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Com S 633: Randomness in Computation Lecture 23 Scribe: K. S. Gopalakrishnan, Hongyu Sun
 

Summary: Com S 633: Randomness in Computation
Lecture 23 Scribe: K. S. Gopalakrishnan, Hongyu Sun
Goldreich-Levin Hardcore Bit Theorem: Let f be a one way permutation. De ne a function
b :
P 2n !
P
, called as hard-core bit as
b(x; r) = hx; ri =
X
x i r i ( mod 2):
If there is a circuit C such that
Pr
x;r2Un
[C[f(x); r] = hx; ri >]  1
2
+ 
then there exist circuit D of size
poly(jCj ; 1
 )
such that

  

Source: Aduri, Pavan - Department of Computer Science, Iowa State University

 

Collections: Computer Technologies and Information Sciences