Results 31 to 40 of about 10,757 (241)
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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Isogeny graphs of ordinary abelian varieties [PDF]
, 2016 Fix a prime number $\ell$. Graphs of isogenies of degree a power of $\ell$ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties.
Brooks, Ernest Hunter +2 more
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Black Box Galois Representations [PDF]
, 2018 We develop methods to study $2$-dimensional $2$-adic Galois representations $\rho$ of the absolute Galois group of a number field $K$, unramified outside a known finite set of primes $S$ of $K$, which are presented as Black Box representations, where we ...
Argáez-García, Alejandro +1 more
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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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Families of abelian varieties with many isogenous fibres [PDF]
, 2015 Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points which correspond to abelian varieties from a single isogeny class.
Orr, Martin
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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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Constructing Cycles in Isogeny Graphs of Supersingular Elliptic Curves
Journal of Mathematical Cryptology, 2021 Loops and cycles play an important role in computing endomorphism rings of supersingular elliptic curves and related cryptosystems. For a supersingular elliptic curve E defined over 𝔽p2, if an imaginary quadratic order O can be embedded in End(E) and a ...
Xiao Guanju, Luo Lixia, Deng Yingpu
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Explicit isogenies in quadratic time in any characteristic [PDF]
, 2016 Consider two elliptic curves $E,E'$ defined over the finite field $\mathbb{F}_q$, and suppose that there exists an isogeny $\psi$ between $E$ and $E'$.
De Feo, Luca +3 more
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