University of California — Berkeley
Handout
CS276: Cryptography
March 15, 2002
Professors Luca Trevisan and David Wagner
Midterm
This midterm is due at the start of class on
Tuesday, March 19th.
When you are asked to prove or disprove a statement
S
, you actually have three options:
you may show that
S
is unconditionally true; you may show that
S
is unconditionally false;
or, you may show that
S
is conditionally true under some standard assumption (e.g., that
oneway functions exist) and false otherwise.
For each problem, be sure to state clearly and precisely what result you are going to prove
before proving it.
You do not need to reprove anything covered in class. This exam is “opennotes” (you may
use anything in your notes or the online scribe notes) but “closedbook” (you may not use
any textbook or other source).
Problem 1.
[Injective Pseudorandom Generators]
We want to show that pseudorandom generators may or may not be 11 functions.
(a)
Assuming the existence of oneway permutations of superpolynomial security,
prove the existence of a pseudorandom generator
G
:
{
0
,
1
}
n
→ {
0
,
1
}
n
+1
of
superpolynomial security with the additional property that
G
is a 11 function.
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 Spring '02
 Trevisan
 Bitwise operation, oneway function, Pseudorandomness, elgamal encryption, pseudorandom generator

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