(Leveled) Fully Homomorphic Encryption without Bootstrapping

Brakerski, Zvika; Gentry, Craig; Vaikuntanathan, Vinod

doi:10.1145/2633600

Cited by 1,102 publications

(1,031 citation statements)

References 34 publications

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“…They showed a number of optimizations that allow implementing all aspects of the scheme, including the bootstrapping functionality. Brakerski et al (2014) presented a new way of constructing leveled FHE schemes which can evaluate arbitrary polynomial-size circuits without Gentry's bootstrapping procedure. The proposed scheme is based on the learning with error (LWE) or ring-LWE (RLWE)…”

Section: Partially Somewhat and Fully Homomorphic Encryption Schemesmentioning

confidence: 99%

A comprehensive meta-analysis of cryptographic security mechanisms for cloud computing

Kiraz

2016

J Ambient Intell Human Comput

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The concept of cloud computing offers measurable computational or information resources as a service over the Internet. The major motivation behind the cloud setup is economic benefits, because it assures the reduction in expenditure for operational and infrastructural purposes. To transform it into a reality there are some impediments and hurdles which are required to be tackled, most profound of which are security, privacy and reliability issues. As the user data is revealed to the cloud, it departs the protection-sphere of the data owner. However, this brings partly new security and privacy concerns. This work focuses on these issues related to various cloud services and deployment models by spotlighting their major challenges. While the classical cryptography is an ancient discipline, modern cryptography, which has been mostly developed in the last few decades, is the subject of study which needs to be implemented so as to ensure strong security and privacy mechanisms in today's real-world scenarios. The technological solutions, short and long term research goals of the cloud security will be described and addressed using various classical cryptographic mechanisms as well as modern ones. This work explores the new directions in cloud computing security, while highlighting the correct selection of these fundamental technologies from cryptographic point of view.

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Section: Partially Somewhat and Fully Homomorphic Encryption Schemesmentioning

confidence: 99%

A comprehensive meta-analysis of cryptographic security mechanisms for cloud computing

Kiraz

2016

J Ambient Intell Human Comput

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“…To cope with the growth of noise, following Brakerski et al [5] we introduce a series of decreasing moduli q 0 > q 1 > · · · > q t−1 ; one modulus per circuit level. Modulus switching is a powerful technique that exponentially reduces the growth of noise during computations.…”

Section: Reducing the Public Key Sizementioning

confidence: 99%

“…AES, using this approach since the norm grows exponentially with the depth of the circuit. To cope with the growth of noise, we employ modulus switching as introduced in [5]. For this, we make use of a series of decreasing moduli q 0 > q 1 > · · · > q t ; one modulus per level.…”

Section: Modulus Switchingmentioning

confidence: 99%

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Homomorphic AES evaluation using the modified LTV scheme

Doröz

Yin

Sunar

2015

Des. Codes Cryptogr.

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Since its introduction more than a decade ago the homomorphic properties of the NTRU encryption scheme have gone largely ignored. A variant of NTRU proposed by Stehlé and Steinfeld was recently extended into a full fledged multi-key fully homomorphic encryption scheme by López-Alt, Tromer and Vaikuntanathan (LTV). This NTRU based FHE presents a viable alternative to the currently dominant BGV style FHE schemes. While the scheme appears to be more efficient, a full implementation and comparison to BGV style implementations has been missing in the literature. In this work, we develop a customized implementation of the LTV. First parameters are selected to yield an efficient and yet secure LTV instantiation. We present an analysis of the noise growth that allows us to formulate a modulus cutting strategy for arbitrary circuits. Furthermore, we introduce a specialization of the ring structure that allows us to drastically reduce the public key size making evaluation of deep circuits such as the AES block cipher viable on a standard computer with a reasonable amount of memory. Moreover, with the modulus specialization the need for key switching is eliminated. Finally, we present a generic bit-sliced implementation of the LTV scheme that embodies a number of optimizations. To assess the performance of the scheme we homomorphically evaluate the full 10 round AES circuit in 29 h with 2048 message slots resulting in 51 s per AES block evaluation time.

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“…Unlike other homomorphic schemes based on polynomial rings [5,7,27], our scheme requires only a single polynomial p(x) for homomorphic evaluations. Using p(x), it is easy to see that we can homomorphically add and multiply ciphertexts in the ring R in a natural way.…”

Section: Introductionmentioning

confidence: 99%