A Discrete Logarithm Attack on Elliptic Curves

Otto Johnston

Paper 2010/575

A Discrete Logarithm Attack on Elliptic Curves

Otto Johnston

Abstract

We give an improved index calculus attack for a large class of elliptic curves. Our algorithm works by efficiently transferring the group structure of an elliptic curve to a weaker group. The running time of our attack poses a significant and realistic threat to the security of the elliptic curves in this class. As a consequence of our construction, we will also derive entirely new point counting algorithms. These algorithms set new run-time complexity records. We discuss implementations of these algorithms and give examples.

Note: Algorithms are available at www.ottojohnston.com/dlp

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): mail @ ottojohnston com
History: 2010-11-11: received
Short URL: https://ia.cr/2010/575
License: CC BY

BibTeX

@misc{cryptoeprint:2010/575,
      author = {Otto Johnston},
      title = {A Discrete Logarithm Attack on Elliptic Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2010/575},
      year = {2010},
      url = {https://eprint.iacr.org/2010/575}
}