CSI-RAShi: Distributed Key Generation for CSIDH
, 2021 We present an honest-majority Distributed Key Generation protocol (DKG) based on Shamir’s (k, n)-threshold secret sharing in the setting of Very Hard Homogenous Spaces (VHHS). DKGs in the discrete logarithm setting use Pedersen commitments, for which there is no known analogue in the VHHS setting.
Beullens, Ward +3 more
openaire +1 more source
Quantum Money from Abelian Group Actions [PDF]
, 2023 We give a candidate construction of public key quantum money, and even a strengthened version called quantum lightning, from abelian group actions, which can in turn be constructed from suitable isogenies over elliptic curves.
Zhandry, Mark
core +3 more sources
Rational isogenies from irrational endomorphisms [PDF]
, 2020 In this paper, we introduce a polynomial-time algorithm to compute a connecting $\mathcal{O}$-ideal between two supersingular elliptic curves over $\mathbb{F}_p$ with common $\mathbb{F}_p$-endomorphism ring $\mathcal{O}$, given a description of their ...
BH Gross +12 more
core +2 more sources
OSIDH and SiGamal : cryptosystems from supersingular elliptic curves (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties) [PDF]
, 2022 We introduce two cryptosystems, OSIDH and SiGamal, which use isogenies between supersingular elliptic curves over a finite field. And we consider computational problems on which these cryptosystems are based.
ONUKI, Hiroshi
core
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 +4 more
doaj +1 more source
Post-Quantum Cryptography from Supersingular Isogenies (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties) [PDF]
, 2022 This paper is based on a presentation made at RIMS conference on “Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties”, so-called “Supersingular 2020”. Post-quantum cryptography is a next-generation public-key cryptosystem
Aikawa, Yusuke
core
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
doaj +1 more source
Weak instances of class group action based cryptography via self-pairings [PDF]
, 2023 This work was supported in part by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement ISOCRYPT - No.
Castryck, Wouter +5 more
core +1 more source
Hard Homogenous Spaces and Commutative Supersingular Isogeny based Diffie-Hellman [PDF]
, 2019 Tema ovog rada jest proces stvaranja 3D stvarnih ili imaginarnih objekata pomoću alata SolidWorks koji je u današnje vrijeme jedan od najpoznatijih alata kod modeliranja mehaničkih i projektnih objekata.
Felderhoff, Joël
core +2 more sources
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
doaj +1 more source