I'm a software developer, not a mathematician. I saw a question about decoding ciphertext so I'm assuming this is not off-topic in this forum.
I have a legacy database that seems to be obfuscated, and the original program used to record this data is lost.
\begin{array} {l|l} \mathbf{PlainText} & \mathbf{Obfuscated} \\ \hline \mathtt{ACURA} & \mathtt{9A929BB646D5}\\ \mathtt{AGRALE} & \mathtt{9A9297AFBF5EEF}\\ \mathtt{AUDI} & \mathtt{9A92A9ABBB}\\ \mathtt{BENELLI} & \mathtt{9A9594A4A6A0A0BC}\\ \mathtt{BETA} & \mathtt{9A9594AEA0}\\ \mathtt{BULL} & \mathtt{9A95A4B64C}\\ \mathtt{CHEVROLET} & \mathtt{9A949291A8A8BB5DE066}\\ \mathtt{CHRYSLER} & \mathtt{9A9492A2B45AEA65F5}\\ \mathtt{CN AUTO} & \mathtt{9A94AC8A848B93B7}\\ \mathtt{DAFRA} & \mathtt{9A97969AA3B6}\\ \mathtt{DKW-VEMAG} & \mathtt{9A97AC42202425272A22}\\ \mathtt{EAGLE} & \mathtt{9A9699A6BD51}\\ \mathtt{ENGESA} & \mathtt{9A96AAB7B355DA}\\ \mathtt{FERRARI} & \mathtt{9AA9A0B448DB62FE}\\ \mathtt{FIAT} & \mathtt{9AA9BCBB5F}\\ \mathtt{GREEN} & \mathtt{9AA8B4BF4ACA}\\ \mathtt{HONDA} & \mathtt{9AABB445C65A}\\ \mathtt{HUMMER} & \mathtt{9AAB4FDA67FE1D}\\ \mathtt{HUSQVARNA} & \mathtt{9AAB4FE4799D92B142D0}\\ \mathtt{HYUNDAI} & \mathtt{9AAB4BE67AEC62FE}\\ \mathtt{JAGUAR} & \mathtt{9AADA0A1B9A8B6}\\ \mathtt{JINBEI} & \mathtt{9AADB841CC40C5}\\ \mathtt{KAWASAKI} & \mathtt{9AACA3BCB254D970FB}\\ \mathtt{LAMBORGHINI} & \mathtt{9AAFBE4AC341DF72F811061C}\\ \mathtt{MAN} & \mathtt{9AAEA1A9}\\ \mathtt{MCLAREN} & \mathtt{9AAEBF4AC445C640}\\ \mathtt{MINI} & \mathtt{9AAEB94ED8}\\ \mathtt{MV AGUSTA} & \mathtt{9AAE4B2D213AC342D445}\\ \mathtt{OLDSMOBILE} & \mathtt{9AA0A2A0BC58EB7B86819F}\\ \mathtt{PIAGGIO} & \mathtt{9AA3A2A5A3B84EC8}\\ \mathtt{PLYMOUTH} & \mathtt{9AA3A1BC45C650F178}\\ \mathtt{ROYAL ENFIELD} & \mathtt{9AA5BA52DC7BD748D448C85DFD07}\\ \mathtt{SATURN} & \mathtt{9AA4AB46D4758F}\\ \mathtt{SCANIA} & \mathtt{9AA4A9ACB5ACA1}\\ \mathtt{SCION} & \mathtt{9AA4A9B44BCB}\\ \mathtt{SEAT} & \mathtt{9AA4A7AE4C}\\ \mathtt{SHINERAY AUTO} & \mathtt{9AA4A2ADB4ABB1A74330282ED663}\\ \mathtt{SINO TRUK} & \mathtt{9AA4A3B748CE6D9798B0}\\ \mathtt{SUZUKI} & \mathtt{9AA4B754E660E5}\\ \mathtt{TRAXX} & \mathtt{9AA7B7BE58E2}\\ \mathtt{TRIUMPH} & \mathtt{9AA7B747D3738F82}\\ \mathtt{VOLARE} & \mathtt{9AB947D558F872}\\ \mathtt{VOLVO} & \mathtt{9AB947D563E0}\\ \mathtt{GASOLINA} & \mathtt{9AA8A7BC43DD6BEC6C}\\ \mathtt{ETANOL} & \mathtt{9A96A4A3BE5CE4}\\ \mathtt{GÁS} & \mathtt{9AA8B849}\\ \mathtt{DIESEL} & \mathtt{9A97AEB546D96A}\\ \mathtt{FLEX} & \mathtt{9AA9BB47D0}\\\hline \end{array}
If we assume the obfuscated text is encoding each character using 2 hexadecimal digits, the length is always the length of the plain text + 1.
The first byte is always 0x9A and the algorithm used is somewhat deterministic: for example,"ACURA", "AGRALE" and "AUDI" start with the same byte, so I guess 0x92 in the first position is "A". Looks like the subsequent characters are a function of the previous.
I would bet it is some combination of XOR and/or shifting with the previous value. I guess I could try to brute-force the data using frequency tables but I wonder if there is a smarter way to find the obfuscation function.
So the question is: given the hypothesis that character of index i in the cipher text is a simple function of character i-1, is it possible to derive the function?
[update]
SmileyCraft noticed it doesn't looks like a simple function of the previous character. In cipher text of DAFRA there is a 0x9A preceding the R but the result is not the same as the R in ROYALENFIELD.
[update 2]
The first byte is always fixed at 9A. Have you figured out the second byte based on the first char of the plain text yet? Somos
Well, no. I was pursuing a curious pattern in the bits but I don't know if it is an useful property. Looking at the bits, the least significant always alternate in a 010101 pattern, the second 00110011, the next 00001111 and so on:
\begin{array} {c|l|l} & \mathbf{PlainText} & \mathbf{Obfuscated} \\ \hline A & 01000001 & 10010010\\ B & 01000010 & 10010101\\ C & 01000011 & 10010100\\ D & 01000100 & 10010111\\ E & 01000101 & 10010110\\ F & 01000110 & 10101001\\ G & 01000111 & 10101000\\ H & 01001000 & 10101011\\ I & 01001001 & 10101010\\ J & 01001010 & 10101101\\ K & 01001011 & 10101100\\ L & 01001100 & 10101111\\ M & 01001101 & 10101110\\ N & 01001110 & 10100001\\ O & 01001111 & 10100000\\ P & 01010000 & 10100011\\ Q & 01010001 & 10100010\\ R & 01010010 & 10100101\\ S & 01010011 & 10100100\\ T & 01010100 & 10100111\\ U & 01010101 & 10100110\\ V & 01010110 & 10111001\\ W & 01010111 & 10111000\\ X & 01011000 & 10111011\\ Y & 01011001 & 10111010\\ Z & 01011010 & 10111101\\ \end{array}
All 141 pairs I have so far, guessed from associated images:
[('9A929BB646D5', 'ACURA'),
('9A9297AFBF5EEF', 'AGRALE'),
('9A9290909EEC7397A6B851', 'ALFA ROMEO'),
('9A9291F770E77AEA7F9386', 'AM GENERAL'),
('9A929194A1A2BCA8B9', 'AMAZONAS'),
('9A92ACB84DCB59CF', 'APRILIA'),
('9A92ABB2BC8E97B34ACA44C4', 'ASIA MOTORS'),
('9A92AB46DA7BD770F315302A2C', 'ASTON MARTIN'),
('9A92A9ABBB', 'AUDI'),
('9A9594A4A6A0A0BC', 'BENELLI'),
('9A9594A4B756D764', 'BENTLEY'),
('9A9594AEA0', 'BETA'),
('9A95909BA5ABA0', 'BIMOTA'),
('9A95AC42', 'BMW'),
('9A95A4AFB453', 'BUELL'),
('9A95A4ADA1A7B754', 'BUGATTI'),
('9A95A4ABA1BE', 'BUICK'),
('9A95A4B64C', 'BULL'),
('9A949B99ADABBBA9AE', 'CADILLAC'),
('9A949BA4A2AAA7', 'CAGIVA'),
('9A9498AA', 'CBT'),
('9A949295ACA1AEA9', 'CHANGAN'),
('9A949291AC54', 'CHERY'),
('9A949291A8A8BB5DE066', 'CHEVROLET'),
('9A9492A2B45AEA65F5', 'CHRYSLER'),
('9A9493A1BC5E66E1', 'CITROEN'),
('9A94AC8A848B93B7', 'CN AUTO'),
('9A94A8B14ACFA3BAB95BC65FE5', 'CROSS LANDER'),
('9A97969FA7BA', 'DACIA'),
('9A97969DA6BD47', 'DAELIM'),
('9A97969DBB59E4', 'DAEWOO'),
('9A97969A', 'DAF'),
('9A97969AA3B6', 'DAFRA'),
('9A979699AEBD5EE478', 'DAIHATSU'),
('9A9796AC4FF609', 'DATSUN'),
('9A97AC42202425272A22', 'DKW-VEMAG'),
('9A97A8AABE56', 'DODGE'),
('9A97A2A3AB52D7', 'DUCATI'),
('9A9699A6BD51', 'EAGLE'),
('9A9696AE', 'EBR'),
('9A96929E90', 'EFFA'),
('9A96AC8A8194A4B0BE58C4', 'EL DETALLE'),
('9A96AAB7B355DA', 'ENGESA'),
('9AA9A0A8A2BD4F', 'F.N.M.'),
('9AA9A4B446DD6D', 'FANTIC'),
('9AA9A0B448DB62FE', 'FERRARI'),
('9AA9BCBB5F', 'FIAT'),
('9AA9B64FDC', 'FORD'),
('9AA9B64DD370', 'FOTON'),
('9AA8A7BC9388858D', 'GAS GAS'),
('9AA8A3AEB55D', 'GEELY'),
('9AA8BF4AC041CE', 'GILERA'),
('9AA8BBB8', 'GMC'),
('9AA8B4BF4ACA', 'GREEN'),
('9AA8B340C85CE4', 'GURGEL'),
('9AABA2AEBC54', 'HAFEI'),
('9AABA2B2B1A4B18B8D9DAAA0B041D36A', 'HARLEY DAVIDSON'),
('9AABB445C65A', 'HONDA'),
('9AABB445C65A36D664EB62E6', 'HONDA MOTOS'),
('9AAB4FDA67FE1D', 'HUMMER'),
('9AAB4FE4799D92B142D0', 'HUSQVARNA'),
('9AAB4BDC7F86988A', 'HYOSUNG'),
('9AAB4BE67AEC62FE', 'HYUNDAI'),
('9AAAB6BC49D86B', 'INDIAN'),
('9AAAB6BA4BCB59F800', 'INFINITI'),
('9AAAB64DDD62FC6BFD143ADB49D0', 'INTERNATIONAL'),
('9AAAB244D8', 'IROS'),
('9AAAB34FE66E', 'ISUZU'),
('9AAA4FD259FA', 'IVECO'),
('9AADA0A5', 'JAC'),
('9AADA0A1B9A8B6', 'JAGUAR'),
('9AADBC44DB', 'JEEP'),
('9AADB841CC40C5', 'JINBEI'),
('9AADB34A', 'JPX'),
('9AACA3B0B657E667F2', 'KASINSKI'),
('9AACA3BCB254D970FB', 'KAWASAKI'),
('9AACBF43D545D2', 'KEEWAY'),
('9AACBBBA95B04CF5070A04', 'KIA MOTORS'),
('9AACB5BC44DF6BEB73E968', 'KOENIGSEGG'),
('9AAC4FDA', 'KTM'),
('9AAFBE45C9', 'LADA'),
('9AAFBE4AC341DF72F811061C', 'LAMBORGHINI'),
('9AAFBE4BC159D6', 'LANCIA'),
('9AAFBE4BC0B249CD66F812', 'LAND ROVER'),
('9AAFBA55E56B', 'LEXUS'),
('9AAFB6BAB451', 'LIFAN'),
('9AAFB643C94BDB7F', 'LINCOLN'),
('9AAFB043D779', 'LOTUS'),
('9AAEA1AFB754D472F1', 'MAHINDRA'),
('9AAEA1A9', 'MAN'),
('9AAEA1B2B859D67E85', 'MASERATI'),
('9AAEA1BD4DDC', 'MAZDA'),
('9AAEBF4AC445C640', 'MCLAREN'),
('9AAEBD56D64EDE7186E07AEC6F8C', 'MERCEDES BENZ'),
('9AAEBD56D67E9CA0', 'MERCURY'),
('9AAEB94ED8', 'MINI'),
('9AAEB948D478F6152A2133', 'MITSUBISHI'),
('9AAEB340C858EA', 'MORGAN'),
('9AAEB34ED2A0AB54EC1404', 'MOTO GUZZI'),
('9AAE4B2D213AC342D445', 'MV AGUSTA'),
('9AA1A4B14AD964', 'NISSAN'),
('9AA0A2A0BC58EB7B86819F', 'OLDSMOBILE'),
('9AA0BE42C1', 'OPEL'),
('9AA3A6BD4ADD61E0', 'PEUGEOT'),
('9AA3A2A5A3B84EC8', 'PIAGGIO'),
('9AA3A1BC45C650F178', 'PLYMOUTH'),
('9AA3BC4DEE6AE77E', 'PONTIAC'),
('9AA3BC49D345C152', 'PORSCHE'),
('9AA3B642CC', 'PUMA'),
('9AA5A4B4BA42C242', 'RENAULT'),
('9AA5BA41C244282F3CC653CB', 'ROLLS ROYCE'),
('9AA5BA57D374', 'ROVER'),
('9AA5BA52DC7BD748D448C85DFD07', 'ROYAL ENFIELD'),
('9AA4ABAAA3', 'SAAB'),
('9AA4ABBE5DE063FF', 'SAMSUNG'),
('9AA4AB46D4758F', 'SATURN'),
('9AA4A9ACB5ACA1', 'SCANIA'),
('9AA4A9B44BCB', 'SCION'),
('9AA4A7AE4C', 'SEAT'),
('9AA4A2ADB4ABB1A74330282ED663', 'SHINERAI AUTO'),
('9AA4A2ADB4ABB1A743302420202A3E', 'SHINERAY MOTOR'),
('9AA4BF47D679', 'SMART'),
('9AA4B9BC44D97F9BABA1', 'SSANGYONG'),
('9AA4B7BF4EF204', 'SUBARU'),
('9AA4B740CB49EC6E', 'SUNDOWN'),
('9AA4B754E660E5', 'SUZUKI'),
('9AA4B754E660E553E261EC6F96', 'SUZUKI MOTOR'),
('9AA7A6BCB2', 'TATA'),
('9AA8A7BF46C65C', 'TORBAL'),
('9AA7B854EC1318', 'TOYOTA'),
('9AA7B7BE58E2', 'TRAXX'),
('9AA7B747D3738F82', 'TRIUMPH'),
('9AA7B741C25DEE14', 'TROLLER'),
('9AA7B340', 'TVR'),
('9AB9B44CEB66EB6DFB', 'VAUXHALL'),
('9AB9B042DD4D', 'VESPA'),
('9AB947D558F872', 'VOLARE'),
('9AB947D56E93A6B2BB52F9', 'VOLKSWAGEN'),
('9AB947D563E0', 'VOLVO'),
('9AB8B740C870F9', 'WANGYE'),
('9ABAB545C940CD', 'YAMAHA')]