Encryption Using Lucas sequences L(Δ,pq) With Arithmetic on L(Δ,pq) via L(Δ,p) and L(Δ,q)

P. Anuradha Kameswari¹ , B. Ravitheja²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.178-186, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.178186

Online published on Feb 28, 2019

Copyright © P. Anuradha Kameswari, B. Ravitheja . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper we first established the ring structure on Lucas sequences L(Δ,N) from the group structure and semigroup structure with the two operations * and ∘ respectively. Using the arithmetic of * and ∘ on L(Δ,N) we propose a public key encryption scheme with the pair of Lucas sequences (V_m,U_m) based on the arithmetic of L(Δ,pq) via L(Δ,p) and L(Δ,q). The security of this encryption scheme is based on the discrete log problem of Lucas sequences(V_m,U_m).

Key-Words / Index Term :
Cryptosystem, Lucas sequences, discrete log problem

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