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Fully Homomorphic Encryption

Author(s):

B. P. Van Parys
Conference/Journal:

Abstract:

In 2009 Gentry came up with the first construction of a fully homomorphic encryption scheme based on ideal lattices, hereby ending the nearly 40 year old quest of finding such scheme. Since then a number of fully homomorphic encryption schemes were constructed. However, a comparison of these constructions has never been conducted. Hence, the primary objective of this thesis is to give a fair comparison between the proposed schemes. More in particular, we compare the 2 fundamental schemes: the Smart-Vercauteren scheme and the DGHV scheme. The Smart-Vercauteren scheme is a concrete instance of the original Gentry schema, described in terms of number fields. The DGHV variant is a scheme that is based only on integers, and hence is conceptually very simple. The conducted timings suggest that the Smart-Vercauteren scheme is considerable faster then the DGHV scheme, this in contrast with what is suggested in literature. The SIMD variant is a fully homomorphic encryption scheme that supports SIMD operations. This scheme is a natural extension of the idea behind the Smart- Vercauteren scheme. Also this scheme is compared to both the Smart-Vercauteren and the DGHV scheme; whereby we consider 3 different methods for recrypting messages. We also suggest a new recryption method, which is very performant when the needed level of parallelization is high. Also in terms of memory usage this method seems to be very competitive. Finally we note that even the most performant scheme proposed in literature can hardly be called practically feasible. Hence we suggest a practical scheme that, using 2 trusted servers, can be considered practically feasible. It should be noted however that this comes at the expense of extra security assumptions.

Year:

2011
Type of Publication:

(12)Diploma/Master Thesis
Supervisor:

B. Preneel

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2011:IFA_4067
}
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