![]() Reverse-engineering a CRC RFID tag output While each of these steps is relatively trivial in itself, the resulting number of possible CRC algorithms is huge too large for practical brute-force search for reverse engineering. After the division, the n-bit CRC may also be reflected, and finally, it may be XOR’d with a constant before use. There may also be an initial starting value for the CRC calculation this is prepended to the message before the division. ![]() ![]() First, the input bytes may be reflected - swapped bit order from left to right. Complicationsīesides the generator polynomial, there are four other parameters that describe a general CRC algorithm. If you do want to dig into the algorithms in more detail, here’s a good place to start. This is all interesting if you want to write your own CRC implementation, but that’s probably not necessary you can easily find implementations in your language of choice. Note that at each step of the long division, an XOR operation is used instead of the more familiar subtraction with borrowing. ![]() For example, to calculate a trivial 2-bit CRC of the message string 1101 with the generator polynomial 11, we first append 00 to the message to get 110100, then divide to get a quotient of 10011 and a (2-bit) remainder of 01. The division operation maps to a sequence of XOR operations that will remind you of basic arithmetic. OK, it’s going to get a little more relatable now. The polynomial remainder of this division algorithm is the CRC. We then divide this message polynomial by a generator polynomial specified as part of the CRC algorithm. (As a mnemonic device, think about x = 2.) To calculate an n-bit CRC, we append n zero bits to our message, then convert to a polynomial. For example, the binary string 11011 can be represented as x 4 + x 3 + x + 1. There’s a simple mapping between binary strings and such polynomials, in which each set bit becomes a term with the bit position as the exponent. In simple terms, the polynomials involved with the CRC algorithms have coefficients of only 0 or 1. But, this is Hackaday, and I’m going to try to give you enough background to be able attack practical situations, so here we go. There’s a lot of interesting math involved, and a simple web search will turn up plenty of resources if you want to dive further into the subject. Mathematically, a CRC is based on division of polynomials over GF(2), the Galois Field of two elements. CRCs vary in length, with the most common ones being 8, 16, or 32-bits long. The receiver applies the same algorithm, then checks that the transmitted and locally calculated CRC values match. The simplest way to use a CRC is to apply the algorithm to the message to be sent, then append the resulting CRC value to the message. More importantly, it can be particularly good at detecting the kinds of errors often seen in common data channels, specifically, runs of bit errors. First, it’s efficiently implemented in hardware or software. There are a number of different types of codes that can be used in this way, but the CRC has some properties that make it especially useful for communications protocols. Let’s have a look at the CRC, how it is commonly used, and how you can reverse-engineer a protocol that includes one, using application as an example.Ī CRC is a type of code designed to add redundancy to a message in such a way that many transmission errors can be detected. Luckily, if you know the right tool, you can figure it out from just a few sample messages.Ī case in point was discussed recently on the hackaday.io Hack Chat, where came for help reverse engineering the protocol for some RFID tags used for race timing. When you’re reverse-engineering a protocol that contains a CRC, although it’s not intended as a security mechanism, it can throw a wrench in your plans. While Ethernet uses a particularly common CRC, there are many, many different possibilities. Any corrupted packets that failed the check were discarded, and the missing data was detected and re-sent by higher-level protocols. For instance, every Ethernet packet that brought you the web page you’re reading now carried with it a frame check sequence that was calculated using a CRC algorithm. Cyclic redundancy codes (CRC) are a type of checksum commonly used to detect errors in data transmission.
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