FHEW: bootstrapping homomorphic encryption in less than a second. The main bottleneck affecting the efficiency of all known fully homomorphic encryption (FHE) schemes is Gentry’s bootstrapping procedure, which is required to refresh noisy ciphertexts and keep computing on encrypted data. Bootstrapping in the latest implementation of FHE, the HElib library of Halevi and Shoup (Crypto 2014), requires about six minutes. We present a new method to homomorphically compute simple bit operations, and refresh (bootstrap) the resulting output, which runs on a personal computer in just about half a second. We present a detailed technical analysis of the scheme (based on the worst-case hardness of standard lattice problems) and report on the performance of our prototype implementation.

References in zbMATH (referenced in 23 articles )

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  1. Chen, Hao; Dai, Wei; Kim, Miran; Song, Yongsoo: Efficient homomorphic conversion between (ring) LWE ciphertexts (2021)
  2. Boura, Christina; Gama, Nicolas; Georgieva, Mariya; Jetchev, Dimitar: CHIMERA: combining ring-LWE-based fully homomorphic encryption schemes (2020)
  3. Chillotti, Ilaria; Gama, Nicolas; Georgieva, Mariya; Izabachène, Malika: TFHE: fast fully homomorphic encryption over the torus (2020)
  4. Carlet, Claude; Méaux, Pierrick: Boolean functions for homomorphic-friendly stream ciphers (2019)
  5. Canteaut, Anne; Carpov, Sergiu; Fontaine, Caroline; Lepoint, Tancrède; Naya-Plasencia, María; Paillier, Pascal; Sirdey, Renaud: Stream ciphers: a practical solution for efficient homomorphic-ciphertext compression (2018)
  6. Cheon, Jung Hee; Han, Kyoohyung; Kim, Andrey; Kim, Miran; Song, Yongsoo: Bootstrapping for approximate homomorphic encryption (2018)
  7. Chung, Heewon; Kim, Myungsun: Encoding of rational numbers and their homomorphic computations for FHE-based applications (2018)
  8. Marcos del Blanco, David Yeregui; Panizo Alonso, Luis; Hermida Alonso, Jose Angel: Review of cryptographic schemes applied to remote electronic voting systems: remaining challenges and the upcoming post-quantum paradigm (2018)
  9. Micciancio, Daniele: On the hardness of learning with errors with binary secrets (2018)
  10. Miccianco, Daniele; Sorrell, Jessica: Ring packing and amortized FHEW bootstrapping (2018)
  11. Benarroch, Daniel; Brakerski, Zvika; Lepoint, Tancrède: FHE over the integers: decomposed and batched in the post-quantum regime (2017)
  12. Boneh, Dan; Ishai, Yuval; Sahai, Amit; Wu, David J.: Lattice-based SNARGs and their application to more efficient obfuscation (2017)
  13. Boyle, Elette; Gilboa, Niv; Ishai, Yuval: Group-based secure computation: optimizing rounds, communication, and computation (2017)
  14. Cramer, Ronald; Ducas, Léo; Wesolowski, Benjamin: Short Stickelberger class relations and application to Ideal-SVP (2017)
  15. Halevi, Shai: Homomorphic encryption (2017)
  16. Li, Zengpeng; Ma, Chunguang; Morais, Eduardo; Du, Gang: Multi-bit leveled homomorphic encryption via dual LWE-based (2017)
  17. Bourse, Florian; Del Pino, Rafaël; Minelli, Michele; Wee, Hoeteck: FHE circuit privacy almost for free (2016)
  18. Chillotti, Ilaria; Gama, Nicolas; Georgieva, Mariya; Izabachène, Malika: Faster fully homomorphic encryption: bootstrapping in less than 0.1 seconds (2016)
  19. Jäschke, Angela; Armknecht, Frederik: Accelerating homomorphic computations on rational numbers (2016)
  20. Katsumata, Shuichi; Yamada, Shota: Partitioning via non-linear polynomial functions: more compact IBEs from ideal lattices and bilinear maps (2016)

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