Results 71 to 80 of about 4,610 (199)
Supersingular K3 Surfaces are Unirational
, 2014 We show that supersingular K3 surfaces in characteristic $p\geq5$ are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda.
Liedtke, Christian
core +1 more source
Non-commutative p-adic L-functions for supersingular primes
, 2012 Let E/Q be an elliptic curve with good supersingular reduction at p with a_p(E)=0. We give a conjecture on the existence of analytic plus and minus p-adic L-functions of E over the Zp-cyclotomic extension of a finite Galois extension of Q where p is ...
ANTONIO LEI, Haran S., Serre J.-P.
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An algorithm for constructing certain differential operators in positive characteristic
Le Matematiche, 2015 Given a non-zero polynomial f in a polynomial ring R with coefficients in a finite field of prime characteristic p, we present an algorithm to compute a differential operator δ which raises 1/ f to its pth power. For some specific families of polynomials,
Alberto F. Boix +2 more
doaj
Non Supersingular Elliptic Curves for Public Key Cryptosystems [PDF]
, 2007 For public key cryptosystems multiplication on elliptic curves can be used instead of exponentiation in finite fields. One attack to such a system is embedding the elliptic curve group into the multiplicative group of a finite field via weilpairing; calculating the discrete logarithm on the curve by solving the discrete logarithm in the finite field ...
Beth, Thomas, Schaefer, Frank
openaire +1 more source
Distortion maps for genus two curves [PDF]
, 2005 Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g.
Galbraith, Steven D. +3 more
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On the Existence of Supersingular Curves of Given Genus [PDF]
, 1994 We give a method to construct explicitly a supersingular curve of given genus g in characteristic 2.Comment: 9 pages, plain TeX, UvA-report 94 ...
van der Geer, Gerard +1 more
core +3 more sources
Complex Multiplication Tests for Elliptic Curves
, 2004 We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm can
Charles, Denis
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Shimura curves and explicit descent obstructions via level structure [PDF]
, 2015 We give large families of Shimura curves defined by congruence conditions, all of whose twists lack $p$-adic points for some $p$. For each such curve we give analytically large families of counterexamples to the Hasse principle via the descent (or ...
Stankewicz, James
core
Local invariants of isogenous elliptic curves
, 2013 We investigate how various invariants of elliptic curves, such as the discriminant, Kodaira type, Tamagawa number and real and complex periods, change under an isogeny of prime degree p.
Dokchitser, Tim, Dokchitser, Vladimir
core