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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EDP Sciences
2024-10-01
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| 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 |