LUCAS BASED EL-GAMAL CRYPTOSYSTEM IN THE ELLIPTIC CURVE GROUP OVER FINITE FIELD UNDER LENSTRA’S ATTACK
TZE JIN WONG *
Department of Basic Science and Engineering, Universiti Putra Malaysia, Bintulu Campus, 97008 Bintulu, Sarawak, Malaysia and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Srdang, Selangor, Malaysia.
LEE FENG KOO
Department of Basic Science and Engineering, Universiti Putra Malaysia, Bintulu Campus, 97008 Bintulu, Sarawak, Malaysia and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Srdang, Selangor, Malaysia.
PANG HUNG YIU
Department of Basic Science and Engineering, Universiti Putra Malaysia, Bintulu Campus, 97008 Bintulu, Sarawak, Malaysia.
*Author to whom correspondence should be addressed.
Abstract
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