Cryptography

9. (5 points) A certain message exchange system only enables the use of the 26 uppercase Roman letters, without any spaces, punctuation, or special characters. The letters take numerical values between 0 and 25 sequentially. A variant of the One-Time Pad was adopted as security mechanism for that system, whereby a key K (a random sequence of letters) has the same length as the message M but the letters are added modulo 26 (i.e. when their sum reaches 26 or more, the remainder of the division by 26 is taken, ensuring that the result still corresponds to a letter) instead of being XOR-ed. However, by a specification failure the designers ended up using the same key for all messages. Show how an attacker who knows a message M its ciphertext C obtained under the key K, and the cryptogram C of some other message M of the same length can be obtained, and use this to compute and recover M from: M = "LOWPRICES", C = "DSYQIMCGZ", C* = "YSVUYIMUN