论文标题
线性复发密码学：高阶线性复发的金色的加密术
Linear recurrent cryptography: golden-like cryptography for higher order linear recurrences
论文作者
论文摘要
我们根据任何允许对野蛮力和选择的明文攻击的序列的线性复发序列开发矩阵密码学。特别是，我们解决了概括误差检测和校正算法的问题，以前仅以特殊形式的复发而闻名。它们基于证明在Golden $ Q $ -Matrix具有强大的Perron-Frobenius属性的情况下，证明了检查关系（密文满足的不平等）。当复发的特征多项式是PISOT多项式时，这些算法被证明是特别有效的。最后，我们概述了为满足我们条件的复发而产生的算法。
We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and correction algorithms of golden cryptography previously known only for recurrences of a special form. They are based on proving the checking relations (inequalities satisfied by the ciphertext) under the condition that the analog of the golden $Q$-matrix has the strong Perron-Frobenius property. These algorithms are proved to be especially efficient when the characteristic polynomial of the recurrence is a Pisot polynomial. Finally, we outline algorithms for generating recurrences that satisfy our conditions.
