On Bounding Problems of Quantitative Information Flow

Abstract. 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 boo...

• Type: Conference
• Year: 2010
• Where: ESORICS
• Authors: Hirotoshi Yasuoka, Tachio Terauchi
• Keywords: ESORICS 2010, Information Theoretic Notions, Quantitative Information Flow, Security Privacy, Shannon Entropy