On bounding problems of quantitative information flow

Hirotoshi Yasuoka*, Tachio Terauchi

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Citations (Scopus)


Researchers have proposed formal definitions of quantitative information flow based on information theoretic notions such as the Shannon entropy, the min entropy, the guessing entropy, and channel capacity. This paper investigates the hardness of precisely checking the quantitative information flow of a program according to such definitions. More precisely, we study the "bounding problem" of quantitative information flow, defined as follows: Given a program M and a positive real number q, decide if the quantitative information flow of M is less than or equal to q. We prove that the bounding problem is not a k-safety property for any k (even when q is fixed, for the Shannon-entropy-based definition with the uniform distribution), and therefore is not amenable to the self-composition technique that has been successfully applied to checking non-interference. We also prove complexity theoretic hardness results for the case when the program is restricted to loop-free boolean programs. Specifically, we show that the problem is PP-hard for all the definitions, showing a gap with non-interference which is coNP-complete for the same class of programs. The paper also compares the results with the recently proved results on the comparison problems of quantitative information flow.

Original languageEnglish
Title of host publicationComputer Security, ESORICS 2010 - 15th European Symposium on Research in Computer Security, Proceedings
Number of pages16
Publication statusPublished - 2010
Externally publishedYes
Event15th European Symposium on Research in Computer Security, ESORICS 2010 - Athens, Greece
Duration: 2010 Sept 202010 Sept 22

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6345 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other15th European Symposium on Research in Computer Security, ESORICS 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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