Caesar Cipher

One of the oldest cryptologic systems, the Caesar cipher, replaces each letter from a message by another letter a fixed number of places further in the alphabet. For example, in a Caesar cipher with shift 2, A becomes C, B becomes D, C becomes E, and so on. The last letters Y and Z "wrap around", becoming A and B, respectively.

A coder encodes the message before it is sent with a a% accuracy and the receiving decoder deciphers with an accuracy of b%. During transmission, there is a c% probability of error due to conditions in the transmission media.

a. Discuss the probability distribution of transmission errors.

b. Define what criteria (in terms of a number of incorrectly encoded and decoded letters) constitutes a message that a recipient can understand.

c. What is the probability that an n-character sentence is understandable using the criteria outlined in Part B?

d. Calculate the probability that a 15-letter sentence will be understood by the recipient for a=95%, b=90%, and c=10%.

e. What strategies could be put in place to increase the accuracy of the transmission process?

f. Research some of the past issues the organizations experienced due to the lack of cryptologic system. Using a meaningful paragraph, explain what the reasons were for not having it in place, and what were the repercussions to the organizations.