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Approximate homomorphic encryption over the conjugate-invariant ring

Cited 3 time in Web of Science Cited 2 time in Scopus

Kim, Duhyeong; Song, Yongsoo

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Springer Verlag
Lecture Notes in Computer Science, Vol.11396 LNCS, pp.85-102
© 2019, Springer Nature Switzerland AG.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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  • College of Engineering
  • Dept. of Computer Science and Engineering
Research Area Cryptography, Privacy, Security


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