Results 61 to 70 of about 4,471 (200)
On singular moduli that are S-units
, 2020 Recently Yu. Bilu, P. Habegger and L. K\"uhne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime numbers there is no singular modulus that is an S-units.
Campagna, Francesco
core +1 more source
A survey on post‐quantum based approaches for edge computing security
WIREs Computational Statistics, Volume 16, Issue 1, January/February 2024.The distribution of reviewed papers by focused area. Abstract With the development of technology and its integration with scientific realities, computer systems continue to evolve as infrastructure. One of the most important obstacles in front of quantum computers with high‐speed processing is that its existing systems cause security vulnerabilities ...
Aykut Karakaya, Ahmet Ulu
wiley +1 more source
Generic Newton polygons for curves of given p-rank [PDF]
, 2013 We survey results and open questions about the $p$-ranks and Newton polygons of Jacobians of curves in positive characteristic $p$. We prove some geometric results about the $p$-rank stratification of the moduli space of (hyperelliptic) curves.
Achter, Jeff, Pries, Rachel
core
Pairing Optimizations for Isogeny‐Based Cryptosystems
IET Information Security, Volume 2024, Issue 1, 2024.In isogeny‐based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public key validation, and torsion basis generation. However, in most isogeny‐based protocols, the performance of pairing computations is unsatisfactory due to the high computational cost of the Miller function.
Shiping Cai +3 more
wiley +1 more source
On random sampling of supersingular elliptic curves
Annali di Matematica Pura ed Applicata (1923 -)Abstract We consider the problem of sampling random supersingular elliptic curves over finite fields of cryptographic size (SRS problem). The currently best-known method combines the reduction of a suitable complex multiplication (CM) elliptic curve and a random walk over some supersingular isogeny graph.
Mula, Marzio +2 more
openaire +3 more sources
The power operation structure on Morava E-theory of height 2 at the prime 3
, 2012 We give explicit calculations of the algebraic theory of power operations for a specific Morava E-theory spectrum and its K(1)-localization. These power operations arise from the universal degree-3 isogeny of elliptic curves associated to the E ...
Zhu, Yifei
core +1 more source
Generalization of Atkin’s orthogonal polynomials and supersingular elliptic curves [PDF]
Proceedings of the American Mathematical Society, 2012 In a 1998 paper, Kaneko and Zagier explain unpublished work of Atkin which exhibits an infinite sequence of polynomials with the property that when suitable polynomials are reduced mod p p for a prime p p , one gets the locus of supersingular elliptic curves.
openaire +2 more sources
THE ANTICYCLOTOMIC MAIN CONJECTURE FOR ELLIPTIC CURVES AT SUPERSINGULAR PRIMES [PDF]
Journal of the Institute of Mathematics of Jussieu, 2007 The Main Conjecture of Iwasawa theory for an elliptic curve is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by Perrin-Riou, Pollack, Kurihara, Kobayashi and Iovita and Pollack are required to handle this case in which many of the simplifying features of the ordinary setting break down.
IOVITA, ADRIAN, DARMON H.
openaire +2 more sources
, 2011 We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of power operations ...
Rezk, Charles
core +3 more sources
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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