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EUROCRYPT
2000
Springer
14 years 1 days ago
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard ove...
Nicolas Courtois, Alexander Klimov, Jacques Patari...
COMGEO
2011
ACM
13 years 3 months ago
On crossing numbers of geometric proximity graphs
Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed prox...
Bernardo M. Ábrego, Ruy Fabila Monroy, Silv...
FOCS
2008
IEEE
13 years 8 months ago
Market Equilibria in Polynomial Time for Fixed Number of Goods or Agents
We consider markets in the classical Arrow-Debreu model. There are n agents and m goods. Each buyer has a concave utility function (of the bundle of goods he/she buys) and an init...
Nikhil R. Devanur, Ravi Kannan
CSC
2006
13 years 9 months ago
On the Number of Minimal Addition Chains
An addition chain for a natural number n is a sequence 1 = a0 < a1 < . . . < ar = n of numbers such that for each 0 < i r, ai = aj + ak for some 0 k j < i. Thurbe...
Hatem M. Bahig
CC
2007
Springer
158views System Software» more  CC 2007»
13 years 8 months ago
The Complexity of Membership Problems for Circuits Over Sets of Natural Numbers
Abstract. The problem of testing membership in the subset of the natural numbers produced at the output gate of a {∪, ∩,− , +, ×} combinational circuit is shown to capture a...
Pierre McKenzie, Klaus W. Wagner