Linear recurrent cryptography: golden-like cryptography for higher order linear recurrences

Autor:	Koshkin, Sergiy, Rodriguez, Daniel
Rok vydání:	2022
Předmět:	Computer Science - Cryptography and Security Computer Science - Discrete Mathematics Mathematics - Number Theory Mathematics - Spectral Theory 94A60 11B37 15A48 15A36 15A18 11B39 11C20 94B60 94B25 11B37 15B36 11K16
Zdroj:	Discrete Mathematics, Algorithms and Applications, 2022
Druh dokumentu:	Working Paper
DOI:	10.1142/S179383092250094X
Popis:	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. Comment: 27 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.11411 Zobrazit plný text záznamu View this record from Arxiv