Results 11 to 20 of about 4,641 (196)
Isogenies on twisted Hessian curves [PDF]
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
doaj +6 more sources
IACR Cryptol. ePrint Arch., 2021 We argue that for all integers $N \geq 2$ and $g \geq 1$ there exist multiradical isogeny formulae, that can be iteratively applied to compute $(N^k, \ldots, N^k)$-isogenies between principally polarized $g$-dimensional abelian varieties, for any value
Castryck, Wouter, Decru, Thomas
core +5 more sources
Journal of High Energy Physics, 2021 We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynman parametrization, lightcone and Baikov (in ...
Hjalte Frellesvig +3 more
doaj +6 more sources
Computing 2-isogenies between Kummer lines [PDF]
IACR Cryptology ePrint ArchiveWe use theta groups to study 2 -isogenies between Kummer lines, with a particular focus on the Montgomery model.
Damien Robert, Nicolas Sarkis
semanticscholar +6 more sources
Brauer relations, isogenies and parities of ranks [PDF]
Journal of Number Theory, 2023 The present paper illustrates the utility of Brauer relations, Galois covers of curves and the theory of regulator constants in the context of studying isogenies between Jacobians and their relevance to the parity conjecture.
Alexandros Konstantinou
semanticscholar +2 more sources
Isogenies and cryptography [PDF]
Cryptography is an essential tool for enabling privacy of electronic communication. However, many of the cryptographic protocols we use nowadays, would be insecure after the development of large-scale quantum computers. Therefore, the cryptographic community is preparing new protocols to replace the would-be broken ones. Protocols based on lattices are
Sotáková, J.
core +11 more sources
Isogenies on Kummer Surfaces [PDF]
Mathematics of ComputationWe first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient ( N ,
Corte-Real Santos, M, Flynn, EV
core +4 more sources
Efficient computation of (3n,3n)-isogenies
IACR Cryptology ePrint Archive, 2023 . The parametrization of (3 , 3)-isogenies by Bruin, Flynn and Testa requires over 37 . 500 multiplications if one wants to evaluate a single isogeny in a point. We simplify their formulae and reduce the amount of required multiplications by 94%. Further
Thomas Decru, S. Kunzweiler
semanticscholar +2 more sources
Computing isogenies between finite Drinfeld modules [PDF]
IACR Cryptology ePrint Archive, 2022 We prove that isogenies between Drinfeld F[x]-modules over a finite field can be computed in polynomial time. This breaks Drinfeld analogs of isogeny-based cryptosystems.
B. Wesolowski
semanticscholar +3 more sources
OPRFs from Isogenies: Designs and Analysis
Proceedings of the 19th ACM Asia Conference on Computer and Communications SecurityOblivious Pseudorandom Functions (OPRFs) are an elementary building block in cryptographic and privacy-preserving applications. While there are numerous pre-quantum secure OPRF constructions, it is unclear which of the proposed options for post-quantum ...
Lena Heimberger +4 more
semanticscholar +3 more sources