2017
DOI: 10.1007/978-3-319-70972-7_29
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Faster Homomorphic Evaluation of Discrete Fourier Transforms

Abstract: Abstract. We present a methodology to achieve low latency homomorphic operations on approximations to complex numbers, by encoding a complex number as an evaluation of a polynomial at a root of unity. We then use this encoding to evaluate a Discrete Fourier Transform (DFT) on data which has been encrypted using a Somewhat Homomorphic Encryption (SHE) scheme, with up to three orders of magnitude improvement in latency over previous methods. We are also able to deal with much larger input sizes than previous met… Show more

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Cited by 15 publications
(22 citation statements)
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“…Example 2. In the case of the 2-power cyclotomic polynomial f pXq " X 2 k`1 , the above map replaces negative powers X´j by´X d´j , which coincides with the approach from [14]: when expressed in terms of the basis 1, X, X 2 , . .…”
Section: Encodingmentioning
confidence: 77%
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“…Example 2. In the case of the 2-power cyclotomic polynomial f pXq " X 2 k`1 , the above map replaces negative powers X´j by´X d´j , which coincides with the approach from [14]: when expressed in terms of the basis 1, X, X 2 , . .…”
Section: Encodingmentioning
confidence: 77%
“…, b´1u is used in practice, such as binary b " 2 or ternary b " 3. For use in SHE schemes, several variations [17,14,12,3] have been proposed. For the purposes of this paper we mention the non-integral base non-adjacent form (NIBNAF) from [3] which is a very sparse expansion w.r.t.…”
Section: Laurent Polynomialsmentioning
confidence: 99%
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“…Since the publication of Gentry's seminal work [15], this research area has evolved rapidly and is on the verge of reaching a first degree of maturity, as was recently demonstrated e.g. by practical implementations of privacy-enhanced electricity load forecasting [2,4], digital image processing [1,10], and medical data management [8,12,17]. Most of the current focus lies on somewhat homomorphic encryption (SHE), where the schemes are capable of homomorphically evaluating an arithmetic circuit having a certain predetermined computational depth.…”
Section: Introductionmentioning
confidence: 99%