Results 1 to 10 of about 122 (48)
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves [PDF]
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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Orienting supersingular isogeny graphs
Journal of Mathematical Cryptology, 2020 We introduce a category of đť“ž-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented â„“-isogeny supersingular isogeny graphs.
Colò Leonardo, Kohel David
exaly +2 more sources
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
Journal of Mathematical Cryptology, 2014 We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases
Luca De Feo, David Jao
exaly +2 more sources
Isolated elliptic curves and the MOV attack
Journal of Mathematical Cryptology, 2017 We present a variation on the CM method that produces elliptic curves over prime fields with nearly prime order that do not admit many efficiently computable isogenies. Assuming the Bateman–Horn conjecture, we prove that elliptic curves produced this way
Travis Scholl
exaly +2 more sources
Central European Journal of Mathematics, 2008 Fedor A Bogomolov, Yuri Tschinkel
exaly +2 more sources
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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Isogenies on twisted Hessian curves
Journal of Mathematical Cryptology, 2021 Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known VĂ©lu'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
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AN IDENTITY-BASED ENCRYPTION SCHEME USING ISOGENY OF ELLIPTIC CURVES [PDF]
, 2021 Identity-Based Encryption is a public key cryptosystem that uses the receiver identifier information such as email address, IP address, name and etc, to compute a public and a private key in a cryptosystem and encrypt a message.
Bahramian, Mojtaba, Hajirezaei, Elham
core +1 more source
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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Hash functions from superspecial genus-2 curves using Richelot isogenies
Journal of Mathematical Cryptology, 2020 In 2018 Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field 𝔽p2.
Castryck Wouter +2 more
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