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Approximate Homomorphic Encryption over the Conjugate-Invariant Ring

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Information Security and Cryptology – ICISC 2018 (ICISC 2018)

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Abstract

The Ring Learning with Errors (RLWE) problem over a cyclotomic ring has been the most widely used hardness assumption for the construction of practical homomorphic encryption schemes. However, this restricted choice of a base ring may cause a waste in terms of plaintext space usage. For example, an approximate homomorphic encryption scheme of Cheon et al. (ASIACRYPT 2017) is able to store a complex number in each of the plaintext slots since its canonical embedding of a cyclotomic field has a complex image. The imaginary part of a plaintext is not underutilized at all when the computation is performed over the real numbers, which is required in most of the real-world applications such as machine learning.

In this paper, we are proposing a new homomorphic encryption scheme which supports arithmetic over the real numbers. Our scheme is based on RLWE over a subring of a cyclotomic ring called conjugate-invariant ring. We show that this problem is no easier than a standard lattice problem over ideal lattices by the reduction of Peikert et al. (STOC 2017). Our scheme allows real numbers to be packed in a ciphertext without any waste of a plaintext space and consequently we can encrypt twice as many plaintext slots as the previous scheme while maintaining the same security level, storage, and computational costs.

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Notes

  1. 1.

    https://eprint.iacr.org/2018/952.

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Acknowledgement

Duhyeong Kim was supported in part by Research Foundation of Korea (NRF) Grant funded by the Korean Government (Global Ph.D. Fellowship Program) under Grant 2016H1A2A1906584, and in part by NRF Grant funded by the Korean Government (MSIT) under Grant 2017R1A5A1015626.

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Authors and Affiliations

  1. Department of Mathematical Sciences and RIM, Seoul National University, Seoul, South Korea

    Duhyeong Kim

  2. University of California, San Diego, USA

    Yongsoo Song

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  1. Duhyeong Kim
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Correspondence to Yongsoo Song .

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  1. Sejong University, Seoul, Korea (Republic of)

    Kwangsu Lee

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Kim, D., Song, Y. (2019). Approximate Homomorphic Encryption over the Conjugate-Invariant Ring. In: Lee, K. (eds) Information Security and Cryptology – ICISC 2018. ICISC 2018. Lecture Notes in Computer Science(), vol 11396. Springer, Cham. https://doi.org/10.1007/978-3-030-12146-4_6

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  • DOI: https://doi.org/10.1007/978-3-030-12146-4_6

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