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Impact of the modulus switching technique on some attacks against learning problems

机译:模量切换技术对学习问题一些攻击的影响

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摘要

The modulus switching technique has been used in some cryptographic applications as well as in cryptanalysis. For cryptanalysis against the learning with errors (LWE) problem and the learning with rounding (LWR) problem, it seems that one does not know whether the technique is really useful or not. This work supplies a complete view of the impact of this technique on the decoding attack, the dual attack and the primal attack against both LWE and LWR. For each attack, the authors give the optimal formula for the switching modulus. The formulas get involved the number of LWE/LWR samples, which differs from the known formula in the literature. They also attain the corresponding sufficient conditions saying when one should utilise the technique. Surprisingly, restricted to the LWE/LWR problem that the secret vector is much shorter than the error vector, they also show that performing the modulus switching before using the so-called rescaling technique in the dual attack and the primal attack make these attacks worse than only exploiting the rescaling technique as reported by Bai and Galbraith at the Australasian conference on information security and privacy (ACISP) 2014 conference. As an application, they theoretically assess the influence of the modulus switching on the LWE/LWR-based second round NIST PQC submissions.
机译:模量切换技术已在某些加密应用以及密码分析中使用。对于用错误(LWE)问题和舍入(LWE)问题的学习的密码分析,似乎人们不知道该技术是否真的有用。这项工作提供了对这种技术对解码攻击的影响,双重攻击和LWE和LWW的原始攻击的完整视图。对于每次攻击,作者给出了开关模量的最佳配方。公式涉及LWE / LWR样品的数量,其不同于文献中的已知式。它们也达到相应的充分条件,说明一个人应该使用该技术时。令人惊讶的是,仅限于秘密矢量的LWE / LWR问题比误差向量短得多,他们还表明,在双攻击中使用所谓的重构技术之前执行模量切换,并使这些攻击更糟糕仅利用BAI和GALBRAITH在澳大利亚信息安全和隐私(ACISP)2014年会议上报告的重新分配技术。作为申请,理论上评估了模量切换对基于LWE / LWR的第二轮NIST PQC提交的影响。<?显示[AQ =“”ID =“Q4]”?><?显示[aq =“id =”q5“”?>

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