CONSTRUCTING SUPERSINGULAR ELLIPTIC CURVES

@inproceedings{Brker2007CONSTRUCTINGSE,
  title={CONSTRUCTING SUPERSINGULAR ELLIPTIC CURVES},
  author={Reinier Br{\"o}ker},
  year={2007}
}
We give an algorithm that constructs, on input of a prime power q and an integer t, a supersingular elliptic curve over Fq with trace of Frobenius t in case such a curve exists. If GRH holds true, the expected run time of our algorithm is e O((log q)). We illustrate the algorithm by showing how to construct supersingular curves of prime order. Such curves can readily be used for pairing based cryptography. 

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
SHOWING 1-8 OF 8 REFERENCES

Primes of the form x2 + ny2

  • D. A. Cox
  • 1989

Elliptic functions, Springer Graduate Texts

  • S. Lang
  • in Mathematics,
  • 1987

Horn , A heuristic asymptotic formula concerning the distribution of prime numbers

  • R. A. P. T. Bateman
  • Math . of Comp .

Similar Papers

Loading similar papers…