Checksum algorithms

( 30th July 2019 )

Checksum algorithms, such as CRC32 and other cyclic redundancy checks, are designed to meet much weaker requirements, and are generally unsuitable as cryptographic hash functions. For example, a CRC was used for message integrity in the WEP encryption standard, but an attack was readily discovered which exploited the linearity of the checksum.

Degree of difficulty

In cryptographic practice, "difficult" generally means "almost certainly beyond the reach of any adversary who must be prevented from breaking the system for as long as the security of the system is deemed important". The meaning of the term is therefore somewhat dependent on the application since the effort that a malicious agent may put into the task is usually proportional to his expected gain. However, since the needed effort usually multiplies with the digest length, even a thousand-fold advantage in processing power can be neutralized by adding a few dozen bits to the latter.

For messages selected from a limited set of messages, for example passwords or other short messages, it can be feasible to invert a hash by trying all possible messages in the set. Because cryptographic hash functions are typically designed to be computed quickly, special key derivation functions that require greater computing resources have been developed that make such brute force attacks more difficult.

In some theoretical analyses "difficult" has a specific mathematical meaning, such as "not solvable in asymptotic polynomial time". Such interpretations of difficulty are important in the study of provably secure cryptographic hash functions but do not usually have a strong connection to practical security. For example, an exponential time algorithm can sometimes still be fast enough to make a feasible attack. Conversely, a polynomial time algorithm (e.g., one that requires n20 steps for n-digit keys) may be too slow for any practical use.

Illustration

An illustration of the potential use of a cryptographic hash is as follows: Alice poses a tough math problem to Bob and claims she has solved it. Bob would like to try it himself, but would yet like to be sure that Alice is not bluffing. Therefore, Alice writes down her solution, computes its hash and tells Bob the hash value (whilst keeping the solution secret). Then, when Bob comes up with the solution himself a few days later, Alice can prove that she had the solution earlier by revealing it and having Bob hash it and check that it matches the hash value given to him before. (This is an example of a simple commitment scheme; in actual practice, Alice and Bob will often be computer programs, and the secret would be something less easily spoofed than a claimed puzzle solution).