The Discrete Logarithm Problem on Elliptic Curves of Trace One

Nigel P. Smart

Journal of Cryptology 1999

Time bound

Polynomial time in log p for trace-one curves

Space bound

Not extracted from the source

Source / version date

Oct 1997

Comparison variant

Anomalous prime-field curves

Cost scale

Expression only

Assumptions and source notes

The HP technical report (October 1997), subsequently published in Journal of Cryptology (1999), gives the p-adic attack for #E(F_p)=p. Its stated linear algorithm is not translated into a bit-complexity exponent here. This exceptional-family attack does not solve general ECDLP.

Source location

HPL-97-128 abstract and construction
Version: HPL-97-128, October 1997; journal publication 1999

Primary source ↗

@article{smart97,
  author = {Nigel P. Smart},
  title = {{The Discrete Logarithm Problem on Elliptic Curves of Trace One}},
  journal = {Journal of Cryptology 12(3), 193–196; earlier report HPL-97-128},
  year = {1999},
  doi = {10.1007/s001459900052},
  url = {https://research-information.bris.ac.uk/en/publications/the-discrete-logarithm-problem-on-elliptic-curves-of-trace-one/},
  keywords = {elliptic curves, anomalous curves, trace one},
  cr_date = {1997-10-31},
  cr_date_precision = {month},
  cr_status = {published},
  cr_venue = {Journal of Cryptology 12(3), 193–196; earlier report HPL-97-128},
  cr_author_ids = {nigel-p-smart}
}