Results 31 to 40 of about 23,538,535 (168)
CTIDH: faster constant-time CSIDH
Transactions on Cryptographic Hardware and Embedded Systems, 2021 This paper introduces a new key space for CSIDH and a new algorithm for constant-time evaluation of the CSIDH group action. The key space is not useful with previous algorithms, and the algorithm is not useful with previous key spaces, but combining the ...
Gustavo Banegas +7 more
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Mathematics of Isogeny Based Cryptography
CoRR, 2017 These lectures notes were written for a summer school on Mathematics for post-quantum cryptography in Thiès, Senegal. They try to provide a guide for Masters' students to get through the vast literature on elliptic curves, without getting lost on their way to learning isogeny based cryptography.
openaire +3 more sources
IEEE Access, 2021 Since the introduction of the Supersingular isogeny Diffie–Hellman (SIDH) key exchange protocol by Jao and de Feo in 2011, it and its variation (SIKE) have gained significant attention as a promising candidate for post-quantum cryptography (PQC ...
Seog Chung Seo
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The Role of Non-Positional Arithmetic on Efficient Emerging Cryptographic Algorithms
IEEE Access, 2020 Number representation systems establish ways in which numbers are mapped to computer architectures, and how operations over the numbers are translated into computer instructions.
Paulo Martins, Leonel Sousa
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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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Counting 5‐isogenies of elliptic curves over Q$\mathbb {Q}$
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We show that the number of 5‐isogenies of elliptic curves defined over Q$\mathbb {Q}$ with naive height bounded by H>0$H > 0$ is asymptotic to C5·H1/6(logH)2$C_5\cdot H^{1/6} (\log H)^2$ for some explicitly computable constant C5>0$C_5 > 0$. This settles the asymptotic count of rational points on the genus zero modular curves X0(m)$\mathcal {X}
Santiago Arango‐Piñeros +3 more
wiley +1 more source
dCTIDH: Fast & Deterministic CTIDH
Transactions on Cryptographic Hardware and Embedded SystemsThis paper presents dCTIDH, a CSIDH implementation that combines two recent developments into a novel state-of-the-art deterministic implementation. We combine the approach of deterministic variants of CSIDH with the batching strategy of CTIDH, which ...
Fabio Campos +3 more
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A subexponential-time, polynomial quantum space algorithm for inverting the CM group action
Journal of Mathematical Cryptology, 2020 We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space.
Jao David +3 more
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
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Graph potentials and topological quantum field theories
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans +2 more
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