Leveled Hierarchical Identity-Based Fully Homomorphic Encryption from Learning with Rounding

Luo, Fucai; Wang, Kunpeng; Lin, Changlu

doi:10.1007/978-3-319-99807-7_7

Cited by 4 publications

(2 citation statements)

References 32 publications

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“…In this work, we focus on designing leveled CLFHE schemes. By utilizing the approximate eigenvector method [3], a lot of leveled identity-based FHE schemes [17]- [20] have been proposed. Considering that the approximate eigenvector method can be used to eliminate a user's evaluation key, we adopt it to design leveled CLFHE schemes.…”

Section: A Our Contributionsmentioning

confidence: 99%

Leveled Certificateless Fully Homomorphic Encryption Schemes From Learning With Errors

2020

IEEE Access

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Fully homomorphic encryption (FHE) is a form of public-key encryption that allows the computation of arbitrary functions on encrypted data without decrypting the data. As a result, it is a useful tool with numerous applications. Certificateless encryption (CLE) is a type of public-key encryption that combines the advantages of PKI-based public-key encryption with those of identity-based encryption (IBE). Thus, certificateless fully homomorphic encryption (CLFHE) has aroused considerable research interest. Recently, Chen, Hu, and Lian proposed a leveled certificateless homomorphic encryption (CLHE) scheme and proved its semantic security based on the learning with errors (LWE) problem in the random oracle model. However, their scheme supports only homomorphic addition, but not homomorphic multiplication. In this work, we construct two leveled CLFHE schemes using the approximate eigenvector method presented by Gentry, Sahai, and Waters. Based on the hardness of the LWE problem, we prove that one scheme satisfies adaptive semantic security and anonymity in the random oracle model, whereas the other satisfies selective semantic security and anonymity in the standard model. INDEX TERMSCertificateless fully homomorphic encryption, learning with errors, random oracle model, standard model.

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Section: A Our Contributionsmentioning

confidence: 99%

Leveled Certificateless Fully Homomorphic Encryption Schemes From Learning With Errors

2020

IEEE Access

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“…Other extensions of levelled FHE constructions include identity-based levelled FHE schemes [47][48][49], multi-identity and multi-key levelled FHE schemes [50,51], levelled certificateless FHE schemes [52,53], leakage resilient levelled FHE schemes [54] etc.…”

Section: Introductionmentioning

confidence: 99%

Towards an efficient LWE‐based fully homomorphic encryption scheme

Dowerah

Krishnaswamy

2022

IET Information Security

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The security of most early fully homomorphic encryption schemes was based on the hardness of the Learning with Errors (LWE) problem. These schemes were inefficient in terms of per gate computations and public‐key size. More efficient schemes were later developed based on the hardness of the Ring‐LWE (RLWE) problem. While the hardness of the LWE problem is based on the hardness of the approximate shortest vector problem (GapSVPγ) over regular lattices, the hardness of the RLWE problem is based on the hardness of the approximate shortest vector problem over ideal lattices. As of now, it has not been proved that the (GapSVPγ) problem over ideal lattices is as difficult as the corresponding problem over regular lattices. In this work, the authors propose a multi‐bit levelled fully homomorphic encryption scheme using multivariate polynomial evaluations whose security depends on the hardness of the LWE problem. In terms of per gate computation cost, this scheme is more efficient than existing LWE‐based schemes. Further, for an appropriate choice of parameters, the per computation cost for homomorphic multiplication can be made asymptotically comparable to RLWE‐based schemes in a parallel computing environment. For homomorphic multiplication, the scheme uses a polynomial‐based technique that does not require relinearization (and key switching).

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Multi-user Fully Homomorphic Encryption Scheme Based on Policy for Cloud Computing

Liu

Huang

2021

Web Information Systems and Applications

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Leveled Hierarchical Identity-Based Fully Homomorphic Encryption from Learning with Rounding

Cited by 4 publications

References 32 publications

Leveled Certificateless Fully Homomorphic Encryption Schemes From Learning With Errors

Leveled Certificateless Fully Homomorphic Encryption Schemes From Learning With Errors

Towards an efficient LWE‐based fully homomorphic encryption scheme

Multi-user Fully Homomorphic Encryption Scheme Based on Policy for Cloud Computing

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