Results 31 to 40 of about 4,641 (196)

A trade-off between classical and quantum circuit size for an attack against CSIDH

Journal of Mathematical Cryptology, 2020
We propose a heuristic algorithm to solve the underlying hard problem of the CSIDH cryptosystem (and other isogeny-based cryptosystems using elliptic curves with endomorphism ring isomorphic to an imaginary quadratic order 𝒪).
Biasse Jean-François, Bonnetain Xavier, Pring Benjamin, Schrottenloher André, Youmans William   +4 more
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, Kudo Momonari, Fukasaku Ryoya, Ikematsu Yasuhiko, Yasuda Masaya, Yokoyama Kazuhiro   +5 more
doaj   +1 more source

On the supersingular GPST attack

Journal of Mathematical Cryptology, 2021
The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange.
Basso Andrea, Pazuki Fabien
doaj   +1 more source

Faster computation of isogenies of large prime degree [PDF]

IACR Cryptology ePrint Archive, 2020
Let $\mathcal{E}/\mathbb{F}_q$ be an elliptic curve, and $P$ a point in $\mathcal{E}(\mathbb{F}_q)$ of prime order $\ell$. Velu's formulae let us compute a quotient curve $\mathcal{E}' = \mathcal{E}/\langle{P}\rangle$ and rational maps defining a ...
D. J. Bernstein, L. De Feo, Antonin Leroux, Benjamin A. Smith   +3 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.
openaire   +4 more sources

Explicit isogenies of prime degree over number fields [PDF]

Algebra & Number Theory, 2022
We provide an explicit and algorithmic version of a theorem of Momose classifying isogenies of prime degree of elliptic curves over number fields, which we implement in Sage and PARI/GP.
Barinder S. Banwait, M. Derickx
semanticscholar   +1 more source

Vectorized and Parallel Computation of Large Smooth-Degree Isogenies using Precedence-Constrained Scheduling

Transactions on Cryptographic Hardware and Embedded Systems, 2023
Strategies and their evaluations play important roles in speeding up the computation of large smooth-degree isogenies. The concept of optimal strategies for such computation was introduced by De Feo et al., and virtually all implementations of isogeny ...
Kittiphon Phalakarn, Vorapong Suppakitpaisarn, Francisco Rodríguez-Henríquez, M. Anwar Hasan   +3 more
doaj   +1 more source

Towards Isogeny-Based Password-Authenticated Key Establishment

Journal of Mathematical Cryptology, 2020
Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure.
Taraskin Oleg, Soukharev Vladimir, Jao David, LeGrow Jason T.   +3 more
doaj   +1 more source

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, Suhri Kim, Kisoon Yoon, Young-Ho Park, Seokhie Hong   +4 more
doaj   +1 more source

Modular isogeny complexes [PDF]

Algebraic & Geometric Topology, 2012
Minor revisions for ...
openaire   +3 more sources