Cryptography Reference
In-Depth Information
of plaintext P using encryption key
K
is
C
, the entire cryptosystem is defined as
follows:
E
K
1
(A)=
B
E
K
1
(B)=
C
E
K
1
(C)=
D
E
K
1
(D)=
A
E
K
2
(A)=
B
E
K
2
(B)=
C
E
K
2
(C)=
A
E
K
2
(D)=
D
E
K
3
(A)=
D
E
K
3
(B)=
B
E
K
3
(C)=
A
E
K
3
(D)=
C
E
K
4
(A)=
A
E
K
4
(B)=
B
E
K
4
(C)=
D
E
K
4
(D)=
C
E
K
5
(A)=
C
E
K
5
(B)=
D
E
K
5
(C)=
A
E
K
5
(D)=
B
(a) What is the size of the keyspace?
(b) If an interceptor sees the ciphertext
B
then which plaintext can he rule out?
(c) What is the ciphertext that results from encrypting plaintext B with
K
3
, and
is this a problem?
(d) Could we replace the bottom right-hand entry of the table with
E
K
5
(D)=
C
?
(e) Suppose that we define a sixth key
K
6
by the rule
E
K
6
(P)=
E
K
5
(
E
K
1
(P)) for
each plaintext P. In other words, for example,
E
K
6
(A)=
E
K
5
(
E
K
1
(A))=
E
K
5
(B)=
D
.
What are the values for
E
K
6
(B),
E
K
6
(C) and
E
K
6
(D)?
(f) Could we use a table such as this to represent a real cryptosystem?
17
. Explainwhether the following scenarios are possible for a symmetric cryptosys-
tem:
(a) two different plaintexts encrypt to the same ciphertext under different keys
(in other words,
E
K
1
(
P
1
)
=
E
K
2
(
P
2
)
=
C
);
(b) two different plaintexts encrypt to the same ciphertext under the same key
(in other words,
E
K
(
P
1
)
=
E
K
(
P
2
)
=
C
);
(c) a plaintext encrypts to the same ciphertext under two different keys (in
other words,
E
K
1
(
P
)
=
E
K
2
(
P
)
=
C
).
18
.
In most of this chapter we assumed that cryptography was being used to
protect data in a communication scenario. However, cryptography can also
be used to protect stored data. Which of the issues that we discussed in
this chapter are exactly the same regardless of whether cryptography is being
used to protect transmitted data or stored data, and which of these are subtly
different? (You might like to consider who the likely players are in the basic
model of a cryptosystem being used to protect stored data, which security
questions they might ask, etc.)
19
. Most people generally regard cryptography as a 'force for good', which can be
used to help protect computer systems.
(a) Explain why government organisations might not always regard cryptogra-
phy as a 'force for good'.
(b) Can you think of any ways in which cryptography could be used as a tool to
attack
computer systems?
