Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 23, Issue.: 4

Original Research Article

LUCAS BASED EL-GAMAL CRYPTOSYSTEM IN THE ELLIPTIC CURVE GROUP OVER FINITE FIELD UNDER LENSTRA’S ATTACK

 

TZE JIN WONG1,2*, LEE FENG KOO1,2 AND PANG HUNG YIU1

1Department of Basic Science and Engineering, Universiti Putra Malaysia, Bintulu Campus, 97008 Bintulu, Sarawak, Malaysia.

2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Srdang, Selangor, Malaysia.

Abstracts

This paper reports on a Lenstra’s attack against the Lucas based El-Gamal Cryptosystem in the elliptic curve group over finite field. Lenstra’s attack is an attack to recover the secret factor of the order of elliptic curve group from a faulty signature. Results show that the success of the Lenstra’s attack depend on cryptographic algorithm implementation practice rather than the weakness of the cryptosystem itself.

Keywords :

Faulty signature; Lucas sequence; elliptic curve; encryption; decryption.