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Many applications deployed to public clouds are concerned about the confidentiality of their outsourced data, such as financial services and electronic patient records. A plausible solution to this problem is homomorphic encryption (HE), which supports certain algebraic operations directly over the ciphertexts. The downside of HE schemes is their significant, if not prohibitive, performance overhead for data-intensive workloads that are very common for outsourced databases, or database-as-a-serve in cloud computing. The objective of this work is to mitigate the performance overhead incurred by the HE module in outsourced databases. To that end, this paper proposes a radix-based parallel caching optimization for accelerating the performance of homomorphic encryption (HE) of outsourced databases in cloud computing. The key insight of the proposed optimization is caching selected radix-ciphertexts in parallel without violating existing security guarantees of the primitive/base HE scheme. We design the radix HE algorithm and apply it to both batch- and incremental-HE schemes; we demonstrate the security of those radix-based HE schemes by showing that the problem of breaking them can be reduced to the problem of breaking their base HE schemes that are known IND-CPA (i.e. Indistinguishability under Chosen-Plaintext Attack). We implement the radix-based schemes as middleware of a 10-node Cassandra cluster on CloudLab; experiments on six workloads show that the proposed caching can boost state-of-the-art HE schemes, such as Paillier and Symmetria, by up to five orders of magnitude.
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On the Security of Homomorphic Encryption on Approximate Numbers
We present passive attacks against CKKS, the homomorphic encryption scheme for arithmetic on approximate numbers presented at Asiacrypt 2017. The attack is both theoretically efficient (running in expected polynomial time) and very practical, leading to complete key recovery with high probability and very modest running times. We implemented and tested the attack against major open source homomorphic encryption libraries, including HEAAN, SEAL, HElib and PALISADE, and when computing several functions that often arise in applications of the CKKS scheme to machine learning on encrypted data, like mean and variance computations, and approximation of logistic and exponential functions using their Maclaurin series. The attack shows that the traditional formulation of IND-CPA security (or indistinguishability against chosen plaintext attacks) achieved by CKKS does not adequately capture security against passive adversaries when applied to approximate encryption schemes, and that a different, stronger definition is required to evaluate the security of such schemes. We provide a solid theoretical basis for the security evaluation of homomorphic encryption on approximate numbers (against passive attacks) by proposing new definitions, that naturally extend the traditional notion of IND-CPA security to the approximate computation setting. We propose both indistinguishability-based and simulation-based variants, as well as restricted versions of the definitions that limit the order and number of adversarial queries (as may be enforced by some applications). We prove implications and separations among different definitional variants, and discuss possible modifications to CKKS that may serve as a countermeasure to our attacks.
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- Award ID(s):
- 1936703
- PAR ID:
- 10340712
- Editor(s):
- Canteaut, A.; Standaert, F.
- Date Published:
- Journal Name:
- Advances in Cryptology – EUROCRYPT 2021
- Volume:
- LNCS 12696
- Page Range / eLocation ID:
- 648 - 677
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-77870-5_23
