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CRYPTO
2006
Springer
232views Cryptology» more  CRYPTO 2006»
14 years 4 days ago
Algebraic Geometric Secret Sharing Schemes and Secure Multi-Party Computations over Small Fields
Abstract. We introduce algebraic geometric techniques in secret sharing and in secure multi-party computation (MPC) in particular. The main result is a linear secret sharing scheme...
Hao Chen, Ronald Cramer
GIAE
2004
Springer
275views Mathematics» more  GIAE 2004»
14 years 1 months ago
Conic Sections and Meet Intersections in Geometric Algebra
This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective ...
Eckhard M. S. Hitzer
ISSAC
2007
Springer
146views Mathematics» more  ISSAC 2007»
14 years 2 months ago
Fast and exact geometric analysis of real algebraic plane curves
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the pla...
Arno Eigenwillig, Michael Kerber, Nicola Wolpert
ISSAC
1997
Springer
194views Mathematics» more  ISSAC 1997»
14 years 18 days ago
The Minimised Geometric Buchberger Algorithm: An Optimal Algebraic Algorithm for Integer Programming
IP problems characterise combinatorial optimisation problems where conventional numerical methods based on the hill-climbing technique can not be directly applied. Conventional me...
Qiang Li, Yike Guo, Tetsuo Ida, John Darlington
COMPGEOM
2001
ACM
14 years 3 days ago
PRECISE: efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computation
: Many geometric problems like generalized Voronoi diagrams, medial axis computations and boundary evaluation involve computation and manipulation of non-linear algebraic primitive...
Shankar Krishnan, Mark Foskey, Tim Culver, John Ke...