The more I work in cryptography, the more I see the cross-over into areas of data communications. For example, in post quantum key exchange, we see the usage of the McEliece method, and which uses data coding methods for its implementation. Also, lattice methods use polynomial representations for its operation. So let’s have a look at some error detection in data communications.
There’s a little method that has been working away in the background and protecting our data like little else. This is CRC: Cyclic Redundancy Check. Overall, it is simple, easy to implement, and effective for most of the typical errors we have in data. With error checking, we can either have error detection or error correction.
For error detection, we are able to detect that there are one or more bits in error in a communication, whereas with error correction, we can not only determine if there are errors in the communication but correct the bits that are in error. Obviously, an error correction code will be larger in size and more complex. But, for most circumstances, we just need to determine if there is an error in our transmission, and request a re-transmission from the send.
The basic idea of a CRC can be illustrated using an example. Suppose the transmitter and receiver were both to agree that the numerical value sent by the transmitter would always be divisible by 9. Then, should the…
