Results 11 to 20 of about 145,858 (328)
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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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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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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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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Electronics Letters, 2022 Fault attacks have been proved for efficiently breaking hardware‐based elliptic curve cryptosystems. One way for fighting against fault attacks is to design the core multiplier circuit of elliptic curve cryptosystem with concurrent error detection ...
Che Wun Chiou +6 more
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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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Application of mathematical optimization in elliptic curve arithmetic
Безопасность информационных технологий, 2017 Currently, a lot of standardized elliptic curve cryptographic algorithms are widely used. Due to the constantly increasing execution speed demands, implementation optimization problem become actual.
Alexander Igorevich Skripko +1 more
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The positive integral points on the elliptic curve 𝒚𝟐=𝟕𝒑𝒙(𝒙𝟐+𝟖) [PDF]
E3S Web of Conferences, 2020 The integral point of elliptic curve is a very important problem in both elementary number theory and analytic number theory. In recent years, scholars have paid great attention to solving the problem of positive integer points on elliptic curve 𝑦2 = 𝑘 ...
Xiancun Du, Zhao Jianhong, Yang Lixing
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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 ...
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Quantum resource estimates for computing elliptic curve discrete logarithms [PDF]
, 2017 We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition ...
A Joux +32 more
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