## Quantifying computational security subject to source constraints, guesswork and inscrutability

##### Author(s)

Beirami, Ahmad; Calderbank, Robert; Duffy, Ken; Medard, Muriel
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Show full item record##### Abstract

Guesswork forms the mathematical framework for quantifying computational security subject to brute-force determination by query. In this paper, we consider guesswork subject to a per-symbol Shannon entropy budget. We introduce inscrutability rate to quantify the asymptotic difficulty of guessing
U out of V secret strings drawn from the string-source and prove that the inscrutability rate of any string-source supported on a finite alphabet X , if it exists, lies between the per-symbol Shannon entropy constraint and log |X|. We show that for a stationary string-source, the inscrutability rate of guessing any fraction (1 - ε) of the V strings for any fixed ε > 0, as V grows, approaches the per-symbol Shannon entropy constraint (which is equal to the Shannon entropy rate for the stationary string-source). This corresponds to the minimum inscrutability rate among all string-sources with the same per-symbol Shannon entropy. We further prove that the inscrutability rate of any finite-order Markov string-source with hidden statistics remains the same as the unhidden case, i.e., the asymptotic value of hiding the statistics per each symbol is vanishing. On the other hand, we show that there exists a string-source that achieves the upper limit on the inscrutability rate, i.e., log |X|, under the same Shannon entropy budget.
Index Terms—Brute-force attack; Guesswork; Inscrutability;
Renyi entropy; Universal methods; Large deviations

##### Date issued

2016-06##### Department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science##### Journal

2015 IEEE International Symposium on Information Theory (ISIT)

##### Publisher

Institute of Electrical and Electronics Engineers (IEEE)

##### Citation

Beirami, Ahmad, et al. "Quantifying Computational Security Subject to Source Constraints, Guesswork and Inscrutability." 2015 IEEE International Symposium on Information Theory (ISIT), 14-19 June, 2015, Hong Kong, China, IEEE, 2015, pp. 2757–61.

Version: Original manuscript

##### ISBN

978-1-4673-7704-1