Public key cryptography is a major interdisciplinary subject with many real-world
applications, such as digital signatures. A strong background in the mathematics underlying …

Given two ordinary elliptic curves over a finite field having the same cardinality and
endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but …

These lectures notes were written for a summer school on Mathematics for post-quantum
cryptography in Thi\es, Senegal. They try to provide a guide for Masters' students to get …

We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev–
Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate …

We introduce a category of 𝓞-oriented supersingular elliptic curves and derive properties of
the associated oriented and nonoriented ℓ-isogeny supersingular isogeny graphs. As an …

Isogenies are the morphisms between elliptic curves and are, accordingly, a topic of interest
in the subject. As such, they have been well studied, and have been used in several …

Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is
believed to be a difficult problem—upon which rests the security of nearly any isogeny …

We present a new algorithm to compute the classical modular polynomial $\Phi _l $ in the
rings $\mathbf {Z}[X, Y] $ and $(\mathbf {Z}/m\mathbf {Z})[X, Y] $, for a prime $ l $ and any …

We present a space-efficient algorithm to compute the Hilbert class polynomial $ H_D (X) $
modulo a positive integer $ P $, based on an explicit form of the Chinese Remainder …

We survey algorithms for computing isogenies between elliptic curves defined over a field of
characteristic either 0 or a large prime. We introduce a new algorithm that computes an …