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» Using number fields to compute logarithms in finite fields
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ISSAC
1997
Springer
138views Mathematics» more  ISSAC 1997»
14 years 17 days ago
Fast Polynomial Factorization Over High Algebraic Extensions of Finite Fields
New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n1+a , where a ...
Erich Kaltofen, Victor Shoup
COCO
2008
Springer
100views Algorithms» more  COCO 2008»
13 years 10 months ago
Detecting Rational Points on Hypersurfaces over Finite Fields
We study the complexity of deciding whether a given homogeneous multivariate polynomial has a nontrivial root over a finite field. Given a homogeneous algebraic circuit C that com...
Swastik Kopparty, Sergey Yekhanin
PRESENCE
2006
104views more  PRESENCE 2006»
13 years 8 months ago
Physically Realistic Virtual Surgery Using the Point-Associated Finite Field (PAFF) Approach
The generation of multimodal virtual environments for surgical training is complicated by the necessity to develop heterogeneous simulation scenarios such as surgical incision, ca...
Suvranu De, Yi-Je Lim, Manivannan Muniyandi, Manda...
ASIACRYPT
2006
Springer
14 years 5 days ago
The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
Abstract. The complex multiplication (CM) method for genus 2 is currently the most efficient way of generating genus 2 hyperelliptic curves defined over large prime fields and suit...
Pierrick Gaudry, T. Houtmann, D. Kohel, Christophe...
FOCM
2008
77views more  FOCM 2008»
13 years 8 months ago
Modular Counting of Rational Points over Finite Fields
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 ...
Daqing Wan