论文标题
某些沙珀组家族的离散对数问题
Discrete logarithm problem in some families of sandpile groups
论文作者
论文摘要
Biggs提出了依靠离散对数问题的难度的密码系统的某些修饰轮图的SandPile组。布莱克本（Blackburn）和独立的shokrieh表明，离散对数问题是有效解决的。我们研究了Shokrieh的方法，以使Sandpile组不是循环的，即方循环图和车轮图。了解该组的发电机或Laplacian矩阵的伪源的形式使问题更加脆弱。在所谓的细分香蕉图的情况下，我们还考虑了离散的对数问题。在某些情况下，沙珀组是循环的，并且已经知道发电机，并且可以在不计算拉普拉斯矩阵的伪源的情况下解决离散的对数问题。
Biggs proposed the sandpile group of certain modified wheel graphs for cryptosystems relying on the difficulty of the discrete logarithm problem. Blackburn and independently Shokrieh showed that the discrete logarithm problem is efficiently solvable. We study Shokrieh's method in cases of graphs such that the sandpile group is not cyclic, namely the square cycle graphs and the wheel graphs. Knowing generators of the group or the form of the pseudoinverse of the Laplacian matrix makes the problem more vulnerable. We also consider the discrete logarithm problem in case of the so-called subdivided banana graphs. In certain cases the sandpile group is cyclic and a generator is known and one can solve the discrete logarithm problem without computing the pseudoinverse of the Laplacian matrix.
