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What is a check sum?

– Hash sum or check sum can be defined as the small sized datum that has been computed using a block of digital block chosen arbitrarily.
– Check sums are used in the purpose of error detection.
– During the transmission or storage of the data, the errors might have crept in.
– At any time later, the integrity of the data can be verified.
– This is done by re-computation of the hash sum and carrying out a comparison between the stored check sum and the currently computed one.
– If there exists a match between the two check sums, this means that no accidental alteration was made to the data.
– A check sum algorithm or check sum function is the procedure that is used for yielding the check sum from the given data.
– Yielding result with a high probability for the accidentally altered data is a characteristic of a good check sum algorithm.
– Now in this case, if a match is found, the high probability means that the data is free from errors to the extent denoted by the probability.

Check sum algorithms are related to the following other algorithms and functions:

  • Hash functions
  • Fingerprints
  • Randomization functions
  • Cryptographic hash functions

– However, the above mentioned concepts have different design goals and thus different applications also.
– It should be noted that in a security related application, check sums should not be used as they do not consist of properties that are necessary for the protection of data from accidental or intentional tampering.
Two special cases of checksums are:

  • Check digits and
  • Parity bits

Both of these cases are suitable for blocks of data of small size such as in the following applications:

  • Social security numbers
  • Bank account numbers
  • Computer words
  • Single bytes and so on

– There are special check sums up on which the correcting codes are based.
– These correcting codes are capable of detecting common errors as well as recovering the data back to original form in some cases.

What is Longitudinal Parity Check?

– This one is the simplest of all the check sum algorithms.
– Here, the data is broken down in to words of fixed length or number of bits.
– Then the algorithm produces the exclusive OR results of all the words.
– This result in form of an extra word is attached to the message.
– Now for checking the integrity of the message, the exclusive OR of the words can be computed by the receiver.
– This includes the check sum also.
– If the result does not consist of n zeroes, then the receiver will come to know that an error has occurred during the transmission.
– The error during transmission that flipped even a single message bit or odd number of message bits will be considered to be an incorrect check sum.
– Suppose there are two bits lying at the same position in two different words.
– In such a case those two bits will also be chosen independently.

What is Modular Sum?

– This is a modified form of the parity check algorithm.
– It adds up all the words by considering them as unsigned binary numbers.
– Any overflowing bits are discarded and the 2’s complement of the result is appended to the message as the check sum. – For the validation purpose, the words are added up by the receiver in the same way as in previous algorithm.
– Here also, if the result does not have n number of zeroes, an error is said to have occurred.

What is Position Dependent Check sums?

– The above mentioned check sum algorithms are not capable of detecting some more common errors that impact multiple bits at the same time.
– These errors may be insertion or deletion of words, making changes to the word order etc.
For such cases, the following algorithms are commonly used:

  • Fletcher’s checksum
  • Adler – 32
  • Cyclic redundancy check

– These algorithms consider both the position of the word in sequence and its value. However the cost is too high.

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