Small interval interpolation fitting bootstrapping method based on residue number system

Aiming at the problem that the bootstrapping time of approximate homomorphic encryption scheme is too long, a small interval interpolation fitting method based on residue system is proposed. In this paper, the sinusoidal function by using interpolating and fitting method between the multiple cells t...

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Main Authors: LI Huixian, WANG Fulei, SHEN Chun, LIU Shiyuan, PANG Liaojun
Format: Article
Language:zho
Published: EDP Sciences 2024-10-01
Series:Xibei Gongye Daxue Xuebao
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Online Access:https://www.jnwpu.org/articles/jnwpu/full_html/2024/05/jnwpu2024425p969/jnwpu2024425p969.html
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author LI Huixian
WANG Fulei
SHEN Chun
LIU Shiyuan
PANG Liaojun
author_facet LI Huixian
WANG Fulei
SHEN Chun
LIU Shiyuan
PANG Liaojun
author_sort LI Huixian
collection DOAJ
description Aiming at the problem that the bootstrapping time of approximate homomorphic encryption scheme is too long, a small interval interpolation fitting method based on residue system is proposed. In this paper, the sinusoidal function by using interpolating and fitting method between the multiple cells to avoid the increase in bootstrapping time or decrease in calculation accuracy caused by the high degree of fitting polynomial is calculated. And the efficiency of modular multiplication and modular inversion in the calculation process is improved by combining the residual system. Lagrange interpolation polynomial is used to interpolate and fit the sine function among different intervals. The comparison function is implemented by the compound implementation of low-degree polynomials, and an interval judgment algorithm is proposed to identify the interval of the ciphertext. Finally, under the precision of 24 bits, the modular operation time in the bootstrapping process decreased to 8% of the HEAAN. When the number of slots is 65 536, the average module operation time per slot is 0.028 ms.
format Article
id doaj-art-5df7cb75193f49988c5dade2cb3549ef
institution Kabale University
issn 1000-2758
2609-7125
language zho
publishDate 2024-10-01
publisher EDP Sciences
record_format Article
series Xibei Gongye Daxue Xuebao
spelling doaj-art-5df7cb75193f49988c5dade2cb3549ef2024-12-13T10:05:06ZzhoEDP SciencesXibei Gongye Daxue Xuebao1000-27582609-71252024-10-0142596997810.1051/jnwpu/20244250969jnwpu2024425p969Small interval interpolation fitting bootstrapping method based on residue number systemLI Huixian0WANG Fulei1SHEN Chun2LIU Shiyuan3PANG Liaojun4School of Computer Science, Northwestern Polytechnical UniversitySchool of Computer Science, Northwestern Polytechnical UniversitySchool of Software, Northwestern Polytechnical UniversitySchool of Computer Science, Northwestern Polytechnical UniversitySchool of Life Science and Technology, Xidian UniversityAiming at the problem that the bootstrapping time of approximate homomorphic encryption scheme is too long, a small interval interpolation fitting method based on residue system is proposed. In this paper, the sinusoidal function by using interpolating and fitting method between the multiple cells to avoid the increase in bootstrapping time or decrease in calculation accuracy caused by the high degree of fitting polynomial is calculated. And the efficiency of modular multiplication and modular inversion in the calculation process is improved by combining the residual system. Lagrange interpolation polynomial is used to interpolate and fit the sine function among different intervals. The comparison function is implemented by the compound implementation of low-degree polynomials, and an interval judgment algorithm is proposed to identify the interval of the ciphertext. Finally, under the precision of 24 bits, the modular operation time in the bootstrapping process decreased to 8% of the HEAAN. When the number of slots is 65 536, the average module operation time per slot is 0.028 ms.https://www.jnwpu.org/articles/jnwpu/full_html/2024/05/jnwpu2024425p969/jnwpu2024425p969.html全同态加密近似计算自举余数系统插值拟合拉格朗日插值
spellingShingle LI Huixian
WANG Fulei
SHEN Chun
LIU Shiyuan
PANG Liaojun
Small interval interpolation fitting bootstrapping method based on residue number system
Xibei Gongye Daxue Xuebao
全同态加密
近似计算
自举
余数系统
插值拟合
拉格朗日插值
title Small interval interpolation fitting bootstrapping method based on residue number system
title_full Small interval interpolation fitting bootstrapping method based on residue number system
title_fullStr Small interval interpolation fitting bootstrapping method based on residue number system
title_full_unstemmed Small interval interpolation fitting bootstrapping method based on residue number system
title_short Small interval interpolation fitting bootstrapping method based on residue number system
title_sort small interval interpolation fitting bootstrapping method based on residue number system
topic 全同态加密
近似计算
自举
余数系统
插值拟合
拉格朗日插值
url https://www.jnwpu.org/articles/jnwpu/full_html/2024/05/jnwpu2024425p969/jnwpu2024425p969.html
work_keys_str_mv AT lihuixian smallintervalinterpolationfittingbootstrappingmethodbasedonresiduenumbersystem
AT wangfulei smallintervalinterpolationfittingbootstrappingmethodbasedonresiduenumbersystem
AT shenchun smallintervalinterpolationfittingbootstrappingmethodbasedonresiduenumbersystem
AT liushiyuan smallintervalinterpolationfittingbootstrappingmethodbasedonresiduenumbersystem
AT pangliaojun smallintervalinterpolationfittingbootstrappingmethodbasedonresiduenumbersystem