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...ent improvements have been made, for example authors have proposed new variants, improved efficiency, suggested other hardness assumptions, etc. Some of these works were accompanied by implementation =-=[19, 10, 6, 20, 14, 7]-=-, but all the implementations so far were either “proofs of concept” that can compute only one basic operation at a time (at great cost), or special-purpose implementations limited to evaluating very ...

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...r verifying computations [4]. Also, Gentry’s fully homomorphic encryption [27] has engendered protocols for verifiable non-interactive computation [20, 24, 26]. However, despite striking improvements =-=[28, 42, 47]-=-, the costs of hiding inputs (among other expenses) prevent any of the aforementioned verified computation schemes from getting close to practical (even by our relaxed standards). PCPs, argument syste...

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...ile researchers are trying to reduce the complexity of FHE, it is worthwhile to consider alleviating the power of FHE to regain efficiency. Naehrig et al. has proposed somewhat homomorphic encryption =-=[98]-=-, which only supports a number of homomorphic operations, which may be much faster and more compact than FHE. Pearson et al. ([42] and [43]) propose privacy manager (D2.5.2) that relies on obfuscation...

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...ltiplication operations executed upon ciphertexts was limited until Gentry et al. proposed a fully homomorphic encryption scheme [11] and implemented it in [12]. However, Lauter et al. pointed out in =-=[16]-=- that the complexity of general HE is too high to use in real application. Lauter also proposed a HE scheme which sacrificed possible number of multiplications for speed, but it still needs too much t...

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...(FHE). PHE supports constant number of additions and multiplications, and FHE supports unlimited additions and multiplications but it is much less efficient than PHE. As discussed by Lauter et al. in =-=[22]-=-, the decryption time of FHE system is too high to be used in a real application, and in most of cases one only needs a few number of multiplications or additions. Therefore, Pallier’s system, which i...

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...it is E · c(λ) n where c(λ) is a constant that depends on the security parameter. As to whether any of these proposals is really practical, the answer is simply “no”. There have been several attempts =-=[18, 10, 19, 16, 11]-=- at implementing most of the schemes mentioned, but none of them comes even close to being practical. The most recent paper [11] manages to execute one AES encryption homomorphically in eight days usi...

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...FHE) [2], which eschews the requirement of two non-colluding parties. Linear regression performs a large number of both multiplication and addition steps. In such a setting, current FHE schemes [35], =-=[50]-=- are not as efficient as our system. Lauter et al. [50] mention using FHE for regression, but do not quantify performance. Also as demonstrated in Section VI-E, we can reduce the execution time in Gra...

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... high level (F 2 8) algebraic structures, allow us to evaluate complex operations relatively easily. Evaluation of AES circuits using FHE operations has been mentioned as a possible usage scenario in =-=[13]-=-. The second example, one of database lookup, provides an example of how data can be searched using SIMD style operations more efficiently than using the bit-wise homomorphic operations envisaged in [...