Results 11 to 20 of about 38,603 (168)
CM liftings of Supersingular Elliptic Curves [PDF]
Journal de Théorie des Nombres de Bordeaux, 2009 Assuming GRH, we present an algorithm which inputs a prime $p$ and outputs the set of fundamental discriminants $D<0$ such that the reduction map modulo a prime above $p$ from elliptic curves with CM by $\order_{D}$ to supersingular elliptic curves in characteristic $p$. In the algorithm we first determine an explicit constant $D_p$ so that $|D|>
Ben Kane
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Supersingular elliptic curves [PDF]
, 2021 In the previous chapter, we showed that Brandt matrices for an order in a definite quaternion algebra B contain a wealth of arithmetic. In the special case where \({{\,\mathrm{disc}\,}}B=p\) is prime, there is a further beautiful connection between Brandt matrices and the theory of supersingular elliptic curves, arising from the following important ...
John Voight
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On supersingular elliptic curves and hypergeometric functions [PDF]
Involve, a Journal of Mathematics, 2012 The Legendre family of elliptic curves has the remarkable property that both its periods and its supersingular locus have descriptions in terms of the hypergeometric function [math] . In this work we study elliptic curves and elliptic integrals with respect to the hypergeometric functions [math] and [math] , and prove that the supersingular [math ...
Keenan Monks
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The main conjecture for CM elliptic curves at supersingular primes [PDF]
Annals of Mathematics, 2004 At a prime of ordinary reduction, the Iwasawa ``main conjecture'' for elliptic curves relates a Selmer group to a $p$-adic $L$-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the $p$-adic $L$-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of
Robert Pollack, Karl Rubin
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Supersingular Elliptic Curves and Moonshine [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2019 We generalize a theorem of Ogg on supersingular $j$-invariants to supersingular elliptic curves with level. Ogg observed that the level one case yields a characterization of the primes dividing the order of the monster. We show that the corresponding analyses for higher levels give analogous characterizations of the primes dividing the orders of other ...
Victor Manuel Aricheta
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APPROACH TO CHECKING THE SUPERSINGULARITY OF ELLIPTIC CURVES AND CALCULATING THEIR ORDER
INFORMATION TECHNOLOGY AND SOCIETY, 2021 Ruslan SKURATOVSKYI
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Simultaneous supersingular reductions of CM elliptic curves [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2022 Abstract We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show – under additional congruence assumptions on the CM order – that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order ...
Menny Aka +3 more
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On oriented supersingular elliptic curves [PDF]
Finite Fields and Their Applications, 2021 We revisit theoretical background on OSIDH, that is an isogeny-based key-exchange protocol proposed by Col and Kohel at NutMiC 2019. We give a proof of a fundamental theorem for OSIDH. The theorem was stated by Col and Kohel without proof. Furthermore, we consider parameters of OSIDH, give a sufficient condition on the parameters that the protocol ...
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On random sampling of supersingular elliptic curves
Annali di Matematica Pura ed ApplicataM G Mula, Nadir Murru, Federico Pintore
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Batching CSIDH Group Actions using AVX-512
Transactions on Cryptographic Hardware and Embedded Systems, 2021 Commutative Supersingular Isogeny Diffie-Hellman (or CSIDH for short) is a recently-proposed post-quantum key establishment scheme that belongs to the family of isogeny-based cryptosystems.
Hao Cheng +4 more
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