Results 11 to 20 of about 117,996 (268)
Security enhanced user authentication protocol for wireless sensor networks using elliptic curves cryptography. [PDF]
Sensors (Basel), 2014 Choi Y +5 more
europepmc +2 more sources
Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography
Cybernetics and Information Technologies, 2021 The survey presents the evolution of Short Weierstrass elliptic curves after their introduction in cryptography. Subsequently, this evolution resulted in the establishment of present elliptic curve computational standards.
Abhishek Kunal +1 more
doaj +1 more source
Isogenies on twisted Hessian curves
Journal of Mathematical Cryptology, 2021 Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Vélu's formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic
Perez Broon Fouazou Lontouo +3 more
doaj +1 more source
Generalized Fibonacci Sequences for Elliptic Curve Cryptography
Mathematics, 2023 The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves.
Zakariae Cheddour +2 more
doaj +1 more source
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 +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
Rank zero elliptic curves induced by rational Diophantine triples [PDF]
, 2020 Rational Diophantine triples, i.e. rationals a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares, are often used in construction of elliptic curves with high rank. In this paper, we consider the opposite problem and ask how small can be the
Dujella, Andrej, Mikić, Miljen
core +3 more sources
On the ρ-values of complete families of pairing-friendly elliptic curves
Journal of Mathematical Cryptology, 2012 The parameter ρ of a complete family of pairing-friendly elliptic curves represents how suitable some given elliptic curves are in pairing-based cryptographic schemes. The superiority of the curves depends on how close ρ is to 1.
Okano Keiji
doaj +1 more source
Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-Weil lattices and their fields of definition [PDF]
, 2016 To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface.
Kumar, Abhinav, Kuwata, Masato
core +1 more source
International Journal of Mathematics and Mathematical Sciences, 2015 Elliptic curves have a wide variety of applications in computational number theory such as elliptic curve cryptography, pairing based cryptography, primality tests, and integer factorization.
Keisuke Hakuta
doaj +1 more source