Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1


Algorithmic Number Theory in Computer Science
EC | FP7 | SP2 | ERC
Contract (GA) number
Start Date
End Date
Open Access mandate
Special Clause 39
More information
Detailed project information (CORDIS)


  • Computing isogenies between Abelian Varieties

    Lubicz , David; Robert , Damien (2012)
    Projects: EC | ANTICS (278537)
    We describe an efficient algorithm for the computation of separable isogenies between abelian varieties represented in the coordinate system given by algebraic theta functions. Let $A$ be an abelian variety of dimension $g$ defined over a field of odd characteristic. Our algorithm decomposes in two principal steps. First, given a theta null point for $A$ and a subgroup $K$ isotropic for the Weil pairing, we explain how to compute the theta null point corresponding to the quotient abelian vari...

    Computing arithmetic Kleinian groups

    Page , Aurel (2015)
    Projects: EC | ANTICS (278537)
    International audience; Arithmetic Kleinian groups are arithmetic lattices in PSL_2(C). We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for Gamma with a computable isomorphism.

    An algorithm for the principal ideal problem in indefinite quaternion algebras

    Page, Aurel (2014)
    Projects: EC | ANTICS (278537)
    International audience; Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quaternion algebras, the decision problem reduces to that in the underlying number field. Finding a generator is hard, and we present a heuristically subexponential algorithm.

    Generalised Weber Functions

    Enge , Andreas; Morain , François (2014)
    Projects: EC | ANTICS (278537)
    International audience; A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to $N=2$. We classify the cases where some power $\w_N^e$ evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating $\w_...

    Short addition sequences for theta functions

    Enge, Andreas; Hart, William; Johansson, Fredrik (2016)
    Projects: EC | ANTICS (278537)
    International audience; The main step in numerical evaluation of classical Sl2 (Z) modular forms and elliptic functions is to compute the sum of the first N nonzero terms in the sparse q-series belonging to the Dedekind eta function or the Jacobi theta constants. We construct short addition sequences to perform this task using N + o(N) multiplications. Our constructions rely on the representability of specific quadratic progressions of integers as sums of smaller numbers of the same kind. For...

    Schertz style class invariants for quartic CM fields

    Enge , Andreas; Streng , Marco (2016)
    Projects: EC | ANTICS (278537)
    A class invariant is a CM value of a modular function that lies in a certain unramified class field. We show that Siegel modular functions over $\mathbb Q$ for $\Gamma^0(N)\subseteq \operatorname {Sp}_4(\mathbb Z)$ yield class invariants under some splitting conditions on $N$. Small class invariants speed up onstructions in explicit class field theory and public-key cryptography. Our results generalise results of Schertz's from elliptic curves to abelian varieties and from classical modular f...

    Vanishing and non-vanishing theta values

    Cohen , Henri; Zagier , Don (2013)
    Projects: EC | ANTICS (278537)
    International audience

    Computing class polynomials for abelian surfaces

    Enge , Andreas; Thomé , Emmanuel (2014)
    Projects: EC | ANTICS (278537)
    International audience; We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating ϑ- constants in quasi-linear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example...

    A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties

    Lubicz, David; Robert, Damien (2014)
    Projects: EC | ANTICS (278537)
    International audience; In this paper, we use the theory of theta functions to generalize to all abelian varieties the usual Miller's algorithm to compute a function associated to a principal divisor. We also explain how to use the Frobenius morphism on abelian varieties defined over a finite field in order to shorten the loop of the Weil and Tate pairings algorithms. This extend preceding results about ate and twisted ate pairings to all abelian varieties. Then building upon the two precedin...
  • No project research data found
  • Scientific Results

    Chart is loading... It may take a bit of time. Please be patient and don't reload the page.


    Chart is loading... It may take a bit of time. Please be patient and don't reload the page.

    Publications in Repositories

    Chart is loading... It may take a bit of time. Please be patient and don't reload the page.

Share - Bookmark

App Box