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Universal elliptic Gauß sums for Atkin primes in Schoof's algorithm
Christian J. Berghoff
This work builds on earlier results. We define universal elliptic Gauß sums for Atkin primes in Schoof's algorithm for counting points on elliptic curves. Subsequently, we show the…
Efficient computation of universal elliptic Gauß sums
Christian J. Berghoff
In a former paper it has been shown that the elliptic Gauß sums, whose use has been proposed in the context of counting points on elliptic curves and primality tests, can be comput…
Universal elliptic Gauß sums and applications
Christian J. Berghoff
We present new ideas for computing elliptic Gauß sums, which constitute an analogue of the classical cyclotomic Gauß sums and whose use has been proposed in the context of counting…
Elliptic Gauß sums and Schoof's algorithm
Christian J. Berghoff
We present a new approach to handling the case of Atkin primes in Schoof's algorithm for counting points on elliptic curves over finite fields. Our approach is based on the theory…