Cryptography is the science of encoding messages. One of the earliest systems for encodi...

Cryptography is the science of encoding messages. One of the earliest systems for encoding messages was used by Julius Caesar and is known as the Caesar cipher. The Caesar cipher consists of replacing each letter in a message by the letter three places beyond it in alphabetical order. For example, suppose the message to be encoded is

SEND THE LEGION NORTH.

Under each letter of the message we write the letter three places further along in the alphabet as follows:

SEND THE LEGION NORTH

VHQG WKH OHJLRQ QRUWK.

Thus, the second line is the encoded message.

The Caesar cipher is an example of a substitution cipher, in which each letter of the original message is replaced by another. The Caesar cipher uses the general system of advancing the letter by adding a fixed number, namely 3, to its numerical equivalent using 26-hour clock arithmetic. Because knowing the number 3 tells you exactly how to encode and decode messages in the Caesar cipher, 3 is called the key. Encoding messages by adding a number in 26-hour clock arithmetic is called a direct standard alphabet code.

a. Encode the message LEAVE TUESDAY using a direct standard alphabet code and key 7.

b. Encode the message MAKE MY DAY using a direct standard alphabet code and key 14.

c. Decode the message WZNVPC WIGT using a direct standard alphabet code and key 11.

d. Decode the message CNM GUACW using a direct standard alphabet code and key 20.