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arXiv 2107.05924cs.CR
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一种基于多项式映射的密钥交换协议的改进

An Improvement of a Key Exchange Protocol Relying on Polynomial Maps

Keita Suzuki, Koji Nuida

摘要:

Akiyama等人(Int.J.Math.Indust.,2019)提出了一种后量子密钥交换协议,该协议基于求解多元非线性多项式方程组的难度,但具有不同于普通多元密码学的设计策略。他们的协议有两个版本,一个原始的一个和一个修改的一个,其中修改的一个有一个权衡,其安全性得到加强,而它有非零的错误概率在建立一个共同的密钥。事实上,他们的论文中的评估表明,使用所提出的参数集的修改后的协议无法建立公共密钥的概率高得不切实际。在本文中,我们改进了Akiyama等人的成功概率。的密钥交换协议在保证安全性的前提下,通过将正确公共密钥的每个组成部分从整个系数域限制到它的一个小的子集,对密钥交换协议进行了显著的改进。我们给出的理论和实验评估表明,我们提出的参数集,我们的协议预计将实现故障概率$2^{-120}$和$128$位安全级别。

英文摘要:

Akiyama et al. (Int. J. Math. Indust., 2019) proposed a post-quantum key exchange protocol that is based on the hardness of solving a system of multivariate non-linear polynomial equations but has a design strategy different from ordinary multivariate cryptography. Their protocol has two versions, an original one and a modified one, where the modified one has a trade-off that its security is strengthened while it has non-zero error probability in establishing a common key. In fact, the evaluation in their paper suggests that the probability of failing to establish a common key by the modified protocol with the proposed parameter set is impractically high. In this paper, we improve the success probability of Akiyama et al.'s modified key exchange protocol significantly while keeping the security, by restricting each component of the correct common key from the whole of the coefficient field to its small subset. We give theoretical and experimental evaluations showing that our proposed parameter set for our protocol is expected to achieve both failure probability $2^{-120}$ and $128$-bit security level.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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