Question

(From Wikipedia) In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key, there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key completely, assuming the underlying message has redundancy. Critique this definition for a ciphertext-only attack on a shift cipher. In particular, considering the ciphertext ALIIP and its possible plaintexts, does this say something about the unicity distance? Textbooks claim that the unicity distance of a shift cipher is about 1.3. Can you reconcile this with your last answer?

Answer 1

When we perform the brute force attack so the calculation that on how many ciphertext we need to be sure that our answer or solution will be true.Which may depends on the redundancy of language.

let take an example that we have a massage and we need to decipher and the ciphered massage is "FJKFPO", . So the question is how we will decipher it. For this we got to find the english words that fit the pattern, sure, but we can never get original plain massage. Below are the many option which could be answer but we do not know which one is right.

thatis
ofyaur
season
onyaur
thatwe
thetop
thetwo
oxford
thatan
thatif

and many more. If   ciphertext is longer , then fewer decryption possible . We want to know,what should be the length of ciphertext so that it has only one possible decryption this minimum length is know as unicity distance .

Redundancy

Every substitution cipher owns a key which is of 26 letters. And the total number of keys will be equal to 26! which show the permutation or ways to rearrange . which will be very large. This information is calculated in bit using the logarithm with base 2

or which is around 88 bits. and same measurement per character will be bits. And the information about the engliah alphabates is around 1.5 so redundancy will be par character 4.7-1.5=3.2.

Now come to actual words definition of unicity distance which is the ratio that how many bits in number are required to show or express the key and per character redundancy in bits in English. for above discussed case s this will be 88.28/3.2 = 27.6. Which shows that at least 28 characters are required, at minimum, for uniquely particular decryption which is the unicity distance.Below is one more clarification.