The direct standard alphabet code relies on addition in 26-hour-clock arithmetic. Anothe...

The direct standard alphabet code relies on addition in 26-hour-clock arithmetic. Another substitution method, called decimation, relies on multiplication in 26-clock arithmetic. The number you multiply by, called the key, can be any number that has no factor in common with 26 such as 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, and 25. Suppose you select a key of 3. The letter A, which corresponds to 1, will be replaced by which corresponds to C. Similarly B, which corresponds to 2, will be replaced by which corresponds to the letter F. Each subsequent replacement letter is obtained by adding another 3 in the 26-clock.

a. Encode or decode each of the following messages using decimation with the key 3.

(i) NEW YORK

(ii) GOW QOEH

b. Encode a message using decimation with 5 as the key.

c. Explain why the key used with decimation must not have factors in common with 26.