A METHOD TO DECREASE THE COMPUTATION TIME FOR THE FOURTH
ORDER LUCAS SEQUENCE
Wong Tze Jin
1, 2
, Mohd. Rushdan Md Said 2, 3, Mohamed Othman 2, 4 and Koo Lee Feng 1,2
1
Department of Basic Sciences and Engineering,
Faculty of Agriculture and Food Sciences,
Universiti Putra Malaysia, Bintulu Campus
2
Institute for Mathematical Research,
Universiti Putra Malaysia
3
3
Department of Mathematics,
Faculty of Sciences,
Universiti Putra Malaysia
Faculty of Computer Science and Information Technology,
Universiti Putra Malaysia
email: sherlock.wong.tj@gmail.com
Abstract
The fourth order Lucas sequence is a linear recurrence relation based on quartic
polynomial. This sequence had been used to develop the LUC4,6 cryptosystem in 2007. As
we know, the efficiency is one of the crutial parts of the cryptosystem and it is ability to
generate the ciphertexts or recover the plaintext in a reasonable time. In this paper, a
method will be proposed to decrease the computation time for fourth order Lucas sequence
which is a part of the process encryption and decryption in the LUC 4,6 cryptosystem. This
method will be omitted some terms of the sequence to decrease the computation time.
Thus, if the LUC4,6 cryptosystem is using this method to compute the plaintexts and
ciphertexts, the computation time had been decrease.
Keywords: Lucas sequence; terms of sequence; computation time