Guesswork, large deviations and Shannon entropy

Christiansen, Mark M. and Duffy, Ken R. (2013) Guesswork, large deviations and Shannon entropy. IEEE Transactions on Information Theory, 59 (2). pp. 796-802. ISSN 0018-9448

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How hard is it to guess a password? Massey showed that a simple function of the Shannon entropy of the distribution from which the password is selected is a lower bound on the expected number of guesses, but one which is not tight in general. In a series of subsequent papers under ever less restrictive stochastic assumptions, an asymptotic relationship as password length grows between scaled moments of the guesswork and specific R´enyi entropy was identified. Here we show that, when appropriately scaled, as the password length grows the logarithm of the guesswork satisfies a Large Deviation Principle (LDP), providing direct estimates of the guesswork distribution when passwords are long. The rate function governing the LDP possesses a specific, restrictive form that encapsulates underlying structure in the nature of guesswork. Returning to Massey’s original observation, a corollary to the LDP shows that expectation of the logarithm of the guesswork is the specific Shannon entropy of the password selection process.

Item Type: Article
Additional Information: This is the preprint version of the published article, which is available at DOI: 10.1109/TIT.2012.2219036
Keywords: Guesswork; Renyi Entropy; Shannon Entropy; Large Deviations;
Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID: 6219
Identification Number: 10.1109/TIT.2012.2219036
Depositing User: Dr Ken Duffy
Date Deposited: 29 Jun 2015 14:41
Journal or Publication Title: IEEE Transactions on Information Theory
Publisher: IEEE
Refereed: Yes

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