论文标题
综合征解码问题的组合解决方案在Grassmann图上使用Copula
Combinatorial Solution of the Syndrome Decoding Problem using Copula on Grassmann graph
论文作者
论文摘要
来自综合征解码问题的计算硬度假设对于设计基于代码的密码系统的安全性很有用，这些密码系统可以安全地防止量子计算。由于使用从子空间建模的高度线性多项式方程的溶液中的复杂性，我们提出了通过使用Copula函数从边界测量图构建的Grassmann图中的子空间之间的依赖性。我们还使用副函数来估计这些子空间中的边际分布。此后，使用基于最大似然的估计方法来搜索最大化条件分布的代码字，并在此过程中近似解决问题的解决方案。从模拟获得的位错误率性能的结果表明，所提出的解决方案的性能要比信息集解码方法更好。
Computational hardness assumption from the syndrome decoding problem has been useful in designing the security of code based cryptosystem that are safe against quantum computing. Due to complexities in solution using high degree linearized polynomial equations modeled from subspaces, we proposed exploiting the dependency between subspaces in a Grassmann graph constructed from Boundary measurement maps by using copula functions. We also used copula functions to estimate the marginal distribution in these subspaces. Thereafter, the Maximum likelihood based estimation approach was used to search the codeword that maximizes the conditional distribution and in the process approximate a solution to the problem. Results of the Bit Error Rate performance obtained from simulation shows that the proposed solution performs better than the information set decoding method.
