Scheduled System Maintenance:
On Monday, April 27th, IEEE Xplore will undergo scheduled maintenance from 1:00 PM - 3:00 PM ET (17:00 - 19:00 UTC). No interruption in service is anticipated.
By Topic

Guesswork, Large Deviations, and Shannon Entropy

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Christiansen, M.M. ; Hamilton Inst., Nat. Univ. of Ireland, Maynooth, Ireland ; Duffy, K.R.

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 Rényi 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 2 )