Page "Cryptographic hash function" Paragraph 21

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 n < sup > 20 </ sup > steps for n-digit keys ) may be too slow for any practical use.