Results 81 to 90 of about 42,992 (209)
Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?
, 2005 The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (DLOG) has the same difficulty for all ...
Jao, David +2 more
core +2 more sources
Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22
, 2015 In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way.
Brandhorst, Simon
core +1 more source
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
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
On the Euler characteristics of signed Selmer groups
, 2019 Let $p$ be an odd prime number, and $E$ an elliptic curve defined over a number field with good reduction at every prime of $F$ above $p$. In this short note, we compute the Euler characteristics of the signed Selmer groups of $E$ over the cyclotomic ...
Ahmed, Suman, Lim, Meng Fai
core +1 more source
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
core +1 more source
On the vanishing of cohomologies of $p$-adic Galois representations associated with elliptic curves
, 2014 Let $K$ be a $p$-adic field and $E$ an elliptic curve over $K$ with potential good reduction. For some large Galois extensions $L$ of $K$ containing all $p$-power roots of unity, we show the vanishing of certain Galois cohomology groups of $L$ with ...
Dimabayao, Jerome T.
core
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
European Journal of Pure and Applied MathematicsThe Elliptic Curve Cryptography (ECC) is one of the most prominent Asymmetric-based cryptosystems as it affords a higher level of security with small keys.
Waleed Abdulraheem
semanticscholar +1 more source
Higher codimension Iwasawa theory for elliptic curves with supersingular reduction
Annales mathématiques du Québec, 2023 26 ...
openaire +2 more sources