Summary: Pseudo-Random Generators and Structure of Complete Degrees
Manindra Agrawal
Dept of CSE, IIT Kanpur 208016, India
email: manindra@iitk.ac.in
Abstract
It is shown that if there exist sets in E that require
¢¡¤£¦¥¢§
-sized circuits then sets that are hard for class P, and
above, under 1-1 reductions are also hard under 1-1, size-
increasing reductions. Under the assumption of the hard-
ness of solving RSA or Discrete Log problem, it is shown
that sets that are hard for class NP, and above, under many-
one reductions are also hard under (non-uniform) 1-1, and
size-increasing reductions.
1 Introduction
Pseudo-random generators, although originally defined
for specific usages, have turned out to be fundamental
objects with applications in many diverse areas. There
exist two types of such generators: one computable in
exponential-time in their seed length (defined by Nisan

Source: Agrawal, Manindra - Department of Computer Science and Engineering, Indian Institute of Technology Kanpur

Collections: Computer Technologies and Information Sciences