Extending the definition of guesswork

To be able to perform an analytical and more exact description of security, quantitative security measures are desirable. In this paper, we continue our investigation of the quantitative security measure guesswork, which gives the average number of guesses in an optimal brute force attack. The definition of guesswork is extended to joint and conditional guesswork. We show that joint guesswork is always at least equal to the marginal guessworks, and that conditioning reduces guesswork. Hence, guesswork possesses the same two properties as entropy, i.e., joint entropy is always at least equal to the marginal entropies, and conditioning reduces entropy. However, unlike entropy, guesswork does not possess the chain rule property. For entropy, this rule states that joint entropy is equal to marginal entropy plus the corresponding conditional entropy.