Results 41 to 50 of about 3,965 (252)
Hash functions from superspecial genus-2 curves using Richelot isogenies
Journal of Mathematical Cryptology, 2020 In 2018 Takashima proposed a version of Charles, Goren and Lauterâs hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field đœp2.
Castryck Wouter +2 more
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Computing endomorphism rings of supersingular elliptic curves and connections to path-finding in isogeny graphs [PDF]
The Open Book Series, 2020 Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems.
Kirsten Eisentraeger +4 more
semanticscholar +1 more source
Isogeny in superstable groups [PDF]
Archive for Mathematical Logic, 2014 We study and develop a notion of isogeny for superstable groups. We prove several fundamental properties of the notion and then use it to formulate and prove uniqueness results. Connections to existing model theoretic notions are explained.
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The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type
Forum of Mathematics, Sigma, 2021 In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$-type. The proof combines Faltingsâ method with Serreâs modularity conjecture, isogeny estimates and results from Arakelov ...
Rafael von KĂ€nel
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Rational Isogenies from Irrational Endomorphisms
, 2020 In this paper, we introduce a polynomial-time algorithm to compute a connecting \(\mathcal {O}\)-ideal between two supersingular elliptic curves over \(\mathbb {F}_p\) with common \(\mathbb {F}_p\)-endomorphism ring \(\mathcal {O}\), given a description of their full endomorphism rings.
Castryck, Wouter +2 more
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Let us walk on the 3-isogeny graph: efficient, fast, and simple
Transactions on Cryptographic Hardware and Embedded SystemsConstructing and implementing isogeny-based cryptographic primitives is an active research. In particular, performing length-n isogenies walks over quadratic field extensions of Fp plays an exciting role in some constructions, including Hash functions ...
JesĂșs-Javier Chi-DomĂnguez +2 more
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Transactions on Cryptographic Hardware and Embedded Systems, 2022 We present new side-channel attacks on SIKE, the isogeny-based candidate in the NIST PQC competition. Previous works had shown that SIKE is vulnerable to differential power analysis, and pointed to coordinate randomization as an effective countermeasure.
Luca De Feo +6 more
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The modular automorphisms of quotient modular curves
Mathematika, Volume 72, Issue 1, January 2026.Abstract We obtain the modular automorphism group of any quotient modular curve of level N$N$, with 4,9â€N$4,9\nmid N$. In particular, we obtain some unexpected automorphisms of order 3 that appear for the quotient modular curves when the AtkinâLehner involution w25$w_{25}$ belongs to the quotient modular group. We also prove that such automorphisms are
Francesc Bars, Tarun Dalal
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Horizontal Racewalking Using Radical Isogenies
, 2022 sponsorship: This work was supported in part by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement ISOCRYPT -No. 101020788) and by CyberSecurity Research Flanders with reference number VR20192203.
Castryck, Wouter +3 more
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Optimization of isogeny computation algorithms for post-quantum cryptography
Scientific AfricanIsogeny-based cryptography has emerged as a strong candidate for post-quantum security due to the believed hardness of finding isogenies between supersingular elliptic curves.
Mohammed El Baraka, Siham Ezzouak
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