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The effect of a checksum algorithm that yields an n-bit checksum is to map each m-bit message to a corner of a larger hypercube, with dimension m + n. The 2 m + n corners of this hypercube represent all possible received messages. The valid received messages (those that have the correct checksum) comprise a smaller set, with only 2 m corners.
The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers.
The Verhoeff checksum calculation is performed as follows: Create an array n out of the individual digits of the number, taken from right to left (rightmost digit is n 0, etc.). Initialize the checksum c to zero. For each index i of the array n, starting at zero, replace c with (, (,)) .
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This is a list of hash functions, including cyclic redundancy checks, checksum functions, and cryptographic hash functions. This list is incomplete ; you can help by adding missing items . ( February 2024 )
The first weakness of the simple checksum is that it is insensitive to the order of the blocks (bytes) in the data word (message). If the order is changed, the checksum value will be the same and the change will not be detected. The second weakness is that the universe of checksum values is small, being equal to the chosen modulus.
The checksum field is the 16 bit one's complement of the one's complement sum of all 16 bit words in the header. For purposes of computing the checksum, the value of the checksum field is zero. If there is no corruption, the result of summing the entire IP header, including checksum, and then taking its one's complement should be zero.
The message stream may be any length. After it has been shifted through the register, followed by 8 zeroes, the result in the register is the checksum. Checking received data with checksum. The received message is shifted through the same register as used in the generator, but the received checksum is attached to it instead of zeroes.