Collecting Super Singular Elliptic Curves (pp. 269-273)
Authors: Reinier Broker
Abstract: 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((logq)3). We illustrate the algorithm by showing how to construct supersingular curves of prime order. Such curves can readily be used for pairing based cryptography.