Searching for authors named "Andreas Enge" – sorted by Relevance.
8 documents found, showing 1 through 8.
-
The complexity of class polynomial computation via floating point approximations
- …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 of the algorithm is the evaluation of modular functions in several arguments. The fastest one of the…
- Cited by 10 (1 self) – Add To MetaCart
-
Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time
- …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 with genus g and underlying finite field Fq satisfying g ≥ ϑ log q for a positive constant ϑ is given…
- Cited by 25 (4 self) – Add To MetaCart
-
A General Framework for Subexponential Discrete Logarithm Algorithms in Groups of Unknown Order
- …We develop a generic framework for the computation of logarithms in nite class groups. The model allows to formulate a probabilistic algorithm based on collecting relations in an abstract way independently of the specific type of group to which it is applied, and to prove a subexponential running ti…
- Cited by 30 (5 self) – Add To MetaCart
-
Smooth ideals in hyperelliptic function fields
- …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 subexponential running time and are using the fact that smooth reduced ideals are sufficiently dense. We ex…
- Cited by 6 (5 self) – Add To MetaCart
-
Practical Non-Interactive Key Distribution Based on Pairings
- …We propose a practical non-interactive key distribution protocol based on pairings and de ne a notion of security for such a scheme. We prove the security of the system in this setting under the GDBH assumption, and present some possible realisations using Weil or Tate pairings on supersingular …
- Cited by 8 (0 self) – Add To MetaCart
-
An L(1/3 + ε) algorithm for the discrete logarithm problem in low degree curves
- …Abstract. The discrete logarithm problem in Jacobians of curves of high genus g over finite fields Fq is known to be computable with subexponential complexity Lqg(1/2, O(1)). We present an algorithm for a family of plane curves whose degrees in X and Y are low with respect to the curve genus, and su…
- Cited by 1 (0 self) – Add To MetaCart
-
The extended Euclidian algorithm on polynomials, and the computational efficiency of hyperelliptic cryptosystems
- …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 exact average number of field operations for computing the greatest common divisor of polynomials over…
- Cited by 2 (1 self) – Add To MetaCart
-
A Counterexample To H. Arsham's "Initialization Of The Simplex Algorithm: An Artificial-Free Approach"
- …. 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 approach" [SIAM Rev., 39 (1997), pp. 736--744], Arsham presents a new Phase 1 algorithm for the simplex method of li…
- Add To MetaCart
Showing 1 through 8.
