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

Naoki Hashizume; Fumiyuki Momose; Jinhui Chao

Paper 2008/215

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

Naoki Hashizume, 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.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Public-key cryptosystem elliptic curve cryptosystem cryptoanalysis number theory
Contact author(s): jchao @ ise chuo-u ac jp
History: 2008-05-23: received
Short URL: https://ia.cr/2008/215
License: CC BY

BibTeX

@misc{cryptoeprint:2008/215,
      author = {Naoki Hashizume and Fumiyuki Momose and Jinhui Chao},
      title = {On Implementation of {GHS} Attack against Elliptic Curve Cryptosystems over Cubic Extension Fields of Odd Characteristics},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/215},
      year = {2008},
      url = {https://eprint.iacr.org/2008/215}
}