ps2 - Computer Science and Engineering UCSD CSE 207 Modern...

Computer Science and Engineering, UCSD Spring 11
CSE 207: Modern Cryptography Instructor: Mihir Bellare
Problem Set 2 April 6, 2010
Problem Set 2
Due: Wednesday April 13, 2010, in class.
Problem 1. [20 points] Define the family of functions F : { 0 , 1 }
128
×{ 0 , 1 }
128
→{ 0 , 1 }
128
by
F ( K,M ) = AES ( M,K ). Assuming AES is a secure PRF, is F a secure PRF? If so, explain why. If
not, present the best attack (with analysis) that you can.
Problem 2. [60 points] Let F : { 0 , 1 }
k
×{ 0 , 1 }
l
→{ 0 , 1 }
L
be a family of functions where
l,L ≥ 128. Consider the game G of Fig. 1.
We define
Adv
lr
F
( B ) = 2 · Pr
bracketleftBig
G
B
⇒ true
bracketrightBig
- 1 .
Let ( x
1
0
,x
1
1
) ,..., ( x
q
0
,x
q
1
) be the queries that B makes to its oracle. (Each query is a pair of l -bit
strings, and there are q queries in all.) We say that B is legitimate if x
1
0
,...,x
q
0
are all distinct,
and also x
1
1
,...,x
q
1
are all distinct. We say that F is LR-secure if Adv
lr
F
( B ) is “small” for every
legitimate B of “practical” resources.