suppose plaintext english is encrypted using a symmetric key cryptosystem with keyspace k. if the unicity distance of the cryptosystem is 20 characters, find the size of the keyspace
The formula for expected unicity distance,
where H(k) is the entropy of key space. If the size of keyspace is "S", H(k) = log2S.
D is defined as plaintext redundancy in bits per character.
For an English character, we have log2(26)= 4.7 bits of information. However, the average amount of information per character in meaningful English is 1.5.
So, D= 4.7 - 1.5 = 3.2 for English plaintext.
We have U= 20. S=?
So, from the equation of U, we get
20= log2S/3.2
=> 20*3.2= log2S
=> 64 = log2S
=> S= 264
So, the size of the key space is 264 .
Please upvote. Thanks.
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