An Improvement of Key Generation Algorithm for Gentry’s Homomorphic Encryption Scheme

Ogura, Naoki; Yamamoto, Go; Kobayashi, Takuya; Uchiyama, Shigenori

doi:10.1007/978-3-642-16825-3_6

Cited by 19 publications

(13 citation statements)

References 13 publications

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“…For identity based cryptography see [2,22,1,78]. For (fully) homomorphic encryption see [33,28,80,65,29,3,82,79,32,25,19,31,30]. For zero-knowledge proofs and identification protocols see [23,46,76,83,41,70].…”

Section: Resultsmentioning

confidence: 99%

“…Beside the potential for efficient implementation, lattice cryptography is very attractive because of its versatility: using lattices, in the last few years, researchers were able to develop solutions for an incredibly rich set of security problems, from simple (but efficient) hash functions [57,68,48,51], to hierarchical identity based public key encryption [34,22,1,2], and much more. As of this writing, the latest and greatest discovery in lattice cryptography is the development of fully homomorphic encryption, pioneered by Gentry in [28], and still a very fast moving research target [82,29,65,79,80,32,25,19,31,30]. In these notes, you will not learn about the most complex applications of lattices, including fully homomorphic encryption, but you will learn enough about lattices and lattice cryptography to proceed on your own and read research papers in the area.…”

Section: Introductionmentioning

confidence: 99%

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The Geometry of Lattice Cryptography

Micciancio

2011

Foundations of Security Analysis and Design VI

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Lattice cryptography is one of the hottest and fastest moving areas in mathematical cryptography today. Interest in lattice cryptography is due to several concurring factors. On the theoretical side, lattice cryptography is supported by strong worst-case/average-case security guarantees. On the practical side, lattice cryptography has been shown to be very versatile, leading to an unprecedented variety of applications, from simple (and efficient) hash functions, to complex and powerful public key cryptographic primitives, culminating with the celebrated recent development of fully homomorphic encryption. Still, one important feature of lattice cryptography is simplicity: most cryptographic operations can be implemented using basic arithmetic on small numbers, and many cryptographic constructions hide an intuitive and appealing geometric interpretation in terms of point lattices. So, unlike other areas of mathematical cryptology even a novice can acquire, with modest effort, a good understanding of not only the potential applications, but also the underlying mathematics of lattice cryptography.In these notes, we give an introduction to the mathematical theory of lattices, describe the main tools and techniques used in lattice cryptography, and present an overview of the wide range of cryptographic applications. This material should be accessible to anybody with a minimal background in linear algebra and some familiarity with the computational framework of modern cryptography, but no prior knowledge about point lattices.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Geometry of Lattice Cryptography

Micciancio

2011

Foundations of Security Analysis and Design VI

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“…Any non-immaterial favorable position in speculating the equality of the plaintext whole number in an arbitrary ciphertext that contains high clamor can be changed over in to the capacity to take care of the two component PAGCD issue utilizing the pair of open key components (Y0, Y1) containing low commotion.Because of the likenesses in the development and type of ciphertexts, the proposed HEL and the DGHV plan are indistinguishable with just contrasts in the plaintexts they encode what's more, the open key size. Henceforth, a similar system utilized in [4] and CMNT plot [8] can be connected in decreasing the security of the plan HEL to taking care of the two-component PAGCD issue.…”

Section: Validation Of the Security Level For The Proposed Schemesmentioning

confidence: 99%

“…The real commitment for the high multifaceted nature is by enormous message development and the encrypted invigorating Decrypt technique amid the security. Focusing on the Gentry's plan and their variations, a limited works has accounted for amid the recent years proposing enhancements [6], development in the key age calculation [7][8] [12,16] and diminished open key size [8], innovative plans taking out the stage two of the discussed before outline [9], expansion to bigger message space and SHE that can assess low degree works productively. For some submissions by and by, a SHE plot, for example, the one proposed in this paper, is adequate for scrambled information preparing.…”

Section: Introductionmentioning

confidence: 99%

Accelerating Information Security in Cloud Computing using a Novel Holomorphic Scheme

V*,

2019

IJITEE

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In the past decades, many security algorithms are invented and used in many applications for encryption and decryption of information or data. All the secure algorithms were uses the security key of size 8bit, 16bit, 32bit, 64bit and 128bits for encryption and decryption but literature survey says that higher the key size, higher the security. But the higher key size has number more bits and its requires more memory for storage and also to perform each and every bit through computational operations leads to more delay. To address these issues, the key and plain text are of 128bits and converted into integer. The converted integer values of key and plaintext are encrypted and decrypted using Holomorphic through Advanced Encryption Standard (AES). The research method is sophisticated and more protected through meaning fully lesser key in size and is accomplished for encryption in terms integer key and plaintext moderately than binary bits, therefore larger size of key and plaintext can be minimized and reduced the computational complexities. Finally the cipher text is uploaded into cloud through Real Time Transport Protocol (RTP) and Real Time Transport Control Protocol (RTCP) for storage. The main problem with continuous sharing of information into cloud is security attacks so in this research work, three different multimedia signals such as ECG, EEG and biomedical images are converted into integer and encrypted using AES. The stored data can access by the authorized users and can decode the information after decryption using AES.

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“…For example [8] has a method to construct keys for essentially random number fields by pulling random elements and analyzing eigenvalues of the corresponding matrices; this method however does not allow the efficiency improvements of [10] and [6] with respect to reduced ciphertext sizes etc. More recent fully homomorphic schemes based on the LWE assumption [3] have more efficient key generation procedures than the original Gentry scheme; and appear to be more suitable in practice.…”

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confidence: 99%

Improved Key Generation for Gentry’s Fully Homomorphic Encryption Scheme

Schöll

Smart

2011

Cryptography and Coding

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Abstract. A key problem with the original implementation of the Gentry Fully Homomorphic Encryption scheme was the slow key generation process. Gentry and Halevi provided a fast technique for 2-power cyclotomic fields. We present an extension of the Gentry-Halevi key generation technique for arbitrary cyclotomic fields. Our new method is roughly twice as efficient as the previous best methods. Our estimates are backed up with experimental data.The major theoretical cryptographic advance in the last three years was the discovery by Gentry in 2009 of a fully homomorphic encryption scheme [4,5]. Gentry's scheme was initially presented as a completely theoretical construction, however it was soon realised that by specialising the construction one could actually obtain a system which could at least be implemented; although not yet in such a way as to enable practical computations. The first such implementation was presented by Smart and Vercauteren [10]. The Smart and Vercauteren implementation used arithmetic of cyclotomic number fields. In particular they focused on the field generated by the polynomial F (X) = X 2 n + 1, but they noted that the scheme could be applied with arbitrary (even non-cyclotomic) number fields. A main problem with the version of Smart and Vercauteren was that the key generation method was very slow indeed.In [6] Gentry and Halevi presented a new implementation of the variant of Smart and Vercauteren, but with a greatly improved key generation phase. In particular Gentry and Halevi note that key generation (for cyclotomic fields) is essentially an application of a Discrete Fourier Transform, followed by a small amount of computation, and then application of the inverse Discrete Fourier Transform. They then show that one does not even need to perform the DFT's if one selects the cyclotomic field to be of the form X 2 n + 1. They do this by providing a recursive method to deduce two constants, from the secret key, which enables the key generation algorithm to construct a valid associate public key. The key generation method of Gentry and Halevi is fast, but appears particularly tailored to working with two-power roots of unity.However, the extra speed of their key generation method comes at a cost. Restricting to two-power roots of unity means that one is precluded from the

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An Improvement of Key Generation Algorithm for Gentry’s Homomorphic Encryption Scheme

Cited by 19 publications

References 13 publications

The Geometry of Lattice Cryptography

The Geometry of Lattice Cryptography

Accelerating Information Security in Cloud Computing using a Novel Holomorphic Scheme

Improved Key Generation for Gentry’s Fully Homomorphic Encryption Scheme

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