Abstract
Most of the current fully homomorphic encryption (FHE) schemes are based on either the learning-with-errors (LWE) problem or on its ring variant (RLWE) for storing plaintexts. During the homomorphic computation of FHE schemes, RLWE formats provide high throughput when considering several messages, and LWE formats provide a low latency when there are only a few messages. Efficient conversion can bridge the advantages of each format. However, converting LWE formats into RLWE format, which is called ring packing, has been a challenging problem.
We propose an efficient solution for ring packing for FHE. The main improvement of this work is twofold. First, we accelerate the existing ring packing methods by using bootstrapping and ring switching techniques, achieving practical runtimes. Second, we propose a new method for efficient ring packing, HERMES, by using ciphertexts in Module-LWE (MLWE) formats, to also reduce the memory. To this end, we generalize the tools of LWE and RLWE formats for MLWE formats.
On a single-thread implementation, HERMES consumes 10.2s for the ring packing of \(2^{15}\) LWE-format ciphertexts into an RLWE-format ciphertext. This gives 41x higher throughput compared to the state-of-the-art ring packing for FHE, PEGASUS [S &P’21], which takes 51.7s for packing \(2^{12}\) LWE ciphertexts with similar homomorphic capacity. We also illustrate the efficiency of HERMES by using it for transciphering from LWE symmetric encryption to CKKS fully homomorphic encryption, significantly outperforming the recent proposals HERA [Asiacrypt’21] and Rubato [Eurocrypt’22].
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References
Bae, Y., Cheon, J.H., Cho, W., Kim, J., Kim, T.: META-BTS: bootstrapping precision beyond the limit. In: CCS (2022)
Boura, C., Gama, N., Georgieva, M., Jetchev, D.: CHIMERA: combining ring-LWE-based fully homomorphic encryption schemes. J. Math. Cryptol. (2020)
Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theory (2014)
Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_50
Bossuat, J.-P., Troncoso-Pastoriza, J., Hubaux, J.-P.: Bootstrapping for approximate homomorphic encryption with negligible failure-probability by using sparse-secret encapsulation. In: Ateniese, G., Venturi, D. (eds.) ACNS 2022. LNCS, vol. 13269, pp. 521–541. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-09234-3_26
Chen, H., Dai, W., Kim, M., Song, Y.: Efficient homomorphic conversion between (ring) LWE ciphertexts. In: Sako, K., Tippenhauer, N.O. (eds.) ACNS 2021. LNCS, vol. 12726, pp. 460–479. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78372-3_18
Chillotti, I., Gama, N., Georgieva, M., Izabachène, M.: Faster fully homomorphic encryption: bootstrapping in less than 0.1 seconds. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 3–33. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_1
Chillotti, I., Gama, N., Georgieva, M., Izabachène, M.: Faster packed homomorphic operations and efficient circuit bootstrapping for TFHE. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 377–408. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_14
Cheon, J.H., Han, K., Kim, A., Kim, M., Song, Y.: Bootstrapping for approximate homomorphic encryption. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 360–384. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_14
Cho, J., et al.: Transciphering framework for approximate homomorphic encryption. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13092, pp. 640–669. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92078-4_22
Cheon, J.H., Kim, A., Kim, M., Song, Y.: Homomorphic encryption for arithmetic of approximate numbers. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 409–437. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_15
CryptoLab.inc. HEaaN private AI: Homomorphic encryption library
Ducas, L., Micciancio, D.: FHEW: bootstrapping homomorphic encryption in less than a second. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 617–640. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_24
Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption (2012). http://eprint.iacr.org/2012/144
Gentry, C., Halevi, S., Peikert, C., Smart, N.P.: Field switching in BGV-style homomorphic encryption. J. Comput. Secur. 21, 663–684 (2013)
Han, K., Ki, D.: Better bootstrapping for approximate homomorphic encryption. In: Jarecki, S. (ed.) CT-RSA 2020. Better bootstrapping for approximate homomorphic encryption., vol. 12006, pp. 364–390. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-40186-3_16
J. Ha, S. Kim, B. Lee, J. Lee, and M. Son. Rubato: Noisy ciphers for approximate homomorphic encryption. In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022. LNCS, vol. 13275, pp. 581–610 (2022). https://doi.org/10.1007/978-3-031-06944-4_20
Halevi, S., Shoup, V.: Algorithms in HElib. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 554–571. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_31
Halevi, S., Shoup, V.: Faster homomorphic linear transformations in HElib. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 93–120. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_4
Halevi, S., Shoup, V.: Bootstrapping for HElib. J. Cryptol. 34, 7 (2021)
Kim, J., et al.: ARK: fully homomorphic encryption accelerator with runtime data generation and inter-operation key reuse. In: MICRO (2022)
Lu, W.-J., Huang, Z., Hong, C., Ma, Y., Qu, H.: PEGASUS: bridging polynomial and non-polynomial evaluations in homomorphic encryption. In: S &P (2021)
Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_1
Langlois, A., Stehlé, D.: Worst-case to average-case reductions for module lattices. Des. Codes Crypt. 75(3), 565–599 (2014). https://doi.org/10.1007/s10623-014-9938-4
Micciancio, D., Sorrell, J.: Ring packing and amortized FHEW bootstrapping. In: ICALP 2018 (2018)
Naehrig, M., Lauter, K.E., Vaikuntanathan, V.: Can homomorphic encryption be practical? In: CCSW 2011 (2011)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (2009)
Stehlé, D., Steinfeld, R., Tanaka, K., Xagawa, K.: Efficient public key encryption based on ideal lattices. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 617–635. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_36
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The research corresponding to this work was conducted while the fourth author was visiting CryptoLab Inc. as an intern student.
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Bae, Y., Cheon, J.H., Kim, J., Park, J.H., Stehlé, D. (2023). HERMES: Efficient Ring Packing Using MLWE Ciphertexts and Application to Transciphering. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14084. Springer, Cham. https://doi.org/10.1007/978-3-031-38551-3_2
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