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Security analysis of elliptic curves with embedding degree 1 proposed in PLOS ONE 2016. [PDF]
PLoS ONE, 2019 Wang et al. proposed a method for obtaining elliptic curves with embedding degree 1 for securing critical infrastructures, and presented several elliptic curves generated by their method with torsion points of 160 bits and 189 bits orders.
Tadanori Teruya
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Cryptographically Strong Elliptic Curves of Prime Order [PDF]
International Journal of Electronics and Telecommunications, 2021 The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers.
Marcin Barański +2 more
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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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THEORETICAL ASSUMPTIONS FOR AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY
STED Journal, 2023 Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat's last theorem.
Ognjen Milivojević, Boris Damjanović
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How to Compute an Isogeny on the Extended Jacobi Quartic Curves? [PDF]
International Journal of Electronics and Telecommunications, 2022 Computing isogenies between elliptic curves is a significant part of post-quantum cryptography with many practical applications (for example, in SIDH, SIKE, B-SIDH, or CSIDH algorithms).
Łukasz Dzierzkowski, Michał Wroński
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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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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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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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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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