Results 31 to 40 of about 136,439 (162)

Elliptic Curve Cryptosystems [PDF]

Mathematics of Computation, 1987
We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially ...
openaire   +2 more sources

Multi-Functional Resource-Constrained Elliptic Curve Cryptographic Processor

IEEE Access, 2023
With the rising data evolution, the demand for secured communications over networks is rising immensely. Elliptic Curve Cryptography (ECC) provides an attractive solution to fulfill the requirements of modern network applications.
Binh Kieu Do-Nguyen, Cuong Pham-Quoc, Ngoc-Thinh Tran, Cong-Kha Pham, Trong-Thuc Hoang   +4 more
doaj   +1 more source

On families of 9-congruent elliptic curves [PDF]

, 2015
We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over Q, i.e.
Fisher, Tom
core   +1 more source

Elliptic curve and k-Fibonacci-like sequence

Scientific African, 2023
In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib   +2 more
doaj  

Visualising Sha[2] in Abelian Surfaces [PDF]

, 2002
Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another elliptic ...
Bruin, Nils
core   +2 more sources

Methods for using elliptic curves in cryptography [PDF]

E3S Web of Conferences
Elliptic Curve Cryptography (ECC), a significant modern cryptography, is more secure and robust than most others due to its construction using an elliptic curve and the application of mathematical operations for encryption and key generation. Furthermore,
Obukhov Vadim, Qadamova Zulayho, Sobirov Muzaffar, Ergashev Otabek, Nabijonov Ravshanbek   +4 more
doaj   +1 more source

A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves

Transactions of the London Mathematical Society, 2021
Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
doaj   +1 more source

Root numbers and ranks in positive characteristic [PDF]

, 2005
For a global field K and an elliptic curve E_eta over K(T), Silverman's specialization theorem implies that rank(E_eta(K(T)))
Conrad, B., Conrad, K., Helfgott, H.
core   +6 more sources

FPGA Based High Speed SPA Resistant Elliptic Curve Scalar Multiplier Architecture

International Journal of Reconfigurable Computing, 2016
The higher computational complexity of an elliptic curve scalar point multiplication operation limits its implementation on general purpose processors.
Khalid Javeed, Xiaojun Wang
doaj   +1 more source

Local root numbers of elliptic curves over dyadic fields [PDF]

, 2015
We consider an elliptic curve over a dyadic field with additive, potentially good reduction. We study the finite Galois extension of the dyadic field generated by the three-torsion points of the elliptic curve.
Imai, Naoki
core   +2 more sources