Fast Elliptic Curve Point Counting Using Gaussian Normal Basis

@inproceedings{Kim2002FastEC,
  title={Fast Elliptic Curve Point Counting Using Gaussian Normal Basis},
  author={Hae Young Kim and Jung Youl Park and Jung Hee Cheon and Je Hong Park and Jae Heon Kim and Sang Geun Hahn},
  booktitle={ANTS},
  year={2002}
}
In this paper we present an improved algorithm for counting points on elliptic curves over finite fields. It is mainly based on SatohSkjernaa-Taguchi algorithm [SST01], and uses a Gaussian Normal Basis (GNB) of small type t ≤ 4. In practice, about 42% (36% for prime N) of fields in cryptographic context (i.e., for p = 2 and 160 < N < 600) have such bases. They can be lifted from FpN to ZpN in a natural way. From the specific properties of GNBs, efficient multiplication and the Frobenius… CONTINUE READING
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