Add to ORKGLet A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and if available the Hilbert modular polynomials to compute the canonical lift of A. As an application, if q = p n , we show how to use the canonical lift to count the number of points on A in quasi-quadratic time Õ(n 2), this is a direct extension of Satoh's original algorithm for elliptic curves. We give a detailed description with the necessary optimizations for an efficient implementation
Let $E$ be an ordinary elliptic curve over a finite field and $g$ be a positive integer. Under some ...
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their Kumm...
We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 c...
Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and i...
Let $p$ be a prime; using modular polynomial $\Phi_p$, T.~Satoh and al\cite{satoh2000canonical,harle...
Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined ove...
We design algorithms to efficiently evaluate genus 2 modular polyno-mials of Siegel and Hilbert type...
AbstractWe give a new method for generating genus 2 curves over a finite field with a given number o...
We study the canonical lifting of ordinary elliptic curves over the ring of Witt vectors. We prove t...
International audienceLet $p$ be a small prime and $q=p^n$. Let $E$ be an elliptic curve over $F_q$...
Substantial rewrite. The main complexity result is improved. An important heuristic assumption is pr...
AbstractLet p be a fixed small prime. We give an algorithm with preprocessing to compute the j-invar...
We show that the canonical lift construction for ordinary elliptic curves over perfect fields of cha...
Algebraic curves and surfaces are playing an increasing role in modern mathematics. From the well k...
Abstract. Genus 2 curves have been an object of much mathematical interest since eighteenth century ...
Let $E$ be an ordinary elliptic curve over a finite field and $g$ be a positive integer. Under some ...
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their Kumm...
We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 c...
Let A/Fq be an ordinary abelian surface. We explain how to use the Siegel modular polynomials, and i...
Let $p$ be a prime; using modular polynomial $\Phi_p$, T.~Satoh and al\cite{satoh2000canonical,harle...
Let k be a field of even characteristic and M2(k) the moduli space of the genus 2 curves defined ove...
We design algorithms to efficiently evaluate genus 2 modular polyno-mials of Siegel and Hilbert type...
AbstractWe give a new method for generating genus 2 curves over a finite field with a given number o...
We study the canonical lifting of ordinary elliptic curves over the ring of Witt vectors. We prove t...
International audienceLet $p$ be a small prime and $q=p^n$. Let $E$ be an elliptic curve over $F_q$...
Substantial rewrite. The main complexity result is improved. An important heuristic assumption is pr...
AbstractLet p be a fixed small prime. We give an algorithm with preprocessing to compute the j-invar...
We show that the canonical lift construction for ordinary elliptic curves over perfect fields of cha...
Algebraic curves and surfaces are playing an increasing role in modern mathematics. From the well k...
Abstract. Genus 2 curves have been an object of much mathematical interest since eighteenth century ...
Let $E$ be an ordinary elliptic curve over a finite field and $g$ be a positive integer. Under some ...
This paper presents an algorithm to construct cryptographically strong genus 2 curves and their Kumm...
We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 c...