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Homomorphic Evaluation Requires Depth [chapter]

Andrej Bogdanov, Chin Ho Lee
2015 Lecture Notes in Computer Science  
size and constant depth, i.e., in the class AC 0 .  ...  We view this as evidence that homomorphic evaluation is inherently more complex than basic operations in encryption schemes.  ...  requires depth Theorem 3.1.  ... 
doi:10.1007/978-3-662-49096-9_15 fatcat:mxxmtxtkp5clzp3eokupmjnvkq

Verifiable Delegation of Computation through Fully Homomorphic Encryption

Alpana Vijay, Vijay Kumar Sharma
2014 International Journal of Computer Applications  
Since it is mostly used by lightweight devices, so mechanisms are required to verify the results of computations efficiently.  ...  In this paper protocols for VDoC are discussed, which focus on verification of aspects of computation other than the results, namely depth and complexity of delegated function which are useful when a user  ...  Eval -The homomorphic evaluation algorithm evaluates the result of a computation f on ciphertexts c 1 , c2,…, c l using evaluation key ek and/or public key pk.  ... 
doi:10.5120/17087-7544 fatcat:zdty72bpmbbuzeffz4pm62q5gm

Quantum Homomorphic Encryption for Circuits of Low T-gate Complexity [chapter]

Anne Broadbent, Stacey Jeffery
2015 Lecture Notes in Computer Science  
key of length given by a polynomial of degree exponential in the circuit's T-gate depth, yielding a homomorphic scheme for quantum circuits with constant T-depth.  ...  procedure whose complexity scales with the square of the number of T-gates (compared with a trivial scheme in which the complexity scales with the total number of gates); the second scheme uses a quantum evaluation  ...  , yielding a homomorphic scheme that is efficient for quantum circuits with constant T-depth.  ... 
doi:10.1007/978-3-662-48000-7_30 fatcat:wsf2x4neurelndt52xvfgrhtcy

Homomorphic Computation of Edit Distance [chapter]

Jung Hee Cheon, Miran Kim, Kristin Lauter
2015 Lecture Notes in Computer Science  
More precisely, given two encrypted sequences of lengths n and m, we show that a somewhat homomorphic scheme of depth O((n + m) log log(n + m)) can evaluate the edit distance algorithm in O(nm log(n +  ...  m)) homomorphic computations.  ...  Then one can evaluate these circuits homomorphically with a SWHE scheme of depth (log(µ − 1) + 2).  ... 
doi:10.1007/978-3-662-48051-9_15 fatcat:vyi4bqayevc6zdro55pzbjhwpa

New packing method in somewhat homomorphic encryption and its applications

Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Kazuhiro Yokoyama, Takeshi Koshiba
2015 Security and Communication Networks  
We relate the homomorphic evaluation algorithms and binary operations on the set C of ciphertexts, and investigate what makes the depth-specific description is enough for a somewhat homomorphic encryption  ...  We conclude that it is sufficient to have C with a ring-like structure with respect to the evaluation algorithms for a somewhat homomorphic encryption with relatively small depth.  ...  We relate the requirements of homomorphic evaluations on ciphertexts with properties of binary operations on the set of integers Z.  ... 
doi:10.1002/sec.1164 fatcat:3ssyoyflcrf2jeouvdgnoau3wm

Accelerating Homomorphic Encryption using Approximate Computing Techniques

Shabnam Khanna, Ciara Rafferty
2020 Proceedings of the 17th International Joint Conference on e-Business and Telecommunications  
The higher power terms which require the extra depth are replaced with the highest powered term of a lower depth.  ...  These works do not take the same explicit approach of replacing the terms requiring higher depth calculations with those requiring lower depth calculations as in this research, however the principle of  ... 
doi:10.5220/0009828803800387 dblp:conf/icete/KhannaR20 fatcat:oycsjlciv5bo7ewxq2plo4kf4q

Exploring the Application of Homomorphic Encryption to a Cross Domain Solution

Cody Tinker, Kevin Millar, Alan Kaminsky, Michael Kurdziel, Marcin Lukowiak, Stanislaw Radziszowski
2019 MILCOM 2019 - 2019 IEEE Military Communications Conference (MILCOM)  
The full evaluation of the comparison circuit requires 5 layers of multiplicative depth.  ...  It features large circuit depth evaluation and optimized operations to compensate but it requires large scale implementations due to such requirements like its large keys.  ...  One such configuration removes the SIMON decryption circuit to significantly decrease the amount of work required to process the encrypted data.  ... 
doi:10.1109/milcom47813.2019.9021015 dblp:conf/milcom/TinkerMKKLR19 fatcat:bl7lqxfxhbbk7p565eoawahbpu

CHET: Compiler and Runtime for Homomorphic Evaluation of Tensor Programs [article]

Roshan Dathathri, Olli Saarikivi, Hao Chen, Kim Laine, Kristin Lauter, Saeed Maleki, Madanlal Musuvathi, Todd Mytkowicz
2018 arXiv   pre-print
Fully Homomorphic Encryption (FHE) refers to a set of encryption schemes that allow computations to be applied directly on encrypted data without requiring a secret key.  ...  This paper demonstrates the capabilities of HISA by building an end-to-end software stack for evaluating neural network models on encrypted data.  ...  This requires increasing space to store the intermediate results, and the required encryption parameters becomes exponential in the multiplicative depth of the circuit, which makes deep circuit evaluations  ... 
arXiv:1810.00845v1 fatcat:txi35axewrhoziiw365m32iofa

Depth Optimized Efficient Homomorphic Sorting [chapter]

Gizem S. Çetin, Yarkın Doröz, Berk Sunar, Erkay Savaş
2015 Lecture Notes in Computer Science  
The reduced depth allows much reduced noise growth and thereby makes it possible to select smaller parameter sizes in somewhat homomorphic encryption instantiations resulting in greater efficiency savings  ...  The technique is obtained by focusing on the multiplicative depth of the sorting circuit alongside the more traditional metrics such as number of comparisons and number of iterations.  ...  As far as homomorphic evaluation is concerned we have another requirement.  ... 
doi:10.1007/978-3-319-22174-8_4 fatcat:fnq2bweewfddnoyblk7d6tsf4y

Bootstrapping BGV ciphertexts with a wider choice of p and q

Emmanuela Orsini, Joop van de Pol, Nigel P. Smart
2016 IET Information Security  
Given an encryption of the secret key, bootstrapping consists in evaluating the above decryption formula homomorphically.  ...  Prior "efficient" methods such as that of Gentry et al (PKC 2012) required a ciphertext modulus q which was close to a power of the plaintext modulus p.  ...  This requires log 2 p · M homomorphic multiplications and depth log 2 p .  ... 
doi:10.1049/iet-ifs.2015.0505 fatcat:dkqi5uw4uvgs3ac7aoesgdajde

PrivFT: Private and Fast Text Classification with Homomorphic Encryption [article]

Ahmad Al Badawi, Luong Hoang, Chan Fook Mun, Kim Laine, Khin Mi Mi Aung
2019 arXiv   pre-print
Training on a relatively large encrypted dataset is more computationally intensive requiring 5.04 days.  ...  In this work, we present an efficient method for Text Classification while preserving the privacy of the content using Fully Homomorphic Encryption (FHE).  ...  This is even more complex compared to the lookup operation as it includes evaluation of transcendental functions and division which require large circuits depth to evaluate.  ... 
arXiv:1908.06972v2 fatcat:qgr3yrqdxvdfpke2lpmqw3q2ra

Bootstrapping BGV Ciphertexts with a Wider Choice of $$p$$ and $$q$$ [chapter]

Emmanuela Orsini, Joop van de Pol, Nigel P. Smart
2015 Lecture Notes in Computer Science  
Given an encryption of the secret key, bootstrapping consists in evaluating the above decryption formula homomorphically.  ...  Prior "efficient" methods such as that of Gentry et al (PKC 2012) required a ciphertext modulus q which was close to a power of the plaintext modulus p.  ...  This requires log 2 p · M homomorphic multiplications and depth log 2 p .  ... 
doi:10.1007/978-3-662-46447-2_30 fatcat:gj2ci7xyujbzforkb6d7obxixq

Datalog Static Analysis in Secrecy

Mojgan Kouhounestani, Woosuk Lee
2022 IEEE Access  
We evaluated our system on two static analyses in Datalog in secrecy, which have not been feasible using the previous techniques.  ...  Considering a family of static analyses written in Datalog, we propose a generic protocol that combines homomorphic encryption (HE) with secure two-party computation to manage the huge cost of HE operations  ...  We have demonstrated the viability of our method by evaluating our system using Andersen pointer analysis for 14 C programs and escape analysis for 10 Java programs.  ... 
doi:10.1109/access.2022.3177841 fatcat:gkjchlxrvzbfbd4ffj5lf77iwa

Efficient Fully Homomorphic Encryption from (Standard) LWE

Zvika Brakerski, Vinod Vaikuntanathan
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
We show that "somewhat homomorphic" encryption can be based on LWE, using a new relinearization technique.  ...  We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption.  ...  Lastly, we require that the multiplicative depth of the circuit (the total number of '×' layers) is exactly L. 21 We homomorphically evaluate the circuit f gate by gate.  ... 
doi:10.1109/focs.2011.12 dblp:conf/focs/BrakerskiV11 fatcat:tv5ku2ylmfcwlatnfrrgok5pre

Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based [chapter]

Craig Gentry, Amit Sahai, Brent Waters
2013 Lecture Notes in Computer Science  
In a leveled FHE scheme, the parameters of the scheme may depend on the depth, but not the size, of the circuits that the scheme can evaluate.  ...  In previous schemes, the homomorphic evaluator needs to obtain the user's "evaluation key", which consists of a chain of encrypted secret keys. Our scheme has no evaluation key.  ...  In all previous FHE schemes, there is also an "evaluation key" required for homomorphic evaluation.  ... 
doi:10.1007/978-3-642-40041-4_5 fatcat:fqwzglav2fhy7olktxlob536jq
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