Weak Fields for ECC

Alfred Menezes; Edlyn Teske; Annegret Weng

Paper 2003/128 Original: eprint.iacr.org/2003/128 ↗

Weak Fields for ECC

Alfred Menezes

Edlyn Teske

Annegret Weng

Abstract

We demonstrate that some finite fields, including GF(2^210) are weak for elliptic curve cryptography in the sense that any instance of the elliptic curve discrete logarithm problem for any elliptic curve over these fields can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We discuss the implications of our observations to elliptic curve cryptography, and list some open problems.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2003-06-27: last updated; 2003-06-27: published
Short URL: https://ia.cr/2003/128
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2003/128,
      author = {Alfred Menezes and Edlyn Teske and Annegret Weng},
      title = {Weak Fields for ECC},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/128},
      year = {2003},
      url = {https://eprint.iacr.org/2003/128}
}