Question:

(a) A string of ciphertext was enciphered using an a±ne transformation of single letters in a 28-letter alphabet consisting of A to Z, a blank and a?, where A to Z have numerical equivalents 0 to 25, blank=26, ?=27. A frequency analysis reveals that the the first, second and third most common letters of this ciphertext are B, ? and I, respectively. Suppose that the first and second most common letters in an English language text written in this 28-letter alphabet are ` '(blank) and E, respectively.

(i) Find the possible deciphering transformations.

(ii) Using the fact that T, is the third most common letter in the English language (of our 28 letters), find the right deciphering transformation.

(b) The ciphertext

¡GSTMTSI XJMUIGHRFKYMV

was generated using a 2£2 enciphering matrix with a 29¡letter alphabet, where A to Z have numerical equivalents 0 to 25, blank=26, !=27, and ¡ = 28. Given that the last five letters of the plaintext are A¡ONE, determine the complete plaintext.