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ECCC
1998
105views more  ECCC 1998»
13 years 7 months ago
Pseudorandom generators without the XOR Lemma
Impagliazzo and Wigderson IW97] have recently shown that if there exists a decision problem solvable in time 2O(n) and having circuit complexity 2 (n) (for all but nitely many n) ...
Madhu Sudan, Luca Trevisan, Salil P. Vadhan
ECCC
2011
223views ECommerce» more  ECCC 2011»
13 years 2 months ago
A Case of Depth-3 Identity Testing, Sparse Factorization and Duality
Polynomial identity testing (PIT) problem is known to be challenging even for constant depth arithmetic circuits. In this work, we study the complexity of two special but natural ...
Chandan Saha, Ramprasad Saptharishi, Nitin Saxena
JACM
2000
119views more  JACM 2000»
13 years 7 months ago
A subdivision-based algorithm for the sparse resultant
Multivariate resultants generalize the Sylvester resultant of two polynomials and characterize the solvability of a polynomial system. They also reduce the computation of all comm...
John F. Canny, Ioannis Z. Emiris
JC
2010
117views more  JC 2010»
13 years 2 months ago
Tractability through increasing smoothness
We prove that some multivariate linear tensor product problems are tractable in the worst case setting if they are defined as tensor products of univariate problems with logarithm...
Anargyros Papageorgiou, Henryk Wozniakowski
PKC
2005
Springer
114views Cryptology» more  PKC 2005»
14 years 1 months ago
Cryptanalysis of the Tractable Rational Map Cryptosystem
In this paper, we present the cryptanalysis of a public key scheme based on a system of multivariate polynomial equations, the ”tractable rational map” cryptosystem. We show co...
Antoine Joux, Sébastien Kunz-Jacques, Fr&ea...