A checksum is a small-sized

block Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 ...

of data derived from another block of

digital data Digital data, in information theory and information systems, is information represented as a string of discrete symbols each of which can take on one of only a finite number of values from some alphabet, such as letters or digits. An example i ...

for the purpose of detecting errors that may have been introduced during its

transmission Transmission may refer to: Medicine, science and technology * Power transmission ** Electric power transmission ** Propulsion transmission, technology allowing controlled application of power *** Automatic transmission *** Manual transmission *** ...

or storage. By themselves, checksums are often used to verify

data integrity Data integrity is the maintenance of, and the assurance of, data accuracy and consistency over its entire Information Lifecycle Management, life-cycle and is a critical aspect to the design, implementation, and usage of any system that stores, proc ...

but are not relied upon to verify data authenticity. The procedure which generates this checksum is called a checksum function or

checksum algorithm A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output r ...

. Depending on its design goals, a good checksum algorithm usually outputs a significantly different value, even for small changes made to the input. This is especially true of

cryptographic hash function A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output re ...

s, which may be used to detect many data corruption errors and verify overall

; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted. Checksum functions are related to

hash function A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually u ...

fingerprint A fingerprint is an impression left by the friction ridges of a human finger. The recovery of partial fingerprints from a crime scene is an important method of forensic science. Moisture and grease on a finger result in fingerprints on surfac ...

randomization function Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outc ...

s, and

s. However, each of those concepts has different applications and therefore different design goals. For instance, a function returning the start of a string can provide a hash appropriate for some applications but will never be a suitable checksum. Checksums are used as cryptographic primitives in larger authentication algorithms. For cryptographic systems with these two specific design goals, see

HMAC In cryptography, an HMAC (sometimes expanded as either keyed-hash message authentication code or hash-based message authentication code) is a specific type of message authentication code (MAC) involving a cryptographic hash function and a secret ...

Check digit A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity ...

s and

parity bit A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes) ...

s are special cases of checksums, appropriate for small blocks of data (such as

Social Security number In the United States, a Social Security number (SSN) is a nine-digit number issued to U.S. citizens, permanent residents, and temporary (working) residents under section 205(c)(2) of the Social Security Act, codified as . The number is issued to ...

bank account A bank account is a financial account maintained by a bank or other financial institution in which the financial transactions between the bank and a customer are recorded. Each financial institution sets the terms and conditions for each type o ...

numbers, computer words, single

byte The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...

s, etc.). Some

error-correcting code In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

s are based on special checksums which not only detect common errors but also allow the original data to be recovered in certain cases.

Algorithms

Parity byte or parity word

The simplest checksum algorithm is the so-called longitudinal parity check, which breaks the data into "words" with a fixed number of bits, and then computes the

exclusive or Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...

(XOR) of all those words. The result is appended to the message as an extra word. In simpler terms, this means adding a bit to the end of the word to guarantee that there is an even number of '1's. To check the integrity of a message, the receiver computes the exclusive or of all its words, including the checksum; if the result is not a word consisting of zeros, the receiver knows a transmission error occurred. With this checksum, any transmission error which flips a single bit of the message, or an odd number of bits, will be detected as an incorrect checksum. However, an error that affects two bits will not be detected if those bits lie at the same position in two distinct words. Also swapping of two or more words will not be detected. If the affected bits are independently chosen at random, the probability of a two-bit error being undetected is .

Sum complement

A variant of the previous algorithm is to add all the "words" as unsigned binary numbers, discarding any overflow bits, and append the

two's complement Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian ...

of the total as the checksum. To validate a message, the receiver adds all the words in the same manner, including the checksum; if the result is not a word full of zeros, an error must have occurred. This variant, too, detects any single-bit error, but the pro modular sum is used in SAE J1708.

Position-dependent

The simple checksums described above fail to detect some common errors which affect many bits at once, such as changing the order of data words, or inserting or deleting words with all bits set to zero. The checksum algorithms most used in practice, such as

Fletcher's checksum The Fletcher checksum is an algorithm for computing a position-dependent checksum devised by John G. Fletcher (1934–2012) at Lawrence Livermore Labs in the late 1970s. The objective of the Fletcher checksum was to provide error-detection proper ...

Adler-32 Adler-32 is a checksum algorithm written by Mark Adler in 1995, modifying Fletcher's checksum. Compared to a cyclic redundancy check of the same length, it trades reliability for speed (preferring the latter). Adler-32 is more reliable than Fletcher ...

, and

cyclic redundancy check A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. Blocks of data entering these systems get a short ''check value'' attached, based on t ...

s (CRCs), address these weaknesses by considering not only the value of each word but also its position in the sequence. This feature generally increases the

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of computing the checksum.

Fuzzy checksum

The idea of fuzzy checksum was developed for detection of

email spam Email spam, also referred to as junk email, spam mail, or simply spam, is unsolicited messages sent in bulk by email (spamming). The name comes from a Monty Python sketch in which the name of the canned pork product Spam is ubiquitous, unavoida ...

by building up cooperative databases from multiple ISPs of email suspected to be spam. The content of such spam may often vary in its details, which would render normal checksumming ineffective. By contrast, a "fuzzy checksum" reduces the body text to its characteristic minimum, then generates a checksum in the usual manner. This greatly increases the chances of slightly different spam emails producing the same checksum. The ISP spam detection software, such as

SpamAssassin Apache SpamAssassin is a computer program used for anti-spam techniques, e-mail spam filtering. It uses a variety of spam-detection techniques, including Domain Name System, DNS and fuzzy checksum techniques, Bayesian spam filtering, Bayesian filt ...

, of co-operating ISPs, submits checksums of all emails to the centralised service such as DCC. If the count of a submitted fuzzy checksum exceeds a certain threshold, the database notes that this probably indicates spam. ISP service users similarly generate a fuzzy checksum on each of their emails and request the service for a spam likelihood.

General considerations

A message that is bits long can be viewed as a corner of the -dimensional hypercube. The effect of a checksum algorithm that yields an -bit checksum is to map each -bit message to a corner of a larger hypercube, with dimension . The 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 corners. A single-bit transmission error then corresponds to a displacement from a valid corner (the correct message and checksum) to one of the adjacent corners. An error which affects bits moves the message to a corner which is steps removed from its correct corner. The goal of a good checksum algorithm is to spread the valid corners as far from each other as possible, to increase the likelihood "typical" transmission errors will end up in an invalid corner.

References

External links

{{wikibooks , 1= Algorithm Implementation , 2= Checksums
Additive Checksums (C)
theory from Barr Group
Checksum CalculatorOpen source python based application with GUI used to verify downloads.