Results 1 to 10 of about 568 (60)
On Types of Elliptic Pseudoprimes [PDF]
Groups, Complexity, Cryptology, 2021 We generalize the notions of elliptic pseudoprimes and elliptic Carmichael numbers introduced by Silverman to analogues of Euler-Jacobi and strong pseudoprimes.
L. Babinkostova +2 more
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Research in the Mathematical Sciences, 2014 PurposeDon Zagier suggested a natural construction, which associates a real number and p-adic numbers for all primes p to the cusp form g=Δ of weight 12. He claimed that these quantities constitute a rational adele. In this paper we prove this statement,
P. Guerzhoy
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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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Classification of Elements in Elliptic Curve Over the Ring 𝔽q[ɛ]
Discussiones Mathematicae - General Algebra and Applications, 2021 Let 𝔽q[ɛ] := 𝔽q [X]/(X4 − X3) be a finite quotient ring where ɛ4 = ɛ3, with 𝔽q is a finite field of order q such that q is a power of a prime number p greater than or equal to 5.
Selikh Bilel +2 more
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On the supersingular GPST attack
Journal of Mathematical Cryptology, 2021 The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange.
Basso Andrea, Pazuki Fabien
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Equidistribution Among Cosets of Elliptic Curve Points in Intervals
Journal of Mathematical Cryptology, 2020 In a recent paper devoted to fault analysis of elliptic curve-based signature schemes, Takahashi et al. (TCHES 2018) described several attacks, one of which assumed an equidistribution property that can be informally stated as follows: given an elliptic ...
Kim Taechan, Tibouchi Mehdi
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On a desingularization of the moduli space of noncommutative tori [PDF]
, 2007 It is shown that the moduli space of the noncommutative tori A θ ad-mits a natural desingularization by the group Ext ( A θ , θ ). Namely, weprove that the moduli space of pairs ( A θ ,Ext ( A θ , θ )) is homeomor-phic to a punctured two-dimensional ...
I. Nikolaev
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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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Ramification in the division fields of elliptic curves with potential supersingular reduction
Research in Number Theory, 2016 Let d≥1 be fixed. Let F be a number field of degree d, and let E/F be an elliptic curve. Let E(F)tors be the torsion subgroup of E(F). In 1996, Merel proved the uniform boundedness conjecture, i.e., there is a constant B(d), which depends on d but not on
Álvaro Lozano‐Robledo
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