Results 11 to 20 of about 4,804,991 (93)
On the distribution of orders of Frobenius action on $\ell$-torsion of abelian surfaces [PDF]
PRIKLADNAYa DISKRETNAYa MATEMATIKA, 2020 The computation of the order of Frobenius action on the $\ell$-torsion is a part of Schoof-Elkies-Atkin algorithm for point counting on an elliptic curve $E$ over a finite field $\mathbb{F}_q$.
N. Kolesnikov, S. Novoselov
semanticscholar +5 more sources
Construction of Secure Random Curves of Genus 2 over Prime Fields
International Conference on the Theory and Application of Cryptographic Techniques, 2004 International audienceFor counting points of Jacobians of genus 2 curves defined over large prime fields, the best known method is a variant of Schoof's algorithm.
P. Gaudry, É. Schost
semanticscholar +4 more sources
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication [PDF]
arXiv.org, 2017 Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit ...
Sean Ballentine +6 more
semanticscholar +3 more sources
Counting points on abelian surfaces over finite fields with Elkies's method [PDF]
arXiv.org, 2022 We generalize Elkies's method, an essential ingredient in the SEA algorithm to count points on elliptic curves over finite fields of large characteristic, to the setting of p.p. abelian surfaces.
J. Kieffer
semanticscholar +1 more source
Speeding-Up Elliptic Curve Cryptography Algorithm
IACR Cryptology ePrint Archive, 2022 In recent decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice.
Diana Maimuţ, A. Matei
semanticscholar +1 more source
Criterions of Supersinguliarity and Groups of Montgomery and Edwards Curves in Cryptography
WSEAS Transactions on Mathematics, 2021 We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves.
R. Skuratovskii, V. Osadchyy
semanticscholar +1 more source
Elliptic and Edwards Curves Order Counting Method
, 2021 We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves.
R. Skuratovskii, V. Osadchyy
semanticscholar +1 more source
Using zeta functions to factor polynomials over finite fields [PDF]
Arithmetic Geometry: Computation and
Applications, 2017 In 2005, Kayal suggested that Schoof's algorithm for counting points on elliptic curves over finite fields might yield an approach to factor polynomials over finite fields in deterministic polynomial time.
B. Poonen
semanticscholar +1 more source
Counting points on hyperelliptic curves over finite fields [PDF]
, 2000 International audienceWe describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an ...
D.G. Cantor +21 more
core +3 more sources
Data Prevention Technique For Securing The Data [PDF]
, 2021 The main aim of this paper is to safeguard information through data security and is considered convergence, exploration, infiltration, and footprint. Cloud computing can be a computer-based type of computer that provides numerous PCs and devices looking ...
et. al., Christy A,
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