Final answer:
Yes, it is theoretically possible for two different plaintexts to result in the same ciphertext using the Hill Cipher due to mathematical properties of matrix operations, but this is generally an exception rather than the norm. The question incorrectly refers to a Transposition Cipher, which is not the same as a Hill Cipher and operates on the principle of rearranging plaintext letters.
Step-by-step explanation:
The question is asking whether it is possible for two different plaintexts to produce the same ciphertext when using the Hill Cipher. This scenario is known as a collision. In the Hill Cipher, which is a type of polygraphic substitution cipher, a matrix is used as the key to encrypt blocks of plaintext letters.
Because of the mathematical properties of matrices, it is theoretically possible for collisions to occur if the key matrix does not have an inverse, or if improper handling of the plaintext (like plaintext blocks that are not co-prime with the modulus) leads to the same encrypted output. However, the design of the Hill Cipher normally aims to avoid such occurrences.
It's also important to note that the question mistakenly refers to a Transposition Cipher which is different from a Hill Cipher. In a transposition cipher, such as the one used in the Zimmerman Telegram, plaintext letters are rearranged according to a rule, typically involving block sizes and order changes guided by a keyword, with no substitutions made as in the Hill Cipher.