With the modulo checksum, this is trivial. The issue with the checksums mentioned above is that it is nearly always possible to modify the data and keep the checksum the same. For example, if the checksum of a firmware image is displayed on the manufacturer’s website, and the attacker wants to modify the firmware. There are situations where an attacker cannot modify both the data and the checksum. Although they have all these variations and can be more challenging to reverse engineer, this does not mean they can prove data is authentic. There are hundreds of common variants, with different lengths – CRC-8, CRC-16, CRC-32 – and different “polynomials” – a set of coefficients used. Why? Because now if we add all the bytes together and do modulo 0x100, we should get 0 if all is well.Ĭyclic Redundancy Checks (CRCs) are more complex but found everywhere around us. Generally, we take what is called the “ two’s complement” (0x100 – 0x33 -> 0xCD) of that and append it. We sum each byte to get 0x433 – too big to fit in a single byte! So we do “modulo 0x100”, leaving us with a remainder of 0x33. If we want to send the following data: 45 67 AB 43 23 98 FD E1 what’s the remainder when divided by 256. You sum up the value of each byte sent, then perform a modulo 256 operation i.e. Modulo checksums are used frequently in custom radio frequency protocols and wire protocols. Clearly this has issues – if two bits are flipped, the error may not be noticed! If it’s not an even number of 1s, then an error has been introduced. The receiver simply needs to sum all the bits including parity together. If it’s an odd number of 1s, the parity bit is 1. If it’s an even number of 1s, the parity bit is 0. The number of 1s in the data are counted. These are generally designed to detect human errors, such as off-by-one (3->4) and transposition (54->45). Credit card numbers, IMEI numbers for phones, VIN numbers on cars. Message: The quick brown cat jumped over the lazy rat.Ĭheck digits are added to numbers all around us. Message: The quick brown fox jumped over the lazy dog. has someone maliciously altered this data? If an attacker can modify the data, they can recalculate the checksum so that changes cannot been detected. They cannot be used to ensure data authenticity i.e. has this data been accidentally modified? Good checksums mean that it is highly unlikely that the data could be changed and the checksum could also be accidentally changed to be valid. They can be used to ensure data integrity i.e. If the checksum does not match the data, then something has gone wrong. What is a checksum?Ī checksum is a short piece of data derived from a longer block of data, generally for the purpose of detecting errors that have been introduced. Whilst checksums and hashes are two distinct terms, they are often used for similar purposes. If you have worked with embedded systems, you will have come across terms like checksums, hashing, password hashes, and CRCs.
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