Guesswork Subject to a Total Entropy Budget
Name
1712.09082.pdf
Description
Submitted version
Size
489.75 KB
Format
Adobe PDF
Checksum (MD5)
4ab4c2d47944d4bcf15fc7a1a6732601
Author(s)
Rezaee, Arman
Beirami, Ahmad
Makhdoumi, Ali
Medard, Muriel
Duffy, Ken
Date Issued
October 2017
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Rezaee, Arman, Beirami, Ahmad, Makhdoumi, Ali, Medard, Muriel and Duffy, Ken. 2017. "Guesswork Subject to a Total Entropy Budget."
Version
Original manuscript
Abstract
© 2017 IEEE. We consider an abstraction of computational security in password protected systems where a user draws a secret string of given length with i.i.d. characters from a finite alphabet, and an adversary would like to identify the secret string by querying, or guessing, the identity of the string. The concept of a 'total entropy budget' on the chosen word by the user is natural, otherwise the chosen password would have arbitrary length and complexity. One intuitively expects that a password chosen from the uniform distribution is more secure. This is not the case, however, if we are considering only the average guesswork of the adversary when the user is subject to a total entropy budget. The optimality of the uniform distribution for the user's secret string holds when we have also a budget on the guessing adversary. We suppose that the user is subject to a 'total entropy budget' for choosing the secret string, whereas the computational capability of the adversary is determined by his 'total guesswork budget.' We study the regime where the adversary's chances are exponentially small in guessing the secret string chosen subject to a total entropy budget. We introduce a certain notion of uniformity and show that a more uniform source will provide better protection against the adversary in terms of his chances of success in guessing the secret string. In contrast, the average number of queries that it takes the adversary to identify the secret string is smaller for the more uniform secret string subject to the same total entropy budget.
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/allerton.2017.8262848
