王明强^{1, 2},
庄金成^{1, 3,,}
1.山东大学密码技术与信息安全教育部重点实验室 青岛 266237
2.山东大学数学学院 济南 250100
3.山东大学网络空间安全学院 青岛 266237
基金项目:国家自然科学基金(61672019)

详细信息

作者简介:王明强：男，1970年生，教授，研究方向为算法数论和公钥密码学
庄金成：男，1987年生，教授，研究方向为算法数论和公钥密码学

通讯作者:庄金成　jzhuang@sdu.edu.cn

中图分类号:TN918; TP309

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被引次数:0

出版历程

收稿日期:2019-08-14
修回日期:2019-12-05
网络出版日期:2019-12-09
刊出日期:2020-02-19

Analysis of Learning With Errors in Query Access Model: A List Decoding Approach

Mingqiang WANG^{1, 2},
Jincheng ZHUANG^{1, 3,,}
1. Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education Shandong University, Qingdao 266237, China
2. School of Mathematics, Shandong University, Jinan 250100, China
3. School of Cyber Science and Technology, Shandong University, Qingdao 266237, China
Funds:The National Natural Science Foundation of China (61672019)


摘要
摘要:Regev在2005年提出了含错学习问题(LWE)，这个问题与随机线性码的译码问题密切相关，并且在密码学特别是后量子密码学中应用广泛。原始的含错学习问题是在随机访问模型下提出的，有证据证明该问题的困难性。许多研究者注意到的一个事实是当攻击者可以选择样本时，该问题是容易的。但是目前据作者所知并没有一个完整的求解算法。该文分析了查询访问模型下的带有错误学习问题，给出了完整的求解算法。分析采用的工具是将该问题联系到隐藏数问题，然后应用傅里叶学习算法进行列表译码。
关键词:含错学习问题/
查询访问模型/
隐藏数问题/
傅里叶学习/
列表译码
Abstract:Regev introduced the Learning With Errors (LWE) problem in 2005, which has close connections to random linear code decoding and has found wide applications to cryptography, especially to post-quantum cryptography. The LWE problem is originally introduced in random access model, and there are evidences that indicate the hardness of this problem. It is well known that the LWE problem is vulnerable if the attacker is allowed to choose samples. However, to the best of the author’s knowledge, a complete algorithm has not been published. In this paper, the LWE problem in query samples access model is analyzed. The technique is to relate the problem to the hidden number problem, and then Fourier learning method is applied to the list decoding.
Key words:Learning With Errors (LWE) problem/
Query access model/
Hidden number problem/
Fourier learning/
List decoding



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