關(guān)于非對稱含錯學習問題的困難性研究
doi: 10.11999/JEIT190685
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密碼科學技術(shù)國家重點實驗室 北京 100878
基金項目: 國家重點研發(fā)計劃(2017YFB0802005, 2018YFB0804105)，國家自然科學基金(61602046, 61932019)，中國科協(xié)“青年人才托舉工程”(2016QNRC001)
On the Hardness of the Asymmetric Learning With Errors Problem
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State Key Laboratory of Cryptology, Beijing 100878, China
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)
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摘要: 由于基于最壞情況困難假設(shè)等優(yōu)點，基于格的密碼被認為是最具前景的抗量子密碼研究方向。作為格密碼的常用的兩個主要困難問題之一，含錯學習(LWE)問題被廣泛用于密碼算法的設(shè)計。為了提高格密碼算法的性能，Zhang等人(2019)提出了非對稱含錯學習問題，該文將從理論上詳細研究非對稱含錯學習問題和標準含錯學習問題關(guān)系，并證明在特定錯誤分布下非對稱含錯學習問題和含錯學習問題是多項式時間等價的，從而為基于非對稱含錯學習問題設(shè)計安全的格密碼算法奠定了理論基礎(chǔ)。Abstract: Due to the advantages such as the worst-case hardness assumption, lattice-based cryptography is believed to the most promising research direction in post-quantum cryptography. As one of the two main hard problems commonly used in lattice-based cryptography, Learning With Errors (LWE) problem is widely used in constructing numerous cryptosystems. In order to improve the efficiency of lattice-based cryptosystems, Zhang et al. (2019) introduced the Asymmetric LWE (ALWE) problem. In this paper, the relation between the ALWE problem and the standard LWE problem is studied, and it shows that for certain error distributions the two problems are polynomially equivent, which paves the way for constructing secure lattice-based cryptosystems from the ALWE problem.
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