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Bootstrapping for Approximate Homomorphic Encryption

  • Jung Hee Cheon
  • Kyoohyung Han
  • Andrey Kim
  • Miran Kim
  • Yongsoo Song
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10820)

Abstract

This paper extends the leveled homomorphic encryption scheme for an approximate arithmetic of Cheon et al. (ASIACRYPT 2017) to a fully homomorphic encryption, i.e., we propose a new technique to refresh low-level ciphertexts based on Gentry’s bootstrapping procedure. The modular reduction operation is the main bottleneck in the homomorphic evaluation of the decryption circuit. We exploit a scaled sine function as an approximation of the modular reduction operation and present an efficient evaluation strategy. Our method requires only one homomorphic multiplication for each of iterations and so the total computation cost grows linearly with the depth of the decryption circuit. We also show how to recrypt packed ciphertexts on the RLWE construction with an open-source implementation. For example, it takes 139.8 s to refresh a ciphertext that encrypts 128 numbers with 12 bits of precision, yielding an amortized rate of 1.1 seconds per slot.

Keywords

Homomorphic encryption Approximate arithmetic Bootstrapping 

Notes

Acknowledgments

We would like to thank the anonymous EUROCRYPT’18 reviewers for useful comments. This work was partially supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIT) (No. B0717-16-0098, Development of homomorphic encryption for DNA analysis and biometry authentication). M. Kim was supported by the National Institute of Health (NIH) under award number U01EB023685.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.Seoul National UniversitySeoulRepublic of Korea
  2. 2.University of CaliforniaSan DiegoUSA

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