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基于列表譯碼方法在查詢訪問模型下含錯學(xué)習(xí)問題的分析

王明強(qiáng),  莊金成

王明強(qiáng), 莊金成. 基于列表譯碼方法在查詢訪問模型下含錯學(xué)習(xí)問題的分析[J]. 電子與信息學(xué)報, 2020, 42(2): 322-326. doi: 10.11999/JEIT190624
引用本文: 王明強(qiáng), 莊金成. 基于列表譯碼方法在查詢訪問模型下含錯學(xué)習(xí)問題的分析[J]. 電子與信息學(xué)報, 2020, 42(2): 322-326. doi: 10.11999/JEIT190624
Mingqiang WANG, Jincheng ZHUANG. Analysis of Learning With Errors in Query Access Model: A List Decoding Approach[J]. Journal of Electronics & Information Technology, 2020, 42(2): 322-326. doi: 10.11999/JEIT190624
Citation: Mingqiang WANG, Jincheng ZHUANG. Analysis of Learning With Errors in Query Access Model: A List Decoding Approach[J]. Journal of Electronics & Information Technology, 2020, 42(2): 322-326. doi: 10.11999/JEIT190624

基于列表譯碼方法在查詢訪問模型下含錯學(xué)習(xí)問題的分析

doi: 10.11999/JEIT190624
  • 1.

    山東大學(xué)密碼技術(shù)與信息安全教育部重點(diǎn)實驗室 青島 266237

  • 2.

    山東大學(xué)數(shù)學(xué)學(xué)院 濟(jì)南 250100

  • 3.

    山東大學(xué)網(wǎng)絡(luò)空間安全學(xué)院 青島 266237

基金項目: 國家自然科學(xué)基金(61672019)
詳細(xì)信息
    作者簡介:

    王明強(qiáng)：男，1970年生，教授，研究方向為算法數(shù)論和公鑰密碼學(xué)

    莊金成：男，1987年生，教授，研究方向為算法數(shù)論和公鑰密碼學(xué)

    通訊作者:

    莊金成　jzhuang@sdu.edu.cn

  • 中圖分類號: TN918; TP309

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

  • 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: Regev在2005年提出了含錯學(xué)習(xí)問題(LWE)，這個問題與隨機(jī)線性碼的譯碼問題密切相關(guān)，并且在密碼學(xué)特別是后量子密碼學(xué)中應(yīng)用廣泛。原始的含錯學(xué)習(xí)問題是在隨機(jī)訪問模型下提出的，有證據(jù)證明該問題的困難性。許多研究者注意到的一個事實是當(dāng)攻擊者可以選擇樣本時，該問題是容易的。但是目前據(jù)作者所知并沒有一個完整的求解算法。該文分析了查詢訪問模型下的帶有錯誤學(xué)習(xí)問題，給出了完整的求解算法。分析采用的工具是將該問題聯(lián)系到隱藏數(shù)問題，然后應(yīng)用傅里葉學(xué)習(xí)算法進(jìn)行列表譯碼。
    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.
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  • 被引次數(shù): 0
出版歷程
  • 收稿日期:  2019-08-14
  • 修回日期:  2019-12-05
  • 網(wǎng)絡(luò)出版日期:  2019-12-09
  • 刊出日期:  2020-02-19

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