论文标题
基于扭曲的二面体组代数的系统的隐脑分析
Cryptanalysis of a System based on Twisted Dihedral Group Algebras
论文作者
论文摘要
基于鲜为人知的算法问题构建的几种加密协议，例如非交通性组，组环，半群等声称量子安全性的问题。因此，严格检查这些算法问题的复杂性是研究的重要主题。在本文中，我们在二面体组的所谓扭曲组代数中，基于分解类型问题的公共密钥交换系统的隐性分析，上面是有限字段$ \ fq $。我们的分析方法依赖于将原始问题的代数减少到涉及循环矩阵的$ \ fq $之上的一组方程，以及随后对这些方程式的解决方案。我们的攻击在多项式时间内进行，并以作者提供的参数值的概率至少$ 90 $ 90 $。我们还表明，基于非共同结构的潜在算法问题可能被称为交换性半群动作问题。
Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods within their specific proposed platforms. A rigorous examination of the complexity of these algorithmic problems is therefore an important topic of research. In this paper, we present a cryptanalysis of a public key exchange system based on a decomposition-type problem in the so-called twisted group algebras of the dihedral group $D_{2n}$ over a finite field $\fq$. Our method of analysis relies on an algebraic reduction of the original problem to a set of equations over $\fq$ involving circulant matrices, and a subsequent solution to these equations. Our attack runs in polynomial time and succeeds with probability at least $90$ percent for the parameter values provided by the authors. We also show that the underlying algorithmic problem, while based on a non-commutative structure, may be formulated as a commutative semigroup action problem.
