Abstract
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 \(O(\log m)\) is able to evaluate a simple pointer analysis with \(O(\log m)\) 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.
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- 1.
For simplicity, we assume that the plaintext space is \({\mathbb Z}_2=\{0,1\}\), but extension to larger plaintext space is immediate.
- 2.
AND and XOR gates are sufficient to simulate all binary circuits.
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Acknowledgment
The authors would like to thank the anonymous reviewers for their valuable comments. The first and third authors were supported by the Engineering Research Center of Excellence Program of Korea Ministry of Science, ICT & Future Planning(MSIP) / National Research Foundation of Korea(NRF) (Grant NRF-2008–0062609), and Samsung Electronics Software R&D Center (No. 0421–20140012). The second and last authors were supported by Samsung Electronics Software R&D Center (No. 0421–20140013).
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Lee, W., Hong, H., Yi, K., Cheon, J.H. (2015). Static Analysis with Set-Closure in Secrecy. In: Blazy, S., Jensen, T. (eds) Static Analysis. SAS 2015. Lecture Notes in Computer Science(), vol 9291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48288-9_2
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DOI: https://doi.org/10.1007/978-3-662-48288-9_2
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