Results 11 to 20 of about 2,536,804 (344)
On hashing into elliptic curves
Journal of Mathematical Cryptology, 2009 We study the hash function from a finite field 𝔽q into an elliptic curve over 𝔽q which has recently been introduced by T. Icart. In particular we slightly adjust and prove the asymptotic formula conjectured by T. Icart for the image size of this function.
Farashahi Reza R. +2 more
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An attack on disguised elliptic curves
Journal of Mathematical Cryptology, 2008 We present an attack on one of the Hidden Pairing schemes proposed by Dent and Galbraith. We drastically reduce the number of variables necessary to perform a multivariate attack and in some cases we can completely recover the private key.
Morales David J. Mireles
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Local and global densities for Weierstrass models of elliptic curves [PDF]
Mathematical Research Letters, 2020 We prove local results on the $p$-adic density of elliptic curves over $\mathbb{Q}_p$ with different reduction types, together with global results on densities of elliptic curves over $\mathbb{Q}$ with specified reduction types at one or more (including ...
John Cremona, Mohammad Sadek
semanticscholar +1 more source
ELLIPTIC CURVES PUBLIC KEY TRAITOR TRACING SCHEME [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2008 In this paper we use the elliptic curves system in the Public Key Traitor Tracing Scheme. The Elliptic Curve points form Abelian group that used in the Public Key Traitor Tracing Scheme.
Ali M. Sagheer
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The Arithmetic of Elliptic Curves
Elliptic Curves, 2020 Our research focuses on 9 specific elliptic curves E over Q, each with complex multiplication by the maximal order in an imaginary quadratic field. Viewed over C, each E gives rise to tori, defined by the generators ω1, ω2 ∈ C of the period lattice ...
G. Ballew, James May
semanticscholar +1 more source
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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On oriented supersingular elliptic curves [PDF]
Finite Fields Their Appl., 2020 We revisit theoretical background on OSIDH, that is an isogeny-based key-exchange protocol proposed by Colo and Kohel at NutMiC 2019. We give a proof of a fundamental theorem for OSIDH. The theorem was stated by Colo and Kohel without proof. Furthermore,
Hiroshi Onuki
semanticscholar +1 more source
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
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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
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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.
openaire +3 more sources