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On the CCA-1 security of somewhat homomorphic encryption over the integers. (English) Zbl 1291.94176
Ryan, Mark D. (ed.) et al., Information security practice and experience. 8th international conference, ISPEC 2012, Hangzhou, China, April 9–12, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-29100-5/pbk). Lecture Notes in Computer Science 7232, 353-368 (2012).
Summary: The notion of fully homomorphic encryption is very important since it enables many important applications, such as the cloud computing scenario. In [Advances in cryptology – EUROCRYPT 2010. 29th annual international conference on the theory and applications of cryptographic techniques. Lect. Notes Comput. Sci. 6110, 24-43 (2010; Zbl 1279.94130)] M. van Dijk et al. proposed an interesting fully homomorphic encryption scheme based on a somewhat homomorphic encryption scheme using integers. In this paper, we demonstrate a very practical CCA-1 attack against this somewhat homomorphic encryption scheme. Given a decryption oracle, we show that within $$O(\lambda ^{2})$$ queries, we can recover the secret key successfully, where $$\lambda$$ is the security parameter for the system.
For the entire collection see [Zbl 1239.68010].

##### MSC:
 94A60 Cryptography 68P25 Data encryption (aspects in computer science)
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