Generalised Weber Functions. I (2009)
Enge, Andreas, Morain, François
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...
An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves (2009)
Enge, Andreas, Gaudry, Pierrick, Thomé, Emmanuel
We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields...
An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves (2009)
Enge, Andreas, Gaudry, Pierrick, Thomé, Emmanuel
We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields...
An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves (2009)
Enge, Andreas, Gaudry, Pierrick, Thomé, Emmanuel
We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields...
Generalised Weber Functions. I (2009)
Enge, Andreas, Morain, François
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...
Generalised Weber Functions. I (2009)
Enge, Andreas, Morain, François
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...
Komplexe Multiplikation: von numerisch bis symbolisch (2009)
Die Theorie der komplexen Multiplikation vereint in bemerkenswerter Weise Analysis (Funktionentheorie, Riemannsche Flächen) und Algebra (Zahlentheorie, Klassenköpertheorie). In der Praxis führt...
Komplexe Multiplikation: von numerisch bis symbolisch (2009)
Die Theorie der komplexen Multiplikation vereint in bemerkenswerter Weise Analysis (Funktionentheorie, Riemannsche Flächen) und Algebra (Zahlentheorie, Klassenköpertheorie). In der Praxis führt...
Computing Hilbert Class Polynomials (2008)
Juliana Belding, Reinier Bröker, Andreas Enge, Kristin Lauter
Abstract. We present and analyze two algorithms for computing the Hilbert class polynomial HD. The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The...
Computing Hilbert Class Polynomials (2008)
Juliana Belding, Reinier Bröker, Andreas Enge, Kristin Lauter
Abstract. We present and analyze two algorithms for computing the Hilbert class polynomial HD. The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The...
Journal de Théorie des Nombres (2008)
De Bordeaux, Andreas Enge, Reinhard Schertz
Constructing elliptic curves over finite fields using double eta-quotients par Andreas ENGE et Reinhard SCHERTZ Résumé. Nous examinons une classe de fonctions modulaires pour Γ 0 (N) dont les...
Computing Hilbert Class Polynomials (2008)
Belding, Juliana, Bröker, Reinier, Enge, Andreas, Lauter, Kristin
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is...
Computing Hilbert Class Polynomials (2008)
Belding, Juliana, Bröker, Reinier, Enge, Andreas, Lauter, Kristin
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is...
Computing Hilbert Class Polynomials (2008)
Belding, Juliana, Bröker, Reinier, Enge, Andreas, Lauter, Kristin
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is...
Computing modular polynomials in quasi-linear time (2008)
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on...
Computing modular polynomials in quasi-linear time (2008)
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on...
Discrete logarithms in curves over finite fields (2007)
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
Lehrstuhl fur Diskrete Mathematik, (2007)
A general framework for subexponential discrete
The complexity of class polynomial computation via floating point approximations (2007)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
Computing modular polynomials in quasi-linear time (2007)
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on...
The complexity of class polynomial computation via floating point approximations (2007)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
Computing modular polynomials in quasi-linear time (2007)
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on...
Computing modular polynomials in quasi-linear time (2007)
We analyse and compare the complexity of several algorithms for computing modular polynomials. We show that an algorithm relying on floating point evaluation of modular functions and on...
An $L (1/3 + \epsilon)$ Algorithm for the Discrete Logarithm Problem for Low Degree Curves (2007)
Enge, Andreas, Gaudry, Pierrick
The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an...
An $L (1/3 + \varepsilon)$ Algorithm for the Discrete Logarithm Problem for Low Degree Curves (2007)
Enge, Andreas, Gaudry, Pierrick
The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an...
An $L (1/3 + \varepsilon)$ Algorithm for the Discrete Logarithm Problem for Low Degree Curves (2007)
Enge, Andreas, Gaudry, Pierrick
The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an...
Discrete logarithms in curves over finite fields (2007)
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
Discrete logarithms in curves over finite fields (2007)
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
The complexity of class polynomial computation via floating point approximations (2007)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
The complexity of class polynomial computation via floating point approximations (2007)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
The complexity of class polynomial computation via floating point approximations (2006)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
The complexity of class polynomial computation via floating point approximations (2006)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
The complexity of class polynomial computation via floating point approximations (2006)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
The complexity of class polynomial computation via floating point approximations (2006)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
The complexity of class polynomial computation via floating point approximations (2006)
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart...
The complexity of class polynomial computation via floating point approximations (2006)
Abstract. We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots....
The complexity of class polynomial computation via floating point approximations (2006)
Abstract. We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots....
The arithmetic of Jacobian groups of superelliptic cubics (2005)
Basiri, Abdolali, Enge, Andreas, Faugère, Jean-Charles, Gürel, Nicolas
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily...
The arithmetic of Jacobian groups of superelliptic cubics (2005)
Basiri, Abdolali, Enge, Andreas, Faugère, Jean-Charles, Gürel, Nicolas
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily...
The arithmetic of Jacobian groups of superelliptic cubics (2005)
Basiri, Abdolali, Enge, Andreas, Faugère, Jean-Charles, Gürel, Nicolas
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily...
The arithmetic of Jacobian groups of superelliptic cubics (2005)
Basiri, Abdolali, Enge, Andreas, Faugère, Jean-Charles, Gürel, Nicolas
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily...
The arithmetic of Jacobian groups of superelliptic cubics (2002)
Basiri, Abdolali, Enge, Andreas, Faugère, Jean-Charles, Gürel, Nicolas
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily...
The arithmetic of Jacobian groups of superelliptic cubics (2002)
Basiri, Abdolali, Enge, Andreas, Faugère, Jean-Charles, Gürel, Nicolas
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily...
The arithmetic of Jacobian groups of superelliptic cubics (2002)
Basiri, Abdolali, Enge, Andreas, Faugère, Jean-Charles, Gürel, Nicolas
We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily...
We propose a practical non-interactive key distribution protocol based on pairings and dene a notion of security for such a scheme. We prove the security of the system in this setting under the GDBH...
Algebraic Curves in Cryptology (2002)
Andreas Enge, Pierrick Gaudry, François Morain, Et Inria Futurs
Number theory provides one of the most important sources of computationally hard problems which lay the foundations of modern cryptology: The security of RSA relies on the hardness of factoring a...
Hyperelliptic cryptosystems : efficiency and subexponential attacks / (2000)
Hergestellt on demand
Smooth ideals in hyperelliptic function fields (2000)
Recently, several algorithms have been suggested for solving the discrete logarithm problem in the Jacobians of high-genus hyperelliptic curves over finite fields. Some of them have a provable...
A General Framework for Subexponential Discrete Logarithm Algorithms (2000)
Andreas Enge, P. Gaudry, Andreas Enge, Pierrick Gaudry
We describe a generic algorithm for computing discrete logarithms in groups of known order in which a smoothness concept is available. The running time of the algorithm can be proved without using...
Smooth ideals in hyperelliptic function fields (2000)
Abstract. Recently, several algorithms have been suggested for solving the discrete logarithm problem in the Jacobians of high-genus hyperelliptic curves over finite fields. Some of them have a...
Abstract. We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over finite fields. Its expected running time for instances...
After generalising two reduction algorithms to characteristic 2, we analyse the average complexity of the arithmetic in hyperelliptic Jacobians over any finite eld. To this purpose we determine the...
We provide a subexponential algorithm for solving the discrete logarithm problem in Jacobians of high-genus hyperelliptic curves over finite fields. More precisely, the running time for instances...
Exact Volume Computation for Polytopes: A Practical Study (1998)
Benno Büeler, Andreas Enge, Komei Fukuda
We study several known volume computation algorithms for convex d-polytopes by classifying them into two classes, triangulation methods and signed-decomposition methods. By incorporating the...
. In "An artificial-free simplex-type algorithm for general LP models" [Math. Comput. Model., 25 (1997), pp. 107--123] and "Initialization of the simplex algorithm: An artificial-free...
Exact Volume Computation for Polytopes: A Practical Study (1998)
Benno Büeler, Andreas Enge, Komei Fukuda
We study several known volume computation algorithms for convex d-polytopes by classifying them into two classes, triangulation methods and signed-decomposition methods. By incorporating the...