11.6 MAC versus CRC
Can we construct a MAC without a cryptographic hash function and without a secret key? Let’s take a look at the Cyclic Redundancy Check (CRC), which is popular error-detecting code used in communication systems to detect accidental errors in messages sent over a noisy or unreliable communication channel.
The working principle of error-detecting code is for the sender to encode their plaintext message in a redundant way. The redundancy, in turn, allows the receiver to detect a certain number of errors – that is, accidental bit flips – in the message they receive. The theory of channel coding, pioneered in the 1940s by the American mathematician Richard Hamming, aims to find code that has minimal overhead (that is, the least redundancy) but, at the same time, has a large number of valid code words and can correct or detect many errors.
CRC is so-called cyclic code, that is, a block code where a circular shift of every code word yields another valid...
