Results 11 to 20 of about 35 (34)
L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces
Bulletin of the London Mathematical Society, Volume 52, Issue 2, Page 395-409, April 2020., 2020 Abstract We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L ...
Evgeny Shinder, Ziyu Zhang
wiley +1 more source
Protecting ECC Against Fault Attacks: The Ring Extension Method Revisited
Journal of Mathematical Cryptology, 2020 Due to its shorter key size, elliptic curve cryptography (ECC) is gaining more and more popularity. However, if not properly implemented, the resulting cryptosystems may be susceptible to fault attacks.
Joye Marc
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Elliptic curve and k-Fibonacci-like sequence
Scientific African, 2023 In this paper, we will introduce a modified k-Fibonacci-like sequence defined on an elliptic curve and prove Binet’s formula for this sequence. Moreover, we give a new encryption scheme using this sequence.
Zakariae Cheddour +2 more
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A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
Transactions of the London Mathematical Society, 2021 Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
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Orienting supersingular isogeny graphs
Journal of Mathematical Cryptology, 2020 We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
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Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings
Forum of Mathematics, Sigma, 2021 The elliptic algebras in the title are connected graded $\mathbb {C}$-algebras, denoted $Q_{n,k}(E,\tau )$, depending on a pair of relatively prime integers $n>k\ge 1$, an elliptic curve E and a point $\tau \in E$.
Alex Chirvasitu +2 more
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On the non-idealness of cyclotomic families of pairing-friendly elliptic curves
Journal of Mathematical Cryptology, 2014 Let k=2mpn$k=2^mp^n$ for an odd prime p and integers m ≥ 0 and n ≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φk(x)$r(x)=\Phi _k(x)$.
Sha Min
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Torsion subgroups of rational Mordell curves over some families of number fields
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 Mordell curves over a number field K are elliptic curves of the form y2 = x3 + c, where c ∈ K \ {0}. Let p ≥ 5 be a prime number, K a number field such that [K : ℚ] ∈ {2p, 3p}.
Gužvić Tomislav, Roy Bidisha
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On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1
Proceedings of the London Mathematical Society, Volume 118, Issue 5, Page 1245-1276, May 2019., 2019 Abstract The main result of this paper is to extend from Q to each of the nine imaginary quadratic fields of class number 1 a result of [Serre, Duke Math. J. 54 (1987) 179–230] and [Mestre–Oesterlé, J. reine. angew. Math. 400 (1989) 173–184], namely that if E is an elliptic curve of prime conductor, then either E or a 2‐, 3‐ or 5‐isogenous curve has ...
John Cremona, Ariel Pacetti
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Efficient computation of pairings on Jacobi quartic elliptic curves
Journal of Mathematical Cryptology, 2014 This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y2=dX4+Z4$Y^{2}=dX^{4}+Z^{4}$.
Duquesne Sylvain +2 more
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