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.

翻译：我们开发基于线性重复序列的矩阵加密法, 以确保对野蛮武力和选定的纯文本攻击进行加密。 特别是, 我们解决了一般化的黄金加密算法的错误检测和纠正算法问题, 先前只对特殊形式的重现有所了解。 这些算法是基于验证核对关系( 由密码文本所满足的不平等), 条件是金价基的模拟具有强大的 Perron- Frobenius 属性。 这些算法被证明特别有效, 当重现的特性多元体为 Pisot 多元模型时。 最后, 我们概述了产生符合我们条件的复发的算法 。