Results 11 to 20 of about 2,244,879 (350)
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 ...
N. Koblitz
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Elliptic nets and elliptic curves [PDF]
Algebra & Number Theory, 2010 An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve.
Ayad +5 more
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On Pythagorean elliptic curves [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 For a primitive Pythagorean triple \((a,b,c)\) with \(a\) even, let \(E= E(a,b,c)\) be the elliptic curve \(y^ 2= x(x- a^ 2)(x- c^ 2)\). The author gives necessary and sufficient conditions for \(E/\mathbb{Q}\) to have non-zero rank. Said conditions are expressed in terms of the existence of non-zero solutions to a system of two diophantine equations ...
Norio Adachi
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Journal of Geometry and Physics, 1995 A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus one considered as algebraic varieties, particularly their relation with their Picard groups. This is the simplest setting in which to study the geometric consequences of the fact that certain cohomology groups of super Riemann surfaces are not freely generated ...
Jeffrey M. Rabin
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Regulators of Elliptic Curves [PDF]
International Mathematics Research Notices, 2018 Abstract We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic $p>0$. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field.
Autissier, Pascal +2 more
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Twists of Elliptic Curves [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2017 In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set $H^1\big(\operatorname{G}_{\overline{K}/K}, \operatorname{Aut}_ ...
Kronberg, M., Soomro, M.A., Top, J.
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Kleptographic Attack on Elliptic Curve Based Cryptographic Protocols
IEEE Access, 2020 Kleptography is the study of pilfering secure data secretly and subliminally. The concept of inserting backdoors was introduced two decades ago by Young and Yung. However, still it is a serious threat for modern cryptography.
Anum Sajjad +5 more
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On the algebra of elliptic curves [PDF]
Proceedings of the Edinburgh Mathematical Society, 2023 AbstractIt is argued that a nonsingular elliptic curve admits a natural or fundamental abelian heap structure uniquely determined by the curve itself. It is shown that the set of complex analytic or rational functions from a nonsingular elliptic curve to itself is a truss arising from endomorphisms of this heap.
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Combined small subgroups and side-channel attack on elliptic curves with cofactor divisible by 2m [PDF]
International Journal of Electronics and Telecommunications, 2019 Nowadays, alternative models of elliptic curves like Montgomery, Edwards, twisted Edwards, Hessian, twisted Hessian, Huff’s curves and many others are very popular and many people use them in cryptosystems which are based on elliptic curve cryptography ...
Michał Wrońska
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Twisted Edwards Elliptic Curves for Zero-Knowledge Circuits
Mathematics, 2021 Circuit-based zero-knowledge proofs have arose as a solution to the implementation of privacy in blockchain applications, and to current scalability problems that blockchains suffer from.
Marta Bellés-Muñoz +4 more
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