samples-auth_key

In the examples below, the transport headers are omitted:

For example, for an abridged version of the transport 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 by 4) followed by the data themselves. 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

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 

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

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

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;

Conversion of encrypted_answer into answer:

encrypted_answer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
tmp_aes_key = F011280887C7BB01DF0FC4E17830E0B91FBB8BE4B2267CB985AE25F33B527253
tmp_aes_iv = 3212D579EE35452ED23E0D0C92841AA7D31B2E9BDEF2151E80D15860311C85DB
answer = BA0D89B53E0549828CCA27E966B301A48FECE2FCA5CF4D33F4A11EA877BA4AA57390733002000000FE000100C71CAEB9C6B1C9048E6C522F70F13F73980D40238E3E21C14934D037563D930F48198A0AA7C14058229493D22530F4DBFA336F6E0AC925139543AED44CCE7C3720FD51F69458705AC68CD4FE6B6B13ABDC9746512969328454F18FAF8C595F642477FE96BB2A941D5BCD1D4AC8CC49880708FA9B378E3C4F3A9060BEE67CF9A4A4A695811051907E162753B56B0F6B410DBA74D8A84B2A14B3144E0EF1284754FD17ED950D5965B4B9DD46582DB1178D169C6BC465B0D6FF9CA3928FEF5B9AE4E418FC15E83EBEA0F87FA9FF5EED70050DED2849F47BF959D956850CE929851F0D8115F635B105EE2E4E15D04B2454BF6F4FADF034B10403119CD8E3B92FCC5BFE000100262AABA621CC4DF587DC94CF8252258C0B9337DFB47545A49CDD5C9B8EAE7236C6CADC40B24E88590F1CC2CC762EBF1CF11DCC0B393CAAD6CEE4EE5848001C73ACBB1D127E4CB93072AA3D1C8151B6FB6AA6124B7CD782EAF981BDCFCE9D7A00E423BD9D194E8AF78EF6501F415522E44522281C79D906DDB79C72E9C63D83FB2A940FF779DFB5F2FD786FB4AD71C9F08CF48758E534E9815F634F1E3A80A5E1C2AF210C5AB762755AD4B2126DFA61A77FA9DA967D65DFD0AFB5CDF26C4D4E1A88B180F4E0D0B45BA1484F95CB2712B50BF3F5968D9D55C99C0FB9FB67BFF56D7D4481B634514FBA3488C4CDA2FC0659990E8E868B28632875A9AA703BCDCE8FCB7AE551

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;

6. Random number b is computed:

b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

Generation of encrypted_data

client_DH_inner_data#6643b654 nonce:int128 server_nonce:int128 retry_id:long g_b:string = Client_DH_Inner_Data

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;

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;