![]() Depending on its design goals, a good checksum algorithm usually outputs a significantly different value, even for small changes made to the input. ![]() The procedure which generates this checksum is called a checksum function or checksum algorithm. By themselves, checksums are often used to verify data integrity but are not relied upon to verify data authenticity. Buck, “Check digit calculator”, US Patent 3,451,619, filed 11-9-1967, patented 24-6-1969, assigned to Westinghouse Air Brake Comp.Effect of a typical checksum function (the Unix cksum utility)Ī checksum is a small-sized block of data derived from another block of digital data for the purpose of detecting errors that may have been introduced during its transmission or storage. Verhoeff, “Data checking system”, US Patent 3,448,254, filed 28-7-1965, patented 3-6-1969, assigned to Anker Werke. Verhoeff, “Device for checking a group of symbols.”, US Patent 3,675,202, filed 1-6-1969, patented 4-7-1972, assigned to U.S. Verhoeff, “Error Detecting Decimal Codes”, ( Mathematical Centre Tracts, 29). Rudolf Malý, “Kontrollrechenapparat,” German Patent 244,183, issued 29-4-1911. Leonard C Zitnik, “Check digit computing apparatus”, US Patent 3,033,450, filed 18-12-1959, patented 8-5-1962, assigned to Pure Oil Comp. Luhn, “Computer for verifying numbers,” US Patent 2,950,048, filed 6-1-1954, patented 23-8-1960, assigned to IBM. Barto, “Economie en Techniek van Codes en Code-Condensors,” PhD Thesis TH Delft, 1933. Kähler, “Rudolf Mosse-Code mit Mosse-Condenser,” Rudolf Mosse, Berlin, 1922. It used only modulo 3, probably because it employed hard-wired tables for multiplication and addition.Ī credit card checksum device following the principles of the Controlex was patented in 1962 by the Pure Oil Company (, Figure 5). ![]() Luhn invented a relay-based checking device for calculators. The scale behind this window runs opposite to the chains, so it shows the tens complement of the number entered, which is exactly what is needed when determining the check digit.īefore that, in 1944, Hans P. In that case, no number is entered into the rightmost slot and the digit is read from the small window. The device can also be used to calculate the check digit for an as yet incomplete credit card number. If a correct credit card number is entered, the number in the small window is zero. Similarly, the number 2 in an odd slot corresponds to 1 in an even slot. Where an odd slot shows a 1, an even one shows a 5, so entering a 5 in an even slot is equivalent to entering a 1 in an odd slot. If we number the slots from the right, starting with 1, the even-numbered input slots have a strange digit distribution. It looks like an ordinary chain adder, but it does not have a tens carry and all chains add to the same number in the small window at the far right. Luhn invented a mechanical calculator for this checksum (, Figure 4). ![]() The calculation of a checksum has to be fast and not error-prone, so it is useful to mechanize this calculation. Other telegram condensers do show checksums in the final message, and sometimes even checksums that contain a check digit to check themselves. When decoding an erroneous message an inconsistency occurs between the possible checksums indicated by the encoding scheme and the checksums of the decoded message. The checksums themselves are not part of the final message, so do not increase the transmission costs directly, but they force the encoding to be not the most efficient one. This final encoding is controlled by the checksums. First common words and phrases are expressed in small numbers using a dictionary, then an intermediate checksum is calculated per five 2-digit numbers, and finally the 2-digit numbers are encoded in 2-character codes. The aim of the Mosse Code is to lower the costs of telegrams by reducing their size. This is, for example, the case in the Rudolf Mosse Code Condenser for telegrams. Checksums are not always explicitly visible in the actual number. ![]()
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