Fletcher's checksum
Overview
Fletcher's checksum is a type of checksum algorithm that is used to validate the integrity of data. Named after its inventor, John G. Fletcher of NASA's Goddard Space Flight Center, it was designed to be a more reliable alternative to the traditional checksum methods used in data transmission and storage.
History
Fletcher's checksum was developed in the late 20th century as a response to the need for more reliable data integrity checks. Traditional checksum methods, such as the simple modulo sum, were found to be lacking in their ability to detect certain types of errors, particularly those involving the transposition or alteration of bits within the data.
John G. Fletcher, a computer scientist at NASA's Goddard Space Flight Center, proposed the Fletcher's checksum as a superior alternative. The algorithm was quickly adopted in various fields, including telecommunications, computer networking, and data storage, due to its improved error-detection capabilities.
Algorithm
The Fletcher's checksum algorithm operates by summing the data in a two-step process. The first step involves adding up all the bytes of data, with the total being stored in a variable often referred to as the "sum1". The second step involves adding up the results of the first step, with the total being stored in a second variable, "sum2". The final checksum is then computed by concatenating the two sums.
The algorithm can be expressed in pseudocode as follows:
``` function Fletcher's_Checksum(data)
sum1 = 0 sum2 = 0
for each byte in data sum1 = (sum1 + byte) mod 255 sum2 = (sum2 + sum1) mod 255 end
return (sum2 << 8) | sum1
end ```
This pseudocode demonstrates the basic operation of the Fletcher's checksum algorithm. However, in practice, the algorithm may be implemented in a variety of ways, depending on the specific requirements of the system in which it is being used.
Error Detection Capabilities
Fletcher's checksum offers improved error detection capabilities over traditional checksum methods. Specifically, it is able to detect all single-bit errors and almost all two-bit errors. It can also detect most larger errors, including those involving the transposition of bits within the data.
However, like all checksum algorithms, Fletcher's checksum is not infallible. It is possible for different sets of data to produce the same checksum, a situation known as a "collision". While collisions are rare, they can lead to undetected errors in the data.
Applications
Fletcher's checksum is widely used in a variety of applications, including telecommunications, computer networking, and data storage. It is often used in protocols that require a reliable means of verifying the integrity of data, such as the Internet Protocol (IP) and the User Datagram Protocol (UDP).
In addition to its use in data transmission and storage, Fletcher's checksum is also used in certain types of error detection and correction systems. For example, it may be used in Reed–Solomon error correction schemes to detect and correct errors in data.