On bounding problems of quantitative information flow

Hirotoshi Yasuoka*, Tachio Terauchi


研究成果: Article査読

15 被引用数 (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.

ジャーナルJournal of Computer Security
出版ステータスPublished - 2011

ASJC Scopus subject areas

  • ソフトウェア
  • 安全性、リスク、信頼性、品質管理
  • ハードウェアとアーキテクチャ
  • コンピュータ ネットワークおよび通信


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