33 citations · 218 across the 26 of their papers we have counts for
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math.NT2009★ 33 cited
Amicable pairs and aliquot cycles for elliptic curves
Katherine E. Stange, Joseph H. Silverman
An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs…
math.NT2009★ 1 cited
Character sums with division polynomials
Igor E Shparlinski, Katherine E. Stange
We obtain nontrivial estimates of quadratic character sums of division polynomials , , evaluated at a given point on an elliptic curve over a finite field o…
math.NT2009★ 4 cited
Pairings on hyperelliptic curves
Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm +3
We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairing-based cryptograph…