A checksum is a small-sized block of data derived from another block of

Additive Checksums (C)

theory from Barr Group

Checksum Calculator

Open source python based application with GUI used to verify downloads.

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 digit (unit), digits. ...

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. 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 (mathematics), 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 particu ...

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

; 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 (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or si ...

s, 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 ...

s, randomization functions, and cryptographic hash function
A cryptographic hash function (CHF) is a hash algorithm (a map (mathematics), 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 particu ...

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 and correction, 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 ...

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 detection and correction, error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, ...

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 United States nationality law, U.S. citizens, Permanent residence (United States), permanent residents, and temporary (working) residents under section 205(c)(2 ...

s, 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 of ...

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 un ...

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 error control, controlling errors in data over unreliable or noisy communication channels. The ce ...

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 theexclusive 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
An infix is an affix inserted i ...

(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 thetwo'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 Most Significant Bit, binary digit with the greatest place value (the leftmos ...

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, Adler-32, andcyclic redundancy check
A cyclic redundancy check (CRC) is an Error correcting code, error-detecting code commonly used in digital Telecommunications network, networks and storage devices to detect accidental changes to digital data. Blocks of data entering these syste ...

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 cost
In Production (economics), production, research, retail, and accounting, a cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one o ...

of computing the checksum.
Fuzzy checksum

The idea of fuzzy checksum was developed for detection ofemail 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 Spam (Monty Python), Monty Python sketch in which the name of the Spam (food), canned pork prod ...

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, 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.See also

General topic *Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

* Check digit
A check digit is a form of redundancy check used for Error detection and correction, 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 ...

* Damm algorithm
* Data rot
* File verification
* Fletcher's checksum
* Frame check sequence
A frame check sequence (FCS) is an error-detecting code added to a Frame (networking), frame in a communication protocol. Frames are used to send payload data from a source to a destination.
Purpose
All frames and the bits, bytes, and fiel ...

* cksum
* md5sum
* sha1sum
* Parchive
* Sum (Unix)
* SYSV checksum
* BSD checksum
* xxHash
This is a list of hash functions, including cyclic redundancy checks, checksum functions, and cryptographic hash functions.
Cyclic redundancy checks
Adler-32 is often mistaken for a CRC, but it is not: it is a #Checksums, checksum.
Checksums
...

Error correction
* Hamming code
In computer science and telecommunication, Hamming codes are a family of linear code, linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contr ...

* Reed–Solomon error correction
Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.
They have many applications, the most prominent of which include consumer technologies such as MiniDisc
Mini ...

* IPv4 header checksum
Hash functions
* List of hash functions
* Luhn algorithm
The Luhn algorithm or Luhn formula, also known as the "modular arithmetic, modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple checksum formula used to validate a variety of identification numbers, ...

* 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 detection and correction, error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, ...

* Rolling checksum
* Verhoeff algorithm
File systems
* ZFS – a file system that performs automatic file integrity checking using checksums
Related concepts
*Isopsephy Isopsephy (; ''isos'' meaning "equal" and ''psephos'' meaning "pebble") or isopsephism is the practice of adding up the Greek numerals, number values of the letters in a word to form a single number. The total number is then used as a metaphorical ...

*Gematria
Gematria (; he, גמטריא or gimatria , plural or , ''gimatriot'') is the practice of assigning a number, numerical value to a name, word or phrase according to an alphanumerical cipher. A single word can yield several values depending on the ...

*File fixity File fixity is a digital preservation term referring to the property of a digital file being fixed, or unchanged. Fixity checking is the process of verifying that a digital object has not been altered or corrupted. During transfer, a repository may ...

References

External links

{{wikibooks , 1= Algorithm Implementation , 2= ChecksumsAdditive Checksums (C)

theory from Barr Group

Checksum Calculator

Open source python based application with GUI used to verify downloads.