So, for each block of the data word, taken in sequence, the block's value is added to the first sum and the new value of the first sum is then added to the second sum. This is the modular sum of the values taken by the simple checksum as each block of the data word is added to it. In our example, there are only 255 possible checksum values, so it is easy to see that even random data has about a 0.4% probability of having the same checksum as our message.įletcher addresses both of these weaknesses by computing a second value along with the simple checksum. The second weakness is that the universe of checksum values is small, being equal to the chosen modulus. If the order is changed, the checksum value will be the same and the change will not be detected. The first weakness of the simple checksum is that it is insensitive to the order of the blocks (bytes) in the data word (message). The receiver of the message can re-compute the checksum and compare it to the value received to determine whether the message has been altered by the transmission process. (In practice, the modulo operation is performed during the summation to control the size of the result.) The checksum value is transmitted with the message, increasing its length to 137 bytes, or 1096 bits. So, the simple checksum is computed by adding together all the 8-bit bytes of the message, dividing by 255 and keeping only the remainder. Similarly, a convenient modulus would be 255, although, again, others could be chosen. A convenient block size would be 8 bits, although this is not required. The data to be protected, in its entirety, is referred to as a "word", and the pieces into which it is divided are referred to as "blocks".)Īs an example, the data may be a message to be transmitted consisting of 136 characters, each stored as an 8-bit byte, making a data word of 1088 bits in total. (Note that the terminology used in this domain can be confusing. The algorithm Review of simple checksums Īs with simpler checksum algorithms, the Fletcher checksum involves dividing the binary data word to be protected from errors into short "blocks" of bits and computing the modular sum of those blocks. 6.5 Bit and byte ordering (endianness / network order).4 Example calculation of the Fletcher-16 checksum.2 Overview of the different algorithm parameters.So, if we change the fifth byte from 00 to 5D, the sum of the five bytes becomes 200, and therefore, the 8-bit checksum becomes 00. an unused byte) so that the 8-bit checksum becomes 00. In this example, what we do is adjust either the fourth or fifth byte (i.e. The 8-bit checksum of the subject 5 bytes is A3 (the least significant 8 bits of 1A3). It is known that the fourth and fifth bytes are not used by the code/data author.Ġ0 <- the fourth byte is known to be unused by the code/data authorĠ0 <- the fifth byte is known to be unused by the code/data author Sometimes, you may see a reference to adjusting code/data to achieve an 8-bit checksum of 00.Ī very simple example follows. The bytes to be checksummed are not always all of the bytes.įor example, in some BIOS expansion ROM's, the 'ROM size' byte indicates that only some of the ROM's bytes are to be checksummed.Īdjustment to get an 8-bit checksum of 00
That allows me to see the result of lots of different hashing algorithms. For example, in the software that I use in Windows 10, which is HxD Hex Editor, I select on the menubar, then choose. Hex editing software usually have functionality in them to calculate checksums, and other types of hashes. I never calculate 8-bit checksums myself I get software to do it. The 16-bit checksum of the subject 5 bytes is the 16 least significant bits of 2B6, which is 2B6, but that would normally be written as 02B6. The 4-bit checksum of the subject 5 bytes is the 4 least significant bits of 2B6, which is 6. Therefore, the 8-bit checksum of the subject 5 bytes is the 8 least significant bits of 2B6, which is B6. Simply sum up the bytes to be checksummed, then of the sum, keep only the least significant 8 bits.ĥ bytes as follows.
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