Historical Cryptosystems - Everyday Cryptography - page 73

(b) How many different possible keys could have been used to encrypt the
plaintext?
(c) Decrypt the ciphertext MBR TRHLRP WHE HTHV CWND PNEYNE ZNN,
which is known to have been encrypted with the same key.
(d) What lesson can be learnt from conducting this exercise?

8 . The Playfair Cipher represents one improvement over monoalphabetic ciphers.
(a) Decrypt the following ciphertext using the Playfair key depicted in Figure 2.4:

NR SH NA SR HF CG FL TN RW NS DN NF SK RW TN DS XN
DS BR NA BI ND SN CR NT WO TQ FR BR HT BM FW MC

(b) Explain what method could be used to attack the Playfair Cipher by
attempting to decrypt ciphertext without knowledge of the decryption key.
(c) Some of the preprocessing rules for the Playfair Cipher are somewhat
arbitrary. Suggest an alternative set of preprocessing rules for the Playfair
Cipher.

9 . Alice wishes to regularly send Bob a plaintext message P 1 or P 2 . On each
occasion she chooses to send either P 1 or P 2 , but on average she chooses the
plaintext P 1 twice as often as she chooses the plaintext P 2 . Each time, Alice uses
a (very simple) symmetric cryptosystem, with the same fixed key K , to encrypt
the plaintext. When she chooses P 1 , the ciphertext is C 1 =

E K ( P 1 ); when she

E K ( P 2 ). Suppose that an attacker knows that
the only possible plaintext messages are P 1 and P 2 .
(a) Suppose that the attacker does not know that Alice chooses P 1 twice
as often as P 2 . What observation will the attacker, who can only see the
ciphertexts sent from Alice to Bob, make?
(b) Suppose that the attacker learns that Alice chooses P 1 twice as often as she
chooses P 2 . What does the attacker now learn?
(c) Explain how homophonic encoding can be used in this case to make
it more difficult for the attacker to learn anything useful from observing
ciphertexts.
10 . The example of homophonic encoding that we gave in Section 2.2.3 was
designed to make it appear as if each plaintext letter occurs equally often.
For each of the following specific requirements, and based on Table 2.1, design
a homophonic code for use with English plaintexts that has significantly less
message expansion than the example we gave (in each case also comment on
the resulting message expansion):
(a) The plaintext letter E appears to occur equally often to the plaintext letter P.
(b) Plaintext vowels all appear to occur equally often.
(c) It is hard for an attacker to identify the eight most frequently occurring
plaintext letters in English.

chooses P 2 , the ciphertext is C 2 =