Creating an Authorization Key (Samples)

In the examples below, the TCP transport headers are omitted:

If a payload (packet) needs to be transmitted from server to client or from client to server, it is encapsulated as follows: 4 bytes are added at the front (to include the length, the sequence number, and CRC32; always divisible by 4) and 4 bytes with the packet sequence number for this TCP connection (the first packet sent is numbered 0, the next one 1, etc.), and 4 CRC32 bytes at the end (length, sequence number, and payload together).

There is an abridged version of the same protocol: if the client sends 0xef as the first byte (**important:** only prior to the very first data packet), then packet length is encoded by a single byte (0x01-0x7e = data length divided by 4; or 0x7f followed by 3 bytes (little endian) divided into 4) followed by the data themselves (sequence number and CRC32 not added). In this case, server responses have the same form (although the server does not send 0xefas the first byte).

Detailed documentation on creating authorization keys is available here ».

1. Request for (p,q) Authorization

req_pq#60469778 nonce:int128 = ResPQ
Parameter Offset, Length in bytes Value Description
auth_key_id 0, 8 0 Since message is in plain text
message_id 8, 8 51e57ac42770964a Exact unixtime * 2^32
message_length 16, 4 20 Message body length
%(req_pq) 20, 4 60469778 req_pq constructor number from TL schema
nonce 24, 16 3E0549828CCA27E966B301A48FECE2FC Random number

The header is 20 bytes long, the message body is 20 bytes long, and the entire message is 40 bytes in length.

0000 | 00 00 00 00 00 00 00 00 4A 96 70 27 C4 7A E5 51
0010 | 14 00 00 00 78 97 46 60 3E 05 49 82 8C CA 27 E9
0020 | 66 B3 01 A4 8F EC E2 FC

2. A response from the server has been received with the following content:

0000 | 00 00 00 00 00 00 00 00 01 C8 83 1E C9 7A E5 51
0010 | 40 00 00 00 63 24 16 05 3E 05 49 82 8C CA 27 E9
0020 | 66 B3 01 A4 8F EC E2 FC A5 CF 4D 33 F4 A1 1E A8
0030 | 77 BA 4A A5 73 90 73 30 08 17 ED 48 94 1A 08 F9
0040 | 81 00 00 00 15 C4 B5 1C 01 00 00 00 21 6B E8 6C
0050 | 02 2B B4 C3
Response decomposition using the following formula:
resPQ#05162463 nonce:int128 server_nonce:int128 pq:string server_public_key_fingerprints:Vector long = ResPQ 
Parameter Offset, Length in bytes Value Description
auth_key_id 0, 8 0 Since message is in plain text
message_id 8, 8 51E57AC91E83C801 Server message ID
message_length 16, 4 64 Message body length
%(resPQ) 20, 4 05162463 resPQ constructor number from TL schema
nonce 24, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 40, 16 A5CF4D33F4A11EA877BA4AA573907330 Server-generated random number
pq 56, 12 17ED48941A08F981 Single-byte prefix denoting length, an 8-byte string, and three bytes of padding
%(Vector long) 68, 4 1cb5c415 Vector long constructor number from TL schema
count 72, 4 1 Number of elements in key fingerprint list
fingerprints[] 76, 8 c3b42b026ce86b21 64 lower-order bits of SHA1 (server_public_key)

The server_public_key public key has been selected whose fingerprint corresponds to the only one received from the server: c3b42b026ce86b21.

3. Pq = 17ED48941A08F981 decomposed into 2 prime cofactors:

p = 494C553B
q = 53911073

4. encrypted_data Generation

p_q_inner_data#83c95aec pq:string p:string q:string nonce:int128 server_nonce:int128 new_nonce:int256 = P_Q_inner_data
Parameter Offset, Length in bytes Value Description
%(p_q_inner_data) 0, 4 83c95aec p_q_inner_data constructor number from TL schema
pq 4, 12 17ED48941A08F981 Single-byte prefix denoting length, 8-byte string, and three bytes of padding
p 16, 8 494C553B First prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
q 24, 8 53911073 Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
nonce 32, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 48, 16 A5CF4D33F4A11EA877BA4AA573907330 Value received from server in Step 2
new_nonce 64, 32 311C85DB234AA2640AFC4A76A735CF5B 1F0FD68BD17FA181E1229AD867CC024D Client-generated random number

The serialization of P_Q_inner_data produces some string data. This is followed by encrypted_data:

SHA1 (data) = DB761C27718A2305044F71F2AD951629D78B2449
RSA (data_with_hash, server_public_key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

The length of the final string was 256 bytes.

Request to Start Diffie-Hellman Key Exchange
req_DH_params#d712e4be 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 0 Since message is in plain text
message_id 8, 8 51e57ac917717a27 Exact unixtime * 2^32
message_length 16, 4 320 Message body length
%(req_DH_params) 20, 4 d712e4be req_DH_params constructor number from TL schema
nonce 24, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 40, 16 A5CF4D33F4A11EA877BA4AA573907330 Value received from server in Step 2
p 56, 8 494C553B First prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
q 64, 8 53911073 Second prime cofactor: single-byte prefix denoting length, 4-byte string, and three bytes of padding
public_key_fingerprint 72, 8 c3b42b026ce86b21 Fingerprint of public key used
encrypted_data 80, 260 See above See “Generation of encrypted_data"
0000 | 00 00 00 00 00 00 00 00 27 7A 71 17 C9 7A E5 51
0010 | 40 01 00 00 BE E4 12 D7 3E 05 49 82 8C CA 27 E9
0020 | 66 B3 01 A4 8F EC E2 FC A5 CF 4D 33 F4 A1 1E A8
0030 | 77 BA 4A A5 73 90 73 30 04 49 4C 55 3B 00 00 00
0040 | 04 53 91 10 73 00 00 00 21 6B E8 6C 02 2B B4 C3
0050 | FE 00 01 00 7B B0 10 0A 52 31 61 90 4D 9C 69 FA
0060 | 04 BC 60 DE CF C5 DD 74 B9 99 95 C7 68 EB 60 D8
0070 | 71 6E 21 09 BA F2 D4 60 1D AB 6B 09 61 0D C1 10
0080 | 67 BB 89 02 1E 09 47 1F CF A5 2D BD 0F 23 20 4A
0090 | D8 CA 8B 01 2B F4 0A 11 2F 44 69 5A B6 C2 66 95
00A0 | 53 86 11 4E F5 21 1E 63 72 22 7A DB D3 49 95 D3
00B0 | E0 E5 FF 02 EC 63 A4 3F 99 26 87 89 62 F7 C5 70
00C0 | E6 A6 E7 8B F8 36 6A F9 17 A5 27 26 75 C4 60 64
00D0 | BE 62 E3 E2 02 EF A8 B1 AD FB 1C 32 A8 98 C2 98
00E0 | 7B E2 7B 5F 31 D5 7C 9B B9 63 AB CB 73 4B 16 F6
00F0 | 52 CE DB 42 93 CB B7 C8 78 A3 A3 FF AC 9D BE A9
0100 | DF 7C 67 BC 9E 95 08 E1 11 C7 8F C4 6E 05 7F 5C
0110 | 65 AD E3 81 D9 1F EE 43 0A 6B 57 6A 99 BD F8 55
0120 | 1F DB 1B E2 B5 70 69 B1 A4 57 30 61 8F 27 42 7E
0130 | 8A 04 72 0B 49 71 EF 4A 92 15 98 3D 68 F2 83 0C
0140 | 3E AA 6E 40 38 55 62 F9 70 D3 8A 05 C9 F1 24 6D
0150 | C3 34 38 E6

5. A response from the server has been received with the following content:

0000 | 00 00 00 00 00 00 00 00 01 54 43 36 CB 7A E5 51
0010 | 78 02 00 00 5C 07 E8 D0 3E 05 49 82 8C CA 27 E9
0020 | 66 B3 01 A4 8F EC E2 FC A5 CF 4D 33 F4 A1 1E A8
0030 | 77 BA 4A A5 73 90 73 30 FE 50 02 00 28 A9 2F E2
0040 | 01 73 B3 47 A8 BB 32 4B 5F AB 26 67 C9 A8 BB CE
0050 | 64 68 D5 B5 09 A4 CB DD C1 86 24 0A C9 12 CF 70
0060 | 06 AF 89 26 DE 60 6A 2E 74 C0 49 3C AA 57 74 1E
0070 | 6C 82 45 1F 54 D3 E0 68 F5 CC C4 9B 44 44 12 4B
0080 | 96 66 FF B4 05 AA B5 64 A3 D0 1E 67 F6 E9 12 86
0090 | 7C 8D 20 D9 88 27 07 DC 33 0B 17 B4 E0 DD 57 CB
00A0 | 53 BF AA FA 9E F5 BE 76 AE 6C 1B 9B 6C 51 E2 D6
00B0 | 50 2A 47 C8 83 09 5C 46 C8 1E 3B E2 5F 62 42 7B
00C0 | 58 54 88 BB 3B F2 39 21 3B F4 8E B8 FE 34 C9 A0
00D0 | 26 CC 84 13 93 40 43 97 4D B0 35 56 63 30 38 39
00E0 | 2C EC B5 1F 94 82 4E 14 0B 98 63 77 30 A4 BE 79
00F0 | A8 F9 DA FA 39 BA E8 1E 10 95 84 9E A4 C8 34 67
0100 | C9 2A 3A 17 D9 97 81 7C 8A 7A C6 1C 3F F4 14 DA
0110 | 37 B7 D6 6E 94 9C 0A EC 85 8F 04 82 24 21 0F CC
0120 | 61 F1 1C 3A 91 0B 43 1C CB D1 04 CC CC 8D C6 D2
0130 | 9D 4A 5D 13 3B E6 39 A4 C3 2B BF F1 53 E6 3A CA
0140 | 3A C5 2F 2E 47 09 B8 AE 01 84 4B 14 2C 1E E8 9D
0150 | 07 5D 64 F6 9A 39 9F EB 04 E6 56 FE 36 75 A6 F8
0160 | F4 12 07 8F 3D 0B 58 DA 15 31 1C 1A 9F 8E 53 B3
0170 | CD 6B B5 57 2C 29 49 04 B7 26 D0 BE 33 7E 2E 21
0180 | 97 7D A2 6D D6 E3 32 70 25 1C 2C A2 9D FC C7 02
0190 | 27 F0 75 5F 84 CF DA 9A C4 B8 DD 5F 84 F1 D1 EB
01A0 | 36 BA 45 CD DC 70 44 4D 8C 21 3E 4B D8 F6 3B 8A
01B0 | B9 5A 2D 0B 41 80 DC 91 28 3D C0 63 AC FB 92 D6
01C0 | A4 E4 07 CD E7 C8 C6 96 89 F7 7A 00 74 41 D4 A6
01D0 | A8 38 4B 66 65 02 D9 B7 7F C6 8B 5B 43 CC 60 7E
01E0 | 60 A1 46 22 3E 11 0F CB 43 BC 3C 94 2E F9 81 93
01F0 | 0C DC 4A 1D 31 0C 0B 64 D5 E5 5D 30 8D 86 32 51
0200 | AB 90 50 2C 3E 46 CC 59 9E 88 6A 92 7C DA 96 3B
0210 | 9E B1 6C E6 26 03 B6 85 29 EE 98 F9 F5 20 64 19
0220 | E0 3F B4 58 EC 4B D9 45 4A A8 F6 BA 77 75 73 CC
0230 | 54 B3 28 89 5B 1D F2 5E AD 9F B4 CD 51 98 EE 02
0240 | 2B 2B 81 F3 88 D2 81 D5 E5 BC 58 01 07 CA 01 A5
0250 | 06 65 C3 2B 55 27 15 F3 35 FD 76 26 4F AD 00 DD
0260 | D5 AE 45 B9 48 32 AC 79 CE 7C 51 1D 19 4B C4 2B
0270 | 70 EF A8 50 BB 15 C2 01 2C 52 15 CA BF E9 7C E6
0280 | 6B 8D 87 34 D0 EE 75 9A 63 8A F0 13
Response decomposition using the following formula:
server_DH_params_fail#79cb045d nonce:int128 server_nonce:int128 new_nonce_hash:int128 = Server_DH_Params;
server_DH_params_ok#d0e8075c nonce:int128 server_nonce:int128 encrypted_answer:string = Server_DH_Params;
Parameter Offset, Length in bytes Value Description
auth_key_id 0, 8 0 Since message is in plain text
message_id 8, 8 51E57ACB36435401 Exact unixtime * 2^32
message_length 16, 4 632 Message body length
%(server_DH_params_ok) 20, 4 d0e8075c server_DH_params_ok constructor number from TL schema
nonce 24, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 40, 16 A5CF4D33F4A11EA877BA4AA573907330 Value received from server in Step 2
encrypted_answer 56, 596 See below See “Decomposition of encrypted_answer"
Conversion of encrypted_answer into answer:
encrypted_answer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
tmp_aes_key = F011280887C7BB01DF0FC4E17830E0B91FBB8BE4B2267CB985AE25F33B527253
tmp_aes_iv = 3212D579EE35452ED23E0D0C92841AA7D31B2E9BDEF2151E80D15860311C85DB
answer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
Server_DH_inner_data decomposition using the following formula:
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;
Parameter Offset, Length in bytes Value Description
%(server_DH_inner_data) 0, 4 b5890dba server_DH_inner_data constructor number from TL schema
nonce 4, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 20, 16 A5CF4D33F4A11EA877BA4AA573907330 Value received from server in Step 2
g 36, 4 2 Value received from server in Step 2
dh_prime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
g_a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
server_time 560, 4 1373993675 Server time

6. Random number b is computed:

b = 6F620AFA575C9233EB4C014110A7BCAF49464F798A18A0981FEA1E05E8DA67D9681E0FD6DF0EDF0272AE3492451A84502F2EFC0DA18741A5FB80BD82296919A70FAA6D07CBBBCA2037EA7D3E327B61D585ED3373EE0553A91CBD29B01FA9A89D479CA53D57BDE3A76FBD922A923A0A38B922C1D0701F53FF52D7EA9217080163A64901E766EB6A0F20BC391B64B9D1DD2CD13A7D0C946A3A7DF8CEC9E2236446F646C42CFE2B60A2A8D776E56C8D7519B08B88ED0970E10D12A8C9E355D765F2B7BBB7B4CA9360083435523CB0D57D2B106FD14F94B4EEE79D8AC131CA56AD389C84FE279716F8124A543337FB9EA3D988EC5FA63D90A4BA3970E7A39E5C0DE5
Generation of encrypted_data
client_DH_inner_data#6643b654 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 6643b654 client_DH_inner_data constructor number from TL schema
nonce 4, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 20, 16 A5CF4D33F4A11EA877BA4AA573907330 Value received from server in Step 2
retry_id 36, 8 0 First attempt
g_b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g^b mod dh_prime

The serialization of Client_DH_Inner_Data produces some string data. This is followed by encrypted_data:

data_with_hash := SHA1(data) + data + (0-15 random bytes); such that the length be divisible by 16;
AES256_ige_encrypt (data_with_hash, tmp_aes_key, tmp_aes_iv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

The length of the final string was 336 bytes.

Request
set_client_DH_params#f5045f1f 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 0 Since message is in plain text
message_id 8, 8 51e57acd2aa32c6d Exact unixtime * 2^32
message_length 16, 4 376 Message body length
%(set_client_DH_params) 20, 4 f5045f1f set_client_DH_params constructor number from TL schema
nonce 24, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 40, 16 A5CF4D33F4A11EA877BA4AA573907330 Value received from server in Step 2
encrypted_data 56, 340 See above See “Generation of encrypted_data"
0000 | 00 00 00 00 00 00 00 00 6D 2C A3 2A CD 7A E5 51
0010 | 78 01 00 00 1F 5F 04 F5 3E 05 49 82 8C CA 27 E9
0020 | 66 B3 01 A4 8F EC E2 FC A5 CF 4D 33 F4 A1 1E A8
0030 | 77 BA 4A A5 73 90 73 30 FE 50 01 00 92 8A 49 57
0040 | D0 46 3B 52 5C 1C C4 8A AB AA 03 0A 25 6B E5 C7
0050 | 46 79 2C 84 CA 4C 5A 0D F6 0A C7 99 04 8D 98 A3
0060 | 8A 84 80 ED CF 08 22 14 DF C7 9D CB 9E E3 4E 20
0070 | 65 13 E2 B3 BC 15 04 CF E6 C9 AD A4 6B F9 A0 3C
0080 | A7 4F 19 2E AF 8C 27 84 54 AD AB C7 95 A5 66 61
0090 | 54 62 D3 18 17 38 29 84 03 95 05 F7 1C B3 3A 41
00A0 | E2 52 7A 4B 1A C0 51 07 87 2F ED 8E 3A BC EE 15
00B0 | 18 AE 96 5B 0E D3 AE D7 F6 74 79 15 5B DA 8E 4C
00C0 | 28 6B 64 CD F1 23 EC 74 8C F2 89 B1 DB 02 D1 90
00D0 | 7B 56 2D F4 62 D8 58 2B A6 F0 A3 02 2D C2 D3 50
00E0 | 4D 69 D1 BA 48 B6 77 E3 A8 30 BF AF D6 75 84 C8
00F0 | AA 24 E1 34 4A 89 04 E3 05 F9 58 7C 92 EF 96 4F
0100 | 00 83 F5 0F 61 EA B4 A3 93 EA A3 3C 92 70 29 4A
0110 | ED C7 73 28 91 D4 EA 15 99 F5 23 11 D7 44 69 D2
0120 | 11 2F 4E DF 3F 34 2E 93 C8 E8 7E 81 2D C3 98 9B
0130 | AE CF E6 74 0A 46 07 75 24 C7 50 93 F5 A5 40 57
0140 | 36 DE 89 37 BB 6E 42 C9 A0 DC F2 2C A5 32 27 D4
0150 | 62 BC CC 2C FE 94 B6 FE 86 AB 7F BF A3 95 02 1F
0160 | 66 66 1A F7 C0 02 4C A2 98 6C A0 3F 34 76 90 54
0170 | 07 D1 EA 9C 01 0B 76 32 58 DB 1A A2 CC 78 26 D9
0180 | 13 34 EF C1 FD C6 65 B6 7F E4 5E D0

7. Computing auth_key using formula g^{ab} mod dh_prime:

auth_key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

8. The server verifies that auth_key_hash is unique.

The key is unique.

9. A response from the server has been received with the following content:

0000 | 00 00 00 00 00 00 00 00 01 30 AA C5 CE 7A E5 51
0010 | 34 00 00 00 34 F7 CB 3B 3E 05 49 82 8C CA 27 E9
0020 | 66 B3 01 A4 8F EC E2 FC A5 CF 4D 33 F4 A1 1E A8
0030 | 77 BA 4A A5 73 90 73 30 CC EB C0 21 72 66 E1 ED
0040 | EC 7F B0 A0 EE D6 C2 20

Set_client_DH_params_answer decomposition using the following formula:

dh_gen_ok#3bcbf734 nonce:int128 server_nonce:int128 new_nonce_hash1:int128 = Set_client_DH_params_answer;
dh_gen_retry#46dc1fb9 nonce:int128 server_nonce:int128 new_nonce_hash2:int128 = Set_client_DH_params_answer;
dh_gen_fail#a69dae02 nonce:int128 server_nonce:int128 new_nonce_hash3:int128 = Set_client_DH_params_answer;
Parameter Offset, Length in bytes Value Description
%(dh_gen_ok) 0, 4 3bcbf734 dh_gen_ok constructor number from TL schema
nonce 4, 16 3E0549828CCA27E966B301A48FECE2FC Value generated by client in Step 1
server_nonce 20, 16 A5CF4D33F4A11EA877BA4AA573907330 Value received from server in Step 2
new_nonce_hash1 36, 16 CCEBC0217266E1EDEC7FB0A0EED6C220