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Licensed Unlicensed Requires Authentication Published by De Gruyter June 5, 2017

On the k-th order lfsr sequence with public key cryptosystems

Bariş Bülent Kirlar and Melek Çİl
From the journal Mathematica Slovaca


In this paper, we propose a novel encryption scheme based on the concepts of the commutative law of the k-th order linear recurrences over the finite field đť”˝q for k > 2. The proposed encryption scheme is an ephemeral-static, which is useful in situations like email where the recipient may not be online. The security of the proposed encryption scheme depends on the difficulty of solving some Linear Feedback Shift Register (LFSR) problems. It has also the property of semantic security. For k = 2, we propose another encryption scheme by using the commutative law of Lucas and Fibonacci sequences having also the same security as proposed for k > 2.

MSC 2010: 11B37; 94A60

E-mail: ,

(Communicated by Stanislav Jakubec)


The authors thank the anonymous referees for their detailed and very helpful comments.


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Received: 2015-1-16
Accepted: 2015-10-13
Published Online: 2017-6-5
Published in Print: 2017-6-27

© 2017 Mathematical Institute Slovak Academy of Sciences