Fully Homomorphic Encryption for Point Numbers

Arita, Seiko; Nakasato, Shota

doi:10.1007/978-3-319-54705-3_16

Cited by 17 publications

(14 citation statements)

References 16 publications

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“…ere have been some attempts to represent encrypted floating-point real numbers before this study. Arita and Nakasato [21] proposed the FHE4FX method that can perform addition and multiplication between encrypted floating-point numbers without decryption based on the FV FHE method [22]. It generates an encrypted floating-point representation by encrypting each sign, exponent, and mantissa part of a real number in separate ciphertexts.…”

Section: Related Workmentioning

confidence: 99%

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An Efficient Encrypted Floating-Point Representation Using HEAAN and TFHE

Moon

Lee

2020

Security and Communication Networks

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As a method of privacy-preserving data analysis (PPDA), a fully homomorphic encryption (FHE) has been in the spotlight recently. Unfortunately, because many data analysis methods assume that the type of data is of real type, the FHE-based PPDA methods could not support the enough level of accuracy due to the nature of FHE that fixed-point real-number representation is supported easily. In this paper, we propose a new method to represent encrypted floating-point real numbers on top of FHE. e proposed method is designed to have analogous range and accuracy to 32-bit floating-point number in IEEE 754 representation. We propose a method to perform arithmetic operations and size comparison operations. e proposed method is designed using two different FHEs, HEAAN and TFHE. As a result, HEAAN is proven to be very efficient for arithmetic operations and TFHE is efficient in size comparison. is study is expected to contribute to practical use of FHE-based PPDA.

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Section: Related Workmentioning

confidence: 99%

“…ere are other methods such as those of Seiko and Nakasato [26] and Dowlin et al [27]. However, they require a very large computation for floating-point operations.…”

Section: Related Workmentioning

confidence: 99%

An Efficient Encrypted Floating-Point Representation Using HEAAN and TFHE

Moon

Lee

2020

Security and Communication Networks

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“…Literatures [58][59][60] expanded the homomorphic encryption scheme of integer domain to the fixed-point and floating-point parts, which has extended the application scenarios of homomorphic algorithm. Literature [61] specifically analyzed the theoretical basis and characteristics of above homomorphic encryption schemes in theory, stipulated various terms, related concepts and definitions used in the homomorphic schemes, and made uniform description of above concepts based on mathematical knowledge.…”

Section: Related Workmentioning

confidence: 99%

A privacy protection-oriented parallel fully homomorphic encryption algorithm in cyber physical systems

Min

Yang

Sangaiah

et al. 2019

J Wireless Com Network

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Cyber physical system (CPS) is facing enormous security challenges because of open and interconnected network and the interaction between cyber components and physical components, the development of cyber physical systems is constrained by security and privacy threats. A feasible solution is to combine the fully homomorphic encryption (FHE) technique to realize the efficient operation of ciphertext without decryption. However, most current homomorphic encryption algorithms only support limited data types, making it difficult to be widely applied in actual environment. To address this limitation, we propose a parallel fully homomorphic encryption algorithm that supports floating-point numbers. The proposed algorithm not only expands the data types supported by the existing fully homomorphic encryption algorithms, but also utilizes the characteristics of multi-nodes in cloud environment to conduct parallel encryption through simultaneous group-wise ciphertext computations. The experimental results show that, in a 16-core 4-node cluster with MapReduce environment, the proposed encryption algorithm achieves the maximum speed-up exceeding 5, which not only solves the limited application problem of the existing fully homomorphic encryption algorithm, but also meets the requirements for the efficient homomorphic encryption of floating-point numbers in cloud computing environment.

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“…Recently, there have been papers focusing on designing a fully homomorphic encryption scheme for real numbers. Seiko, Arita, and Shota Nakasato [30] proposed a fully homomorphic encryption for point numbers based on the FV [31] scheme, which is based on the LWE problem. They construct a first homomorphic encryption scheme that supports operations for fixed-point numbers.…”

Section: Related Workmentioning

confidence: 99%

Privacy-Preserving Oriented Floating-Point Number Fully Homomorphic Encryption Scheme

Bai

Yang

Shi

et al. 2018

Security and Communication Networks

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The issue of the privacy-preserving of information has become more prominent, especially regarding the privacy-preserving problem in a cloud environment. Homomorphic encryption can be operated directly on the ciphertext; this encryption provides a new method for privacy-preserving. However, we face a challenge in understanding how to construct a practical fully homomorphic encryption on non-integer data types. This paper proposes a revised floating-point fully homomorphic encryption scheme (FFHE) that achieves the goal of floating-point numbers operation without privacy leakage to unauthorized parties. We encrypt a matrix of plaintext bits as a single ciphertext to reduce the ciphertext expansion ratio and reduce the public key size by encrypting with a quadratic form in three types of public key elements and pseudo-random number generators. Additionally, we make the FFHE scheme more applicable by generalizing the homomorphism of addition and multiplication of floating-point numbers to analytic functions using the Taylor formula. We prove that the FFHE scheme for ciphertext operation may limit an additional loss of accuracy. Specifically, the precision of the ciphertext operation's result is similar to unencrypted floating-point number computation. Compared to other schemes, our FFHE scheme is more practical for privacy-preserving in the cloud environment with its low ciphertext expansion ratio and public key size, supporting multiple operation types and high precision.

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Fully Homomorphic Encryption for Point Numbers

Cited by 17 publications

References 16 publications

An Efficient Encrypted Floating-Point Representation Using HEAAN and TFHE

An Efficient Encrypted Floating-Point Representation Using HEAAN and TFHE

A privacy protection-oriented parallel fully homomorphic encryption algorithm in cyber physical systems

Privacy-Preserving Oriented Floating-Point Number Fully Homomorphic Encryption Scheme

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