… elliptic curves are used in an isogeny-based system, we propose using supersingular curves
of … Finally, we discuss the possibility of adapting the quantum algorithm of Childs et al. [5] for …

… Now is the right time for quantum algorithms experts to learn … This separation of elliptic curves
into supersingular and ordinary … final remarks about supersingular elliptic curves. First, any …

… We present new candidates for quantum-resistant public-key cryptosystems based on the
conjectured difficulty of finding isogenies between supersingular elliptic curves. The main …

… quantum algorithm for computing an isogeny between any two supersingular elliptic curves
… both classical and quantum computers). We also discuss the cryptographic relevance of our …

… is a natural algorithmic problem which is known to be equivalent to computing the curves…
supersingular elliptic curves over Fp2 . We present improved classical and quantum algorithms …

… which was shown to be vulnerable are what are called super singular elliptic curves. For …
For a detailed implementation of a polynomial time quantum algorithm for the elliptic curve …

… -time quantum algorithm for constructing nonzero isogenies between two such elliptic curves…
of cryptographic protocols based on isogenies between supersingular curves [17], and it …

… against quantum attacks. The fastest known quantum attack on CSSI is Tani’s algorithm [26]…
N\) and \(\# Y \gg N\), Tani’s quantum algorithm finds a claw, ie, a pair \((x_1,x_2) \in X_1 \…

… quantum algorithm for discrete logarithms applied to elliptic curve groups forms the basis of
a “quantum attack” of elliptic … the case of a supersingular curve). The set of points on a given …

… begins by providing a brief introduction to elliptic curves, isogenies, and the SIDH …
supersingular elliptic curves, which are important for visualizing the isogeny graphs in the algorithm …