Homophonic cipher:-
Suppose that a language using an alphabet of J letters has the property that the i-th letter has a frequency of ki/N, for each i, where the ki's and N are integers with
A homophonic cipher is made up of exactly N symbols, with ki of these assigned to the i-th letter of the alphabet (and with no duplications). When a letter i is to be encrypted, one of the ki cipher symbols assigned to it is chosen at random. This will make all N code symbols appear with probability 1/N. To determine the unicity point of such a code, it is necessary to modify the basic relation for H(K|C) because H(C|M,K) is not zero.
(a) Show that in general
(b) Show that for the situation of this exercise
(c) If the language has an entropy determined only by the frequency of its letters, can the homophonic cipher be broken?
(d) The number of ways of assigning symbols for this cipher is
If the entropy of the language is H per letter, what is the unicity point of the cipher?
(e) Assuming that the entropy of English is 1.5 bits/letter and that the homophonic code of 100 symbols in the text is used, what is the unicity point? (Note that log W = 377.)