On bounding problems of quantitative information flow

Hirotoshi Yasuoka*, Tachio Terauchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 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, belief, 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 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
Pages (from-to)1029-1082
Number of pages54
JournalJournal of Computer Security
Issue number6
Publication statusPublished - 2011
Externally publishedYes


  • Security
  • program verification
  • quantitative information flow

ASJC Scopus subject areas

  • Software
  • Safety, Risk, Reliability and Quality
  • Hardware and Architecture
  • Computer Networks and Communications


Dive into the research topics of 'On bounding problems of quantitative information flow'. Together they form a unique fingerprint.

Cite this