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关于非对称含错学习问题的困难性研究

张江 范淑琴

张江, 范淑琴. 关于非对称含错学习问题的困难性研究[J]. 电子与信息学报, 2020, 42(2): 327-332. doi: 10.11999/JEIT190685
引用本文: 张江, 范淑琴. 关于非对称含错学习问题的困难性研究[J]. 电子与信息学报, 2020, 42(2): 327-332. doi: 10.11999/JEIT190685
Jiang ZHANG, Shuqin FAN. On the Hardness of the Asymmetric Learning With Errors Problem[J]. Journal of Electronics & Information Technology, 2020, 42(2): 327-332. doi: 10.11999/JEIT190685
Citation: Jiang ZHANG, Shuqin FAN. On the Hardness of the Asymmetric Learning With Errors Problem[J]. Journal of Electronics & Information Technology, 2020, 42(2): 327-332. doi: 10.11999/JEIT190685

关于非对称含错学习问题的困难性研究

doi: 10.11999/JEIT190685
基金项目: 国家重点研发计划(2017YFB0802005, 2018YFB0804105),国家自然科学基金(61602046, 61932019),中国科协“青年人才托举工程”(2016QNRC001)
详细信息
    作者简介:

    张江:男,1986年生,副研究员,主要研究方向为基于格的密码协议及其可证明安全

    范淑琴:女,1978年生,教授,主要研究方向为基于格的密码分析

    通讯作者:

    张江 jiangzhang09@gmail.com

  • 中图分类号: TN918, TP309.7

On the Hardness of the Asymmetric Learning With Errors Problem

Funds: The National Key Research and Development Program of China (2017YFB0802005, 2018YFB0804105), The National Natural Science Foundation of China (61602046, 61932019), The Young Elite Scientists Sponsorship Program by China Association for Science and Technology (2016QNRC001)
  • 摘要: 由于基于最坏情况困难假设等优点,基于格的密码被认为是最具前景的抗量子密码研究方向。作为格密码的常用的两个主要困难问题之一,含错学习(LWE)问题被广泛用于密码算法的设计。为了提高格密码算法的性能,Zhang等人(2019)提出了非对称含错学习问题,该文将从理论上详细研究非对称含错学习问题和标准含错学习问题关系,并证明在特定错误分布下非对称含错学习问题和含错学习问题是多项式时间等价的,从而为基于非对称含错学习问题设计安全的格密码算法奠定了理论基础。
  • 图  1  高斯分布和二项分布

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出版历程
  • 收稿日期:  2019-09-14
  • 修回日期:  2019-11-20
  • 网络出版日期:  2019-11-29
  • 刊出日期:  2020-02-19

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