Results 21 to 30 of about 10,181 (241)
Derived isogenies and isogenies for abelian surfaces
, 2021 In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence between abelian surfaces. We show that there is a twisted derived Torelli theorem for abelian surfaces over algebraically closed fields with characteristic $\neq 2,3$.
Li, Zhiyuan, Zou, Haitao
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Heights and isogenies of Drinfeld modules [PDF]
Acta Arithmetica, 2021 We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular polynomials attached to Drinfeld modules.
Breuer, Florian +2 more
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Algebraic approaches for solving isogeny problems of prime power degrees
Journal of Mathematical Cryptology, 2020 Recently, supersingular isogeny cryptosystems have received attention as a candidate of post-quantum cryptography (PQC). Their security relies on the hardness of solving isogeny problems over supersingular elliptic curves. The meet-in-the-middle approach
Takahashi Yasushi +5 more
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The Open Book Series, 2013 The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that ...
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Karpatsʹkì Matematičnì Publìkacìï, 2013 A proof of nondegeneracy of the Tate pairing and Kolyvagin's formula for elliptic curves with good reductions over an $n$-dimensional $(n\leq 3)$ pseudolocal field, the Tate pairing associated to an isogeny between abelian varieties over pseudolocal ...
V.I. Nesteruk
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Optimized CSIDH Implementation Using a 2-Torsion Point
Cryptography, 2020 The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when ...
Donghoe Heo +4 more
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Isogenies of abelian varieties
Journal of Pure and Applied Algebra, 1993 This paper deals with the following problems: Given two polarized abelian varieties \(X\) and \(Y\) over a field \(F\) which are isogenous over \(\overline F\), are they isogenous over \(F\)? And if they are not, how much of the \(n\)-torsion must be adjoined to \(F\) in order that they are?
Yu. G. Zarhin, Alice Silverberg
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Proposal of a New Isogeny-Based Cryptographic Protocol: Formal Analysis and Comparison [PDF]
Mathematics Interdisciplinary ResearchThis paper proposes a novel isogeny-based cryptographic protocol that leverages the dual hardness of the isogeny problem and linear code decoding for secure post-quantum key exchange.
mohammed EL BARAKA, Siham Ezzouak
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On the Performance Analysis for CSIDH-Based Cryptosystems
Applied Sciences, 2020 In this paper, we present the performance and security analysis for various commutative SIDH (CSIDH)-based algorithms. As CSIDH offers a smaller key size than SIDH and provides a relatively efficient signature scheme, numerous CSIDH-based key exchange ...
Donghoe Heo +3 more
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An efficient post-quantum KEM from CSIDH
Journal of Mathematical Cryptology, 2022 The SIDH and CSIDH are now the two most well-known post-quantum key exchange protocols from the supersingular isogeny-based cryptography, which have attracted much attention in recent years and served as the building blocks of other supersingular isogeny-
Qi Mingping
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