Cryptanalysis of factoring-based fully homomorphic encryption
Pages 80 - 83
Abstract
This paper deals with fully homomorphic cryptosystems exploiting the problem of big integers factoring. We give a short review of them and highlight two main types of such fully homomorphic cryptosystems (FHCs): polynomial-based and matrix-based. The main focus of the discussion is placed on one recently proposed polynomial-based FHC. Its construction is recalled, but mainly we concentrate on security issues. And here our contribution is twofold.
First, we review a known-plaintext attack (KPA) proposed in literature on this FHC. We give the general idea of KPA, the probability of its success and the number of pairs (plaintext, ciphertext) necessary to break the FHC. Second, we discuss how the reviewed KPA may be extended in order to decrease the necessary number of pairs. On a high level the proposed extension of KPA may be applied not only to this concrete FHC, but to all reviewed here FHCs. Our KPA essentially uses non-uniformity of probabilistic distribution over plaintexts to obtain a high probability of success. And instead of missing pairs it requires an additional sequence of ciphertexts produced on the same key.
References
[1]
A. T. Benjamin and C. D. Bennett. The probability of relatively prime polynomials. Mathematics Magazine, pages 196--202, 2007.
[2]
C. Gentry. A fully homomorphic encryption scheme. PhD thesis, Stanford University, 2009.
[3]
A. Kipnis and E. Hibshoosh. Efficient methods for practical fully homomorphic symmetric-key encrypton, randomization and verification. IACR Cryptology ePrint Archive, 2012:637, 2012.
[4]
A. Rostovtsev, A. Bogdanov, and M. Mikhaylov. Secure evaluation of polynomial using privacy ring homomorphisms. IACR Cryptology ePrint Archive, 2011:24, 2011.
[5]
K. Shatilov, V. Boiko, S. Krendelev, D. Anisutina, and A. Sumaneev. Solution for secure private data storage in a cloud. In Computer Science and Information Systems (FedCSIS), 2014 Federated Conference on, pages 885--889. IEEE, 2014.
[6]
A. Trepacheva. Known plaintext attack on a fully homomorphic cryptosystem based on factorization. In Proceedings of 4th Workshop on Current Trends in Cryptology CTCrypt15, 2015.
[7]
A. Trepacheva and L. Babenko. Known plaintexts attack on polynomial based homomorphic encryption. In Proceedings of the 7th International Conference on Security of Information and Networks, page 157. ACM, 2014.
[8]
B. Van der Varden. Algebra (algebra), 1979.
[9]
D. Vizár and S. Vaudenay. Analysis of chosen symmetric homomorphic schemes. In Central European Crypto Conference, number EPFL-CONF-198992, 2014.
[10]
L. Xiao, O. Bastani, and I.-L. Yen. An efficient homomorphic encryption protocol for multi-user systems. IACR Cryptology ePrint Archive, 2012:193, 2012.
[11]
A. Zhirov, O. Zhirova, and S. F. Krendelev. Practical fully homomorphic encryption over polynomial quotient rings. In Internet Security (WorldCIS), 2013 World Congress on, pages 70--75. IEEE, 2013.
Index Terms
- Cryptanalysis of factoring-based fully homomorphic encryption
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Information & Contributors
Information
Published In
September 2015
350 pages
ISBN:9781450334532
DOI:10.1145/2799979
- Conference Chairs:
- Oleg Makarevich,
- Ron Poet,
- Atilla Elçi,
- Manoj Singh Gaur,
- Mehmet Orgun,
- Program Chairs:
- Ludmila Babenko,
- Sadek Ferdous,
- Anthony T. S. Ho,
- Vijay Laxmi,
- Josef Pieprzyk
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 08 September 2015
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SIN '15
SIN '15: The 8th International Conference on Security of Information and Networks
September 8 - 10, 2015
Sochi, Russia
Acceptance Rates
SIN '15 Paper Acceptance Rate 34 of 92 submissions, 37%;
Overall Acceptance Rate 102 of 289 submissions, 35%
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