A Memory Efficient Version of Satoh's Algorithm

@inproceedings{Vercauteren2001AME,
  title={A Memory Efficient Version of Satoh's Algorithm},
  author={Frederik Vercauteren and Bart Preneel and Joos Vandewalle},
  booktitle={EUROCRYPT},
  year={2001}
}
In this paper we present an algorithm for counting points on elliptic curves over a finite field Fpn of small characteristic, based on Satoh’s algorithm. The memory requirement of our algorithm is O(n), where Satoh’s original algorithm needs O(n) memory. Furthermore, our version has the same run time complexity of O(n) bit operations, but is faster by a constant factor. We give a detailed description of the algorithm in characteristic 2 and show that the amount of memory needed for the… CONTINUE READING
Highly Cited
This paper has 46 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 14 references

Satoh's algorithm in characteristic 2

Math. Comput. • 2003
View 5 Excerpts
Highly Influenced

The canonical lift of an ordinary elliptic curve over a finite field and its point counting

T. Satoh
J. Ramanujan Math. Soc., • 2000
View 3 Excerpts
Highly Influenced

Elliptic curves and formal groups. Lecture notes prepared in connection with the seminars held at the Summer Institute on Algebraic Geometry, Whitney Estate

J. Lubin, J. P. Serre, J. Tate
Woods Hole, Massachusetts, • 1964
View 3 Excerpts
Highly Influenced

On Satoh’s algorithm and its implementation

M. Fouquet, P. Gaudry, R. Harley
J. Ramanujan Math. Soc., • 2000
View 2 Excerpts

Counting the number of points on an elliptic curve on a low-memory device

J. A. Csirik
1998
View 1 Excerpt

Quelques calculs en théorie des nombres

J. M. Couveignes
PhD thesis, Université de Bordeaux, • 1994
View 2 Excerpts

The number of points on an elliptic curve modulo a prime

A.O.L. Atkin
Series of e-mails to the NMBRTHRY mailing list, • 1992
View 2 Excerpts

Similar Papers

Loading similar papers…