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CSE 794 Homework 1
Due: Monday, April 12 by class time
1.
Show that if an encryption scheme is perfectly secret and
M
K
C
, then all
ciphertexts
have the same probability, i.e.,
1
Pr
for all
.

c
c C
C
2.
For any fixed integer
0,
n
Vernam’s onetime pad over message space
0,1
n
M
can
be described as follows.
To encrypt a message
0,1
n
m
, one generates a key
0,1
n
u
k
and encrypt
as
:
m
c
m k
bit by bit.
By Shannon’s Theorem, this scheme
is perfectly secret for each
n
.
Now, for a fixed
1,
n
consider Vernam’s onetime pad
over message space
1
0,1 ,
n
i
i
M
the set of all strings of length
.
n
To encrypt a
message
,
mM
we generate a key
0,1
(where   denotes the length of
)
m
u
k
m
m
and encrypt
as
:
m
c
m k
bit by bit. Question:
is this scheme perfectly secret?
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This note was uploaded on 01/22/2011 for the course CSE 794 taught by Professor Tenh.lai during the Spring '10 term at Ohio State.
 Spring '10
 TenH.Lai

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