string is 336 bytes.

7.2) set_client_DH_params query

Sent payload (excluding transport headers/trailers):

0000 | 00 00 00 00 00 00 00 00 04 47 01 00 A6 76 42 6A
0010 | 78 01 00 00 1F 5F 04 F5 7A 85 B8 E2 13 B2 DD BB
0020 | 21 68 85 19 D4 DC FD 57 12 92 3F 9A 3D 0F 00 CF
0030 | 2F 2B 96 C7 55 6A 7F 1C FE 50 01 00 BF 16 3A DA
0040 | 85 20 95 04 E9 8D C0 64 98 3B AC 3E 0D 25 A5 44
0050 | D7 BD 4C DB E8 CF 10 2B 49 41 50 AC 39 61 1C F0
0060 | 84 5B 9B 68 77 4C B8 72 5C 8D B0 D5 21 EB 0F 60
0070 | 73 C8 11 39 A2 DD 93 10 82 72 72 84 21 EB 5A 7D
0080 | FE 4F 9B 03 59 FA 94 12 13 C7 70 9A B8 C0 31 6A
0090 | 88 49 6E 87 3A 48 12 C7 8B 87 89 3D 12 BE 5D D2
00A0 | B7 ED 1A 10 E3 77 13 5F 99 1E ED 84 ED 3F 05 E1
00B0 | CB B1 0C CA 67 F5 B0 A3 1F DB 84 67 D1 1D 0E F0
00C0 | BC 15 11 2A AF 90 DA 4E 8B 9E 12 71 4D 36 E5 39
00D0 | EF DB 00 5A 65 0C 3E 53 07 D7 FB 7D 8A B4 29 31
00E0 | 04 2A 1F 16 52 13 3B 41 F0 B3 86 DE FB 2D 13 D4
00F0 | 5C A3 97 E1 1D 89 62 DD F9 E6 64 37 2F 94 DB DF
0100 | FF D0 2C 39 4E 68 FD BD 00 E9 3E 4F 73 49 63 9A
0110 | 7E 29 DC FA ED 16 D2 A1 C6 AE 5E 17 F5 47 63 77
0120 | 29 D0 DA ED C1 16 10 98 3B E4 97 4B 74 0D DA 9E
0130 | EB 36 F2 89 AC E6 E1 14 3F D2 19 DD 07 7B DC D9
0140 | A8 02 DA F0 7A 90 AB 0A 62 0E 14 10 E0 F4 69 4F
0150 | 29 E2 E8 B1 E5 D1 CA 7B 42 21 17 D8 4F EE BB E5
0160 | F5 E4 69 47 C0 19 48 6A 52 1A DB E6 91 25 78 D6
0170 | A1 03 42 4C 9C 0D D8 2F D0 89 69 DA 1B 67 51 76
0180 | A2 D9 85 7F 6C EB C3 8E E1 19 C7 5F

Payload (de)serialization:

set_client_DH_params#00000000 nonce:int128 server_nonce:int128 encrypted_data:string = Set_client_DH_params_answer;

Parameter	Offset, Length in bytes	Value	Description
auth_key_id	0, 8	`0000000000000000`	0 since the message is in plain text
message_id	8, 8	`04470100A676426A`	Message ID generated as specified here » (unixtime() << 32) + (N*4)
message_length	16, 4	`78010000` (376 in decimal)	Message body length
%(set_client_DH_params)	20, 4	`1f5f04f5`	set_client_DH_params constructor number from TL schema
nonce	24, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	40, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Value received from server in Step 2
encrypted_data	56, 340	`FE500100BF163ADA85209504E98DC064` `983BAC3E0D25A544D7BD4CDBE8CF102B` `494150AC39611CF0845B9B68774CB872` `5C8DB0D521EB0F6073C81139A2DD9310` `8272728421EB5A7DFE4F9B0359FA9412` `13C7709AB8C0316A88496E873A4812C7` `8B87893D12BE5DD2B7ED1A10E377135F` `991EED84ED3F05E1CBB10CCA67F5B0A3` `1FDB8467D11D0EF0BC15112AAF90DA4E` `8B9E12714D36E539EFDB005A650C3E53` `07D7FB7D8AB42931042A1F1652133B41` `F0B386DEFB2D13D45CA397E11D8962DD` `F9E664372F94DBDFFFD02C394E68FDBD` `00E93E4F7349639A7E29DCFAED16D2A1` `C6AE5E17F547637729D0DAEDC1161098` `3BE4974B740DDA9EEB36F289ACE6E114` `3FD219DD077BDCD9A802DAF07A90AB0A` `620E1410E0F4694F29E2E8B1E5D1CA7B` `422117D84FEEBBE5F5E46947C019486A` `521ADBE6912578D6A103424C9C0DD82F` `D08969DA1B675176A2D9857F6CEBC38E` `E119C75F`	Encrypted client_DH_inner_data generated previously, serialized as a TL byte string

8) Auth key generation

The client computes the auth_key using formula g_a^b mod dh_prime:

auth_key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

9) Final server reply

The server verifies and confirms that auth_key_hash is unique: since it's unique, it replies with the following:

Received payload (excluding transport headers/trailers):

0000 | 00 00 00 00 00 00 00 00 01 F4 FC 37 A7 76 42 6A
0010 | 34 00 00 00 34 F7 CB 3B 7A 85 B8 E2 13 B2 DD BB
0020 | 21 68 85 19 D4 DC FD 57 12 92 3F 9A 3D 0F 00 CF
0030 | 2F 2B 96 C7 55 6A 7F 1C 10 17 63 7B 8D A3 9F 0C
0040 | D0 1A 73 89 6F B3 37 FE

Payload (de)serialization:

dh_gen_ok#00000004 nonce:int128 server_nonce:int128 new_nonce_hash1:int128 = Set_client_DH_params_answer;

Parameter	Offset, Length in bytes	Value	Description
auth_key_id	0, 8	`0000000000000000`	0 since the message is in plain text
message_id	8, 8	`01F4FC37A776426A`	Message ID generated as specified here » (unixtime() << 32) + (N*4)
message_length	16, 4	`34000000` (52 in decimal)	Message body length
%(dh_gen_ok)	20, 4	`34f7cb3b`	dh_gen_ok constructor number from TL schema
nonce	24, 16	`7A85B8E213B2DDBB21688519D4DCFD57`	Value generated by client in Step 1
server_nonce	40, 16	`12923F9A3D0F00CF2F2B96C7556A7F1C`	Value received from server in Step 2
new_nonce_hash1	56, 16	`1017637B8DA39F0CD01A73896FB337FE`	The 128 lower-order bits of SHA1 of the byte string derived from the `new_nonce` string by adding a single byte with the value of 1, 2, or 3, and followed by another 8 bytes with `auth_key_aux_hash`. Different values are required to prevent an intruder from changing server response dh_gen_ok into dh_gen_retry.

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Auth key generation example

DH exchange initiation

1) Client sends query to server

2) Server sends response of the form

Proof of work

3) Client decomposes pq into prime factors such that p < q.

Presenting proof of work; Server authentication

4) `encrypted_data` payload generation

5) Send req_DH_params query with generated `encrypted_data`

6) Server responds with:

7) Client computes random 2048-bit number b (using a sufficient amount of entropy) and sends the server a message

7.1) generation of encrypted_data

7.2) set_client_DH_params query

8) Auth key generation

9) Final server reply

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Auth key generation example

DH exchange initiation

1) Client sends query to server

2) Server sends response of the form

Proof of work

3) Client decomposes pq into prime factors such that p < q.

Presenting proof of work; Server authentication

4) encrypted_data payload generation

5) Send req_DH_params query with generated encrypted_data

6) Server responds with:

7) Client computes random 2048-bit number b (using a sufficient amount of entropy) and sends the server a message

7.1) generation of encrypted_data

7.2) set_client_DH_params query

8) Auth key generation

9) Final server reply

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4) `encrypted_data` payload generation

5) Send req_DH_params query with generated `encrypted_data`