Information leakage of boolean functions and its relationship to other cryptographic criteria

Authors:
M. Zhang;S. E. Tavares;L. L. Campbell
Affiliations:
Depamnent of Electrical and Computer Engineering, Queen's University at Kingston, Ontario, Canada K7L 3N6;Depamnent of Electrical and Computer Engineering, Queen's University at Kingston, Ontario, Canada K7L 3N6;Department of Mathematics and Statistics, Queen's University at Kingston, Ontario, Canada K7L 3N6
Venue:
CCS '94 Proceedings of the 2nd ACM Conference on Computer and communications security
Year:
1994

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Abstract

This paper presents some results on the cryptographic strength of Boolean functions from the information theoretic point of view. It is argued that a Boolean function is resistant to statistical analysis if there is no significant static and dynamic information leakage between its inputs and its output(s). In particular we relate information leakage to nonlinearity, higher order SAC, correlation immunity and resilient functions. It is shown that reducing information leakage increases resistance to the differential attack and the linear attack. We note that some conventional cryptographic criteria require zero static or dynamic information leakage in only one domain. Such a requirement can result in a large information leakage in another domain. To avoid this weakness, it is better to jointly constrain all kinds of information leakage in the function. In fact, we claim that information leakage can be used as a fundamental measure of the strength of a cryptographic algorithm.