# Estimate password cracking time given Shannon Entropy

Is there some algorithm that, given the Shannon entropy of a string, compute an estimation of the time that an average home computer will take to crack the password? Thank you.

• What's the "string"? Is it the password, the plain or cipher text? – Paul Uszak Oct 15 '19 at 11:40
• @PaulUszak the string is the password. – Yamar69 Oct 15 '19 at 11:56

In particular, the direct use of Shannon entropy can give misleading results, and the best case brute force number of guesses can be much lower than that implied by shannon entropy (say $$H_0$$ bits, should imply roughly $$2^{H_0}$$ guesses in the worst case.
$$2^{𝐻_{1/2}(𝑋)−1}$$ and lowerbounded by $$\frac{2^{𝐻_{1/2}}(𝑋)−1}{\log |X|}$$ where $$H_{1/2}(X)$$ is the Renyi entropy. In general Renyi entropy can be much lower than Shannon entropy, hence Shannon gives a misleading result for this problem. See the answers to this question for details and references.