基于列表譯碼方法在查詢訪問模型下含錯學習問題的分析
doi: 10.11999/JEIT190624 cstr: 32379.14.JEIT190624
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1.
山東大學密碼技術與信息安全教育部重點實驗室 青島 266237
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2.
山東大學數(shù)學學院 濟南 250100
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3.
山東大學網(wǎng)絡空間安全學院 青島 266237
基金項目: 國家自然科學基金(61672019)
Analysis of Learning With Errors in Query Access Model: A List Decoding Approach
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1.
Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education Shandong University, Qingdao 266237, China
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2.
School of Mathematics, Shandong University, Jinan 250100, China
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3.
School of Cyber Science and Technology, Shandong University, Qingdao 266237, China
Funds: The National Natural Science Foundation of China (61672019)
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摘要: Regev在2005年提出了含錯學習問題(LWE)，這個問題與隨機線性碼的譯碼問題密切相關，并且在密碼學特別是后量子密碼學中應用廣泛。原始的含錯學習問題是在隨機訪問模型下提出的，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習問題，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，然后應用傅里葉學習算法進行列表譯碼。
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關鍵詞:
- 含錯學習問題 /
- 查詢訪問模型 /
- 隱藏數(shù)問題 /
- 傅里葉學習 /
- 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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