TY - GEN
T1 - F-FHEW
T2 - 29th Australasian Conference on Information Security and Privacy, ACISP 2024
AU - Chen, Man
AU - Chen, Yu Yue
AU - Zong, Rui
AU - Li, Zeng Peng
AU - Jiang, Zoe L.
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
PY - 2024
Y1 - 2024
N2 - Floating-point fully homomorphic encryption (FPFHE) supports arbitrary computation on ciphertexts and yields approximate results. On one hand, for the state-of-the-art, the CKKS-like scheme (Jutla et al., EUROCRYPT 2022) achieves a precision of 100-bit decimal as the messages originally include some encoding noise, as well as some additional errors will be generated by bootstrapping operation. Nonetheless, operations with higher precision are also appreciated by various kinds of applications, such as Semidefinite Programming requiring 128-bit precision. On the other hand, the CKKS-like scheme is very computationally intensive. Compared to processing the same data in clear, it is slower, less efficient, and more energy-consuming. In this paper, we propose a high-precision approximate homomorphic encryption with batch bootstrapping based on the Gentry-Sahai-Waters scheme over rings (or RingGSW). Firstly, to support a precision of 128-bit decimal, mapping floating-point numbers to B-based cyclotomic polynomials with 128-fraction coefficients. Furthermore, we use polynomial truncation in homomorphic multiplication to support deep-level circuit with upper-bound depth O(logq/(Bgσ)). Next, we utilize trace function computation to achieve batch multiplication, achieving an amortized multiplication complexity of O(n1.75logq). Overall, the proposed scheme has half amortized multiplication time and supports deeper-level circuit >O(logq0/(Bgσ)), when compared to the CKKS-like scheme.
AB - Floating-point fully homomorphic encryption (FPFHE) supports arbitrary computation on ciphertexts and yields approximate results. On one hand, for the state-of-the-art, the CKKS-like scheme (Jutla et al., EUROCRYPT 2022) achieves a precision of 100-bit decimal as the messages originally include some encoding noise, as well as some additional errors will be generated by bootstrapping operation. Nonetheless, operations with higher precision are also appreciated by various kinds of applications, such as Semidefinite Programming requiring 128-bit precision. On the other hand, the CKKS-like scheme is very computationally intensive. Compared to processing the same data in clear, it is slower, less efficient, and more energy-consuming. In this paper, we propose a high-precision approximate homomorphic encryption with batch bootstrapping based on the Gentry-Sahai-Waters scheme over rings (or RingGSW). Firstly, to support a precision of 128-bit decimal, mapping floating-point numbers to B-based cyclotomic polynomials with 128-fraction coefficients. Furthermore, we use polynomial truncation in homomorphic multiplication to support deep-level circuit with upper-bound depth O(logq/(Bgσ)). Next, we utilize trace function computation to achieve batch multiplication, achieving an amortized multiplication complexity of O(n1.75logq). Overall, the proposed scheme has half amortized multiplication time and supports deeper-level circuit >O(logq0/(Bgσ)), when compared to the CKKS-like scheme.
KW - Bootstrapping
KW - FPFHE
KW - Laurent polynomial
KW - Truncation
UR - https://www.scopus.com/pages/publications/85200650674
U2 - 10.1007/978-981-97-5025-2_7
DO - 10.1007/978-981-97-5025-2_7
M3 - 会议稿件
AN - SCOPUS:85200650674
SN - 9789819750245
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 121
EP - 140
BT - Information Security and Privacy - 29th Australasian Conference, ACISP 2024, Proceedings
A2 - Zhu, Tianqing
A2 - Li, Yannan
PB - Springer Science and Business Media Deutschland GmbH
Y2 - 15 July 2024 through 17 July 2024
ER -