Threshold Fully Homomorphic Encryption Over the Torus

Yukimasa Sugizaki; Hikaru Tsuchida; Takuya Hayashi; Koji Nuida; Akira Nakashima; Toshiyuki Isshiki; Kengo Mori

doi:10.1007/978-3-031-50594-2_3

Threshold Fully Homomorphic Encryption Over the Torus

Yukimasa Sugizaki, Hikaru Tsuchida, Takuya Hayashi, Koji Nuida, Akira Nakashima, Toshiyuki Isshiki, Kengo Mori

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Fully homomorphic encryption (FHE) enables arithmetic operations to be performed over plaintext by operations on undecrypted ciphertext. The Chillotti-Gama-Georgieva-Izabachene (CGGI) scheme is a typical FHE scheme, has attracted attention because of its fast bootstrapping and the availability of open-source implementation software. A threshold FHE (ThFHE) scheme has protocols for distributed key generation and distributed decryption that are executed cooperatively among the parties while keeping the decryption key distributed among them. It is useful for secure computations with inputs from multiple parties. However, a ThFHE scheme based on CGGI has yet to be proposed. In this paper, we propose a client-aided ThFHE scheme based on CGGI. Our scheme achieves the same bootstrapping as CGGI without affecting the noise analysis or any CGGI parameter. Therefore, existing open-source software implementing CGGI can easily be extended to our scheme, a ThFHE variant of the CGGI scheme, without changing the implementation part regarding homomorphic operations.

Original language	English
Title of host publication	Computer Security – ESORICS 2023 - 28th European Symposium on Research in Computer Security, 2023, Proceedings
Editors	Gene Tsudik, Mauro Conti, Kaitai Liang, Georgios Smaragdakis
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	45-65
Number of pages	21
ISBN (Print)	9783031505935
DOIs	https://doi.org/10.1007/978-3-031-50594-2_3
Publication status	Published - 2024
Event	28th European Symposium on Research in Computer Security, ESORICS 2023 - The Hague, Netherlands Duration: Sept 25 2023 → Sept 29 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14344 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	28th European Symposium on Research in Computer Security, ESORICS 2023
Country/Territory	Netherlands
City	The Hague
Period	9/25/23 → 9/29/23

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-50594-2_3

Cite this

Sugizaki, Y., Tsuchida, H., Hayashi, T., Nuida, K., Nakashima, A., Isshiki, T., & Mori, K. (2024). Threshold Fully Homomorphic Encryption Over the Torus. In G. Tsudik, M. Conti, K. Liang, & G. Smaragdakis (Eds.), Computer Security – ESORICS 2023 - 28th European Symposium on Research in Computer Security, 2023, Proceedings (pp. 45-65). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14344 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-50594-2_3

Threshold Fully Homomorphic Encryption Over the Torus. / Sugizaki, Yukimasa; Tsuchida, Hikaru; Hayashi, Takuya et al.
Computer Security – ESORICS 2023 - 28th European Symposium on Research in Computer Security, 2023, Proceedings. ed. / Gene Tsudik; Mauro Conti; Kaitai Liang; Georgios Smaragdakis. Springer Science and Business Media Deutschland GmbH, 2024. p. 45-65 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14344 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Sugizaki, Y, Tsuchida, H, Hayashi, T, Nuida, K, Nakashima, A, Isshiki, T & Mori, K 2024, Threshold Fully Homomorphic Encryption Over the Torus. in G Tsudik, M Conti, K Liang & G Smaragdakis (eds), Computer Security – ESORICS 2023 - 28th European Symposium on Research in Computer Security, 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14344 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 45-65, 28th European Symposium on Research in Computer Security, ESORICS 2023, The Hague, Netherlands, 9/25/23. https://doi.org/10.1007/978-3-031-50594-2_3

Sugizaki Y, Tsuchida H, Hayashi T, Nuida K, Nakashima A, Isshiki T et al. Threshold Fully Homomorphic Encryption Over the Torus. In Tsudik G, Conti M, Liang K, Smaragdakis G, editors, Computer Security – ESORICS 2023 - 28th European Symposium on Research in Computer Security, 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2024. p. 45-65. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-50594-2_3

Sugizaki, Yukimasa ; Tsuchida, Hikaru ; Hayashi, Takuya et al. / Threshold Fully Homomorphic Encryption Over the Torus. Computer Security – ESORICS 2023 - 28th European Symposium on Research in Computer Security, 2023, Proceedings. editor / Gene Tsudik ; Mauro Conti ; Kaitai Liang ; Georgios Smaragdakis. Springer Science and Business Media Deutschland GmbH, 2024. pp. 45-65 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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