@inproceedings{B-The-Complexity-Of-Factors-Of-Multivariate-Polynomials-1,
Title = {The Complexity of Factors of Multivariate Polynomials},
Author = {Peter Bürgisser},
Booktitle = {Proceedings 42nd FOCS},
Pages = {378-385},
Year = {2001},
Address = {Las Vegas},
Month = {October 14-17},
Abstract = {The existence of string functions, which are not polynomial time computable, but whose graph is checkable in polynomial time, is a basic assumption in cryptography. We prove that in the framework of algebraic complexity, there are no such families of polynomial functions of p-bounded degree over fields of characteristic zero. The proof relies on a polynomial upper bound on the approximative complexity of a factor g of a polynomial f in terms of the (approximative) complexity of f and the degree of the factor g. This extends a result by Kaltofen (STOC 1986). The concept of approximative complexity allows to cope with the case that a factor has an exponential multiplicity, by using a perturbation argument. Our result extends to randomized (two-sided error) decision complexity.},
Url = {http://www3.math.tu-berlin.de/algebra/work/focs2001.pdf},
Url2 = {http://link.springer.com/article/10.1007/s10208-002-0059-5},
Reviewed = {True}
}