Results 1 to 10 of about 290 (181)
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 +2 more sources
Orienting supersingular isogeny graphs
Journal of Mathematical Cryptology, 2020 We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
exaly +2 more sources
Practical Usage of Radical Isogenies for CSIDH
IEEE Access, 2023 Recently, a radical isogeny was proposed to boost commutative supersingular isogeny Diffie–Hellman (CSIDH) implementation. Radical isogenies reduce the generation of a kernel of a small prime order when implementing CSIDH.
Donghoe Heo, Suhri Kim, Seokhie Hong
doaj +1 more source
A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
Transactions of the London Mathematical Society, 2021 Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
doaj +1 more source
Torsion point attacks on ‘SIDH‐like’ cryptosystems
IET Information Security, 2023 Isogeny‐based cryptography is a promising approach for post‐quantum cryptography. The best‐known protocol following that approach is the supersingular isogeny Diffie–Hellman protocol (SIDH); this protocol was turned into the CCA‐secure key encapsulation ...
Péter Kutas, Christophe Petit
doaj +1 more source
Review of Chosen Isogeny-Based Cryptographic Schemes
Cryptography, 2022 Public-key cryptography provides security for digital systems and communication. Traditional cryptographic solutions are constantly improved, e.g., to suppress brute-force attacks.
Bartosz Drzazga, Łukasz Krzywiecki
doaj +1 more source
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
doaj +1 more source
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
doaj +3 more sources
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
doaj +1 more source
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
doaj +1 more source