Results 21 to 30 of about 1,931 (172)
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
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Fully projective radical isogenies in constant-time [PDF]
, 2021 At PQCrypto-2020, Castryck and Decru proposed CSURF (CSIDH on the surface) as an improvement to the CSIDH protocol. Soon after that, at Asiacrypt-2020, together with Vercauteren they introduced radical isogenies as a further improvement.
Jesús-Javier Chi-Domínguez +1 more
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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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Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
Journal of Mathematical Cryptology, 2020 We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n ≥ 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be ...
Boneh Dan +7 more
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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 +3 more
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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 +3 more
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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
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The isogeny conjecture for A-motives [PDF]
Inventiones mathematicae, 2011 We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree ≤1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M′ over K for which there exists a separable isogeny M′→M.
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Modular isogeny complexes [PDF]
Algebraic & Geometric Topology, 2012 Minor revisions for ...
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A simple and compact algorithm for SIDH with arbitrary degree isogenies [PDF]
, 2017 We derive a new formula for computing arbitrary odd-degree isogenies between elliptic curves in Montgomery form. The formula lends itself to a simple and compact algorithm that can efficiently compute any low odd-degree isogenies inside the supersingular
Huseyin Hisil, Craig Costello
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