Weak Fields for ECC

Alfred Menezes; Edlyn Teske; Annegret Weng

Paper 2003/128

Weak Fields for ECC

Alfred Menezes, Edlyn Teske, and 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): PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): ajmeneze @ uwaterloo ca
History: 2003-06-27: received
Short URL: https://ia.cr/2003/128
License: CC BY

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}
}