Cryptology ePrint Archive: Report 2008/215

On Implementation of GHS Attack against Elliptic Curve Cryptosystems over Cubic Extension Fields of Odd Characteristics

Naoki Hashizume and Fumiyuki Momose and Jinhui Chao

Abstract: In this paper, we present algorithms for implementation of the GHS attack to Elliptic curve cryptosystems (ECC). In particular, we consider two large classes of elliptic curves over cubic extension fields of odd characteristics which have weak covering curves against GHS attack, whose existence have been shown recently. We show an algorithm to find definition equation of the covering curve and an algorithm to transfer DLP of the elliptic curve to Jacobian of the covering curve. An algorithm to test if the covering curve is hyperelliptic is also shown in the appendix.

Category / Keywords: Public-key cryptosystem, elliptic curve cryptosystem, cryptoanalysis, number theory

Date: received 14 May 2008, last revised 14 May 2008

Contact author: jchao at ise chuo-u ac jp

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Version: 20080523:071633 (All versions of this report)

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