Constructing Supersingular Elliptic Curves

  title={Constructing Supersingular Elliptic Curves},
  author={Reinier Br{\"o}ker},
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. 
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