Question

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

Answer 1

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 .

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