Static Analysis with Set-Closure in Secrecy

• Published in: Static Analysis Vol. 9291; pp. 18 - 35
• Main Authors: Lee, Woosuk, Hong, Hyunsook, Yi, Kwangkeun, Cheon, Jung Hee
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2015; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Ciphertext Packing; Computer programming / software development; HE Scheme; Program Owner; Programming & scripting languages: general; Software Engineering; Somewhat Homomorphic Encryption (SWHE); SWHE Schemes
• ISBN: 9783662482872; 3662482878
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-662-48288-9_2

We report that the homomorphic encryption scheme can unleash the possibility of static analysis of encrypted programs. Static analysis in cipher-world is desirable in the static-analysis-as-a-service setting, because it allows the program owners to encrypt and upload their programs to the static analysis service while the service provider can still analyze the encrypted programs without decrypting them. Only the owner of the decryption key (the program owner) is able to decrypt the analysis result. As a concrete example, we describe how to perform a pointer analysis in secrecy. In our method, a somewhat homomorphic encryption scheme of depth O(logm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\log m)$$\end{document} is able to evaluate a simple pointer analysis with O(logm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\log m)$$\end{document} homomorphic matrix multiplications, for the number m of pointer variables when the maximal pointer level is bounded. We also demonstrate the viability of our method by implementing the pointer analysis in secrecy.