A checksum is a form of redundancy check, a simple way to protect the integrity of data by detecting errors in data that are sent through space (telecommunications) or time (storage). It works by adding up the basic components of a message, typically the asserted bits, and storing the resulting value. Anyone can later perform the same operation on the data, compare the result to the authentic checksum, and (assuming that the sums match) conclude that the message was probably not corrupted. In telecommunication, a redundancy check is extra data added to a message for the purposes of error detection and error correction. ... In computer science and information theory, error correction consists of using methods to detect and/or correct errors in the transmission or storage of data by the use of some amount of redundant data and (in the case of transmission) the selective retransmission of incorrect segments of the data. ... Copy of the original phone of Alexander Graham Bell at the Musée des Arts et Métiers in Paris Telecommunication is the transmission of signals over a distance for the purpose of communication. ... This article or section does not cite any references or sources. ... This article is about the unit of information. ...

An example of a simple checksum:

• Given 4 bytes of data (can be done with any number of bytes): 25h, 62h, 3Fh, 52h
• Step 1: Adding all bytes together gives 118h.
• Step 2: Drop the Carry Nibble to give you 18h.
• Step 3: Get the two's complement of the 18h to get E8h. This is the checksum byte.
• To Test the Checksum byte simply add it to the original group of bytes. This should give you 100h.
• Drop the carry nibble again giving 00h. Since it is 00h this means the bytes were probably not changed.

The simplest form of checksum, which simply adds up the asserted bits in the data, cannot detect a number of types of errors. Such a checksum, for example, is not changed by: A nibble (or less commonly but more accurately, nybble) is the computing term for a four-bit aggregation, or half an octet (an octet being an 8-bit byte). ... The twos complement of a binary number is the value obtained by subtracting the number from a large power of two (specifically, from 2N for an N-bit twos complement). ...

• reordering of the bytes in the message
• inserting or deleting zero-valued bytes
• multiple errors which sum to zero

More sophisticated types of redundancy check, including Fletcher's checksum, Adler-32, and cyclic redundancy checks (CRCs), are designed to address these weaknesses by considering not only the value of each byte but also its position. The cost of the ability to detect more types of errors is the increased complexity of computing the redundancy check value. Fletchers checksum is one of several types of checksum algorithms, which are relatively simple processes used by computers to check the integrity of data. ... Adler-32 is a checksum algorithm which was invented by Mark Adler. ... A cyclic redundancy check (CRC) is a type of function that takes as input a data stream of any length and produces as output a value of a certain fixed size. ... Complexity in general usage is the opposite of simplicity. ...

These types of redundancy check are useful in detecting accidental modification such as corruption to stored data or errors in a communication channel. However, they provide no security against a malicious agent as their simple mathematical structure makes them trivial to circumvent. To provide this level of integrity, the use of a cryptographic hash function, such as SHA-256, is necessary. (Collisions have been found in the popular MD5 algorithm and finding collisions in SHA-1 seems possible, but there is no evidence as of 2006 that SHA-256 suffers similar weaknesses.) In mathematics, a structure on a set is some additional mathematical objects that, loosely speaking, attach to the set, making it easier to visualize or work with. ... In cryptography, a cryptographic hash function is a hash function with certain additional security properties to make it suitable for use as a primitive in various information security applications, such as authentication and message integrity. ... The SHA (Secure Hash Algorithm) family is a set of related cryptographic hash functions designed by the National Security Agency (NSA) and published by the National Institute of Standards and Technology (NIST). ... In cryptography, MD5 (Message-Digest algorithm 5) is a widely used cryptographic hash function with a 128-bit hash value. ... The SHA (Secure Hash Algorithm) family is a set of related cryptographic hash functions designed by the National Security Agency (NSA) and published by the National Institute of Standards and Technology (NIST). ... 2006 is a common year starting on Sunday of the Gregorian calendar. ...

On Unix, there is a tool called "cksum" that generates both a 32 bit CRC and a byte count for any given input file. Filiation of Unix and Unix-like systems Unix (officially trademarked as UNIX®) is a computer operating system originally developed in the 1960s and 1970s by a group of AT&T employees at Bell Labs including Ken Thompson, Dennis Ritchie and Douglas McIlroy. ... Cksum is a POSIX command that reads the files specified by the File parameter and calculates a checksum, cyclic redundancy check (CRC) and the byte count for a file or files. ...

See also

• Check digit
• file verification
• Hamming code
• Integrity check value
• List of checksum algorithms
• Luhn algorithm
• Parity bit

A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. ... File verification means that an algorithm is used to verify the integrity or authenticity of a file. ... In telecommunication, a Hamming code is a linear error-correcting code named after its inventor, Richard Hamming. ... There are very few or no other articles that link to this one. ... This is a list of checksum algorithms. ... The Luhn algorithm or Luhn formula, also known as the modulus 10 or mod 10 algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers. ... A parity bit is a binary digit that indicates whether the number of bits with value of one in a given set of bits is even or odd. ...

External links

• Additive Checksum Algorithms as Error Detection Codes