Hash functions, in general, are mathematical functions that take variable-size input and return a fixed-size output based on the nature of the function.
There are certain characteristics that define and differentiate between cryptographic and regular hash functions.
An ideal cryptographic hash function possesses the following main properties that make them better than regular hash functions:
They're deterministic. For a given input, the function always generates the same hash value.
They're collision-resistant. This means that until now, there are no two inputs that produce the same output hash.
They have an avalanche effect. If cryptographic hash functions are given input that is slightly different from the already present input, it would still produce an entirely different and uncorrelated output.
They're faster. Since it guarantees that all the quality standards are met, it ensures quick computation of hash value from a given input.
They're one-way hash functions. If given a hash value, it is computationally infeasible to produce its input.
Regular hash functions are a poor version of the cryptographic hash function that doesn't ensure all the performance standards. They don't assure collision resistance and produce the same output on certain inputs. That's why chaining was introduced to cater to these collisions. Similarly, they produce an output hash that is sometimes correlated, helping the adversaries to produce more inputs that lead to the same output (by following trends in the output.). This also helps compromise its one-way function property.
However, there are no significant differences between the two. The differences are limited to time constraints. For example, previously, MD5 hash functions were assumed to be cryptographic until it was collision-resistant. When a collision was detected, it was moved under regular hash functions.
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