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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.

An example of a simple checksum:

• Given 4 bytes of data (can be done with any number of bytes): 0x25, 0x62, 0x3F, 0x52
• Step 1: Adding all bytes together gives 0x118.
• Step 2: Drop the Carry Nibble to give you 0x18.
• Step 3: Get the two's complement of the 0x18 to get 0xE8. This is the checksum byte.
• To Test the Checksum byte simply add it to the original group of bytes. This should give you 0x100.
• Drop the carry nibble again giving 0x00. Since it is 0x00 this means no error was detected (although an undetectable error could have occurred).

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:

• 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.

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.)

On Unix, there is a tool called "cksum" that generates both a 32-bit CRC and a byte count for any given input file.

• Check digit
• file verification
• Hamming code
• List of checksum algorithms
• Luhn algorithm
• Parity bit
• Frame Check Sequence

• Additive Checksum Algorithms as Error Detection Codes