32 research outputs found
Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets
Goldreich suggested candidates of one-way functions and pseudorandom
generators included in . It is known that randomly generated
Goldreich's generator using -wise independent predicates with input
variables and output variables is not pseudorandom generator with
high probability for sufficiently large constant . Most of the previous
works assume that the alphabet is binary and use techniques available only for
the binary alphabet. In this paper, we deal with non-binary generalization of
Goldreich's generator and derives the tight threshold for linear programming
relaxation attack using local marginal polytope for randomly generated
Goldreich's generators. We assume that input
variables are known. In that case, we show that when , there is an
exact threshold
such
that for , the LP relaxation can determine
linearly many input variables of Goldreich's generator if
, and that the LP relaxation cannot determine
input variables of Goldreich's generator if
. This paper uses characterization of LP solutions by
combinatorial structures called stopping sets on a bipartite graph, which is
related to a simple algorithm called peeling algorithm.Comment: 14 pages, 1 figur
Academic catalog (Florida International University). [1986-1987]
https://digitalcommons.fiu.edu/catalogs/1045/thumbnail.jp
Academic catalog (Florida International University). [1984-1985]
https://digitalcommons.fiu.edu/catalogs/1047/thumbnail.jp
Academic catalog (Florida International University). [1987-1988]
https://digitalcommons.fiu.edu/catalogs/1044/thumbnail.jp
Academic catalog (Florida International University). [1985-1986]
https://digitalcommons.fiu.edu/catalogs/1046/thumbnail.jp
Academic catalog (Florida International University). [1983-1984]
https://digitalcommons.fiu.edu/catalogs/1048/thumbnail.jp
Catalog (Florida International University: 1988). [1990-1991]
https://digitalcommons.fiu.edu/catalogs/1041/thumbnail.jp
Catalog (Florida International University: 1988). [1989-1990]
https://digitalcommons.fiu.edu/catalogs/1042/thumbnail.jp