Sains Malaysiana 41(7)(2012): 907–910

Key Exchange in Elliptic Curve Cryptography Based on the Decomposition Problem

(Pertukaran Kekunci dalam Lengkungan Kriptografi Eliptik berdasarkan Masalah Perlupusan)

Hilyati Hanina Zazali & Wan Ainun Mior Othman*

Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya

50603 Kuala Lumpur, Malaysia

Diserahkan: 30 Disember 2010 / Diterima: 21 Februari 2012

ABSTRACT

In this paper, we presented a new key exchange method based on decomposition problem for elliptic curve cryptography. We showed that our key exchange method was not only an alternative method for designing keys in cryptography, but it also has improved security condition from the previous key exchange based on decomposition problem over non-commutative groups. We proposed elliptic an curve cryptography to be the new platform for our key exchange protocol and showed how it was implemented. The security of our protocol was based on discrete logarithm problem, which was not infeasible and strictly difficult to retrieve in elliptic curve cryptography without any prior knowledge.

Keywords: Discrete logarithm problem; elliptic curve cryptography; key exchange using decomposition problem; non-commutative groups

ABSTRAK

Kertas ini membentangkan satu kaedah pertukaran kekunci baru berdasarkan masalah pelupusan untuk lengkungan eliptik kriptografi. Kaedah pertukaran ini bukan sahaja suatu kaedah alternatif bagi mereka cipta kekunci dalam kriptografi, tetapi ia juga menambah baik lagi sistem keselamatan berbanding kaedah pertukaran kekunci berdasarkan masalah pelupusan tak kalis tukar tertib yang terdahulu. Lengkungan kriptografi eliptik akan digunakan sebagai platform utama dalam kaedah pertukaran kekunci berdasarkan masalah pelupusan tak kalis tukar tertib dan bagaimana kaedah aplikasinya akan ditunjukkan. Keselamatan bagi protokol baru ini adalah berdasarkan penyelesaian masalah diskrit logarithma dalam lengkungan eliptik kriptografi, dan kaedah ini adalah tak tersaur dan sukar untuk diselesaikan tanpa syarat-syarat tertentu.

Kata kunci: Kumpulan tak kalis tukar tertib; lengkungan elliptik kriptografi; masalah diskrit logaritma; pertukaran kekunci bagi masalah perlupusan

RUJUKAN

Agnew, G.B., Mullin R.C. & Vanstone S.A. 1993. An implementation of Elliptic Curve Cryptosystems over, IEEE Journal On Selected Area Communication11(5): 804-813.

Forouzan, B.A. 2008. Cryptography and Network Security. 1st ed. pp. 98 -103. New York: McGraw-Hill.

Koblitz, N., Menezes, A. & Vanstone, S. 2000. The State of Elliptic Curve Cryptography, Designs, Codes and Cryptography 19(5): 173-193.

Shpilrain, V. & Ushakov, A. 2005. A New Key Exchange Protocol Based on the Decomposition Problem. International Association for Cryptologic Research, available at: eprint.iacr.org/2005/447.pdf

Závadský, P. & Horňanová J. 2008. Group Signatures and Elliptic Curve Cryptography. Bezadis Cryptography Symposium, available at: bezadis.ics.upjs.sk/old/cryptosymposium/files/paper15.pdf

*Pengarang untuk surat-menyurat; email: wanainun@um.edu.my