Cryptography Reference
In-Depth Information
Exercise 1.4.
Let n be an integer. A Latin square of order n is an n
×
n array L with
entries in
such that each integer appears exactly once in each row and each
column of L. It defines a cipher over the message space
{
1
,...,
n
}
{
1
,...,
n
}
and the key space
{
1
,...,
n
}
in which the encryption of i under the key k is L
(
k
,
i
)
.
Prove that a Latin square defines a cipher which achieves perfect secrecy if a key
is used once and is uniformly distributed.
Exercise 1.5.
We assume that the plaintext
conversation
is encrypted into the ciphertext
HIARRTNUYTUS
by using the Hill cipher. This cipher uses an m
m invertible matrix in
Z
26
as a secret
key. First the messages are encoded into sequences of blocks of m
Z
26
-integers. Each
block is then separately encrypted by making a product with the secret matrix.
×
Recover m and the secret key by a known plaintext attack.
Exercise 1.6.
Product of Vigenere ciphers.
1. Given a fixed key length, prove that the set of all Vigenere encryption function
defined by all possible keys of given length is a group.
2. What is the product cipher of two Vigenere ciphers with different key lengths?
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