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Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform [PDF]
Sensors, 2020 We implement elliptic curve cryptography on the MSP430 which is a commonly used microcontroller in wireless sensor network nodes. We use the number theoretic transform to perform finite field multiplication and squaring as required in elliptic curve ...
Utku Gulen, Selcuk Baktir
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Armed with Faster Crypto: Optimizing Elliptic Curve Cryptography for ARM Processors [PDF]
SensorsElliptic curve cryptography is a widely deployed technology for securing digital communication. It is the basis of many cryptographic primitives such as key agreement protocols, digital signatures, and zero-knowledge proofs.
Ruben De Smet +4 more
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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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On Pythagorean elliptic curves [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 Norio Adachi
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The review on elliptic curves as cryptographic pairing groups [PDF]
Mathematics and Computational Sciences, 2021 Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted by an addition operation that forms a group structure. The motivation of this study is the mathematics behind that elliptic curve to the applicability within a ...
E Khamseh
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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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Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography
Cybernetics and Information Technologies, 2021 Short Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature
Abhishek Kunal +1 more
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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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Speeding-Up Elliptic Curve Cryptography Algorithms
Mathematics, 2022 In recent decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice.
Diana Maimuţ, Alexandru Cristian Matei
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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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