Results 71 to 80 of about 42,992 (209)
Quantitative upper bounds related to an isogeny criterion for elliptic curves
Bulletin of the London Mathematical Society, Volume 56, Issue 8, Page 2661-2679, August 2024.Abstract For E1$E_1$ and E2$E_2$ elliptic curves defined over a number field K$K$, without complex multiplication, we consider the function FE1,E2(x)${\mathcal {F}}_{E_1, E_2}(x)$ counting nonzero prime ideals p$\mathfrak {p}$ of the ring of integers of K$K$, of good reduction for E1$E_1$ and E2$E_2$, of norm at most x$x$, and for which the Frobenius ...
Alina Carmen Cojocaru +2 more
wiley +1 more source
K3 surfaces of Kummer type in characteristic two
Bulletin of the London Mathematical Society, Volume 56, Issue 6, Page 1903-1919, June 2024.Abstract We discuss K3 surfaces in characteristic two that contain the Kummer configuration of smooth rational curves.
Igor V. Dolgachev
wiley +1 more source
Picard sheaves, local Brauer groups, and topological modular forms
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract We develop tools to analyze and compare the Brauer groups of spectra such as periodic complex and real K$K$‐theory and topological modular forms, as well as the derived moduli stack of elliptic curves. In particular, we prove that the Brauer group of TMF$\mathrm{TMF}$ is isomorphic to the Brauer group of the derived moduli stack of elliptic ...
Benjamin Antieau +2 more
wiley +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
, 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
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
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
core +3 more sources
Endomorphism algebras of QM abelian surfaces
, 2013 We determine endomorphism algebras of abelian surfaces with quaternion multiplication.Comment: 14 pages.
Yu, Chia-Fu
core +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
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.
core +1 more source