| 3 3 3 | | 3 3 3 | | 3 3 3 |
Alice is using a 3-by-3 secret matrix to encrypt a written text and send it to Bob. Her encryption method is as follows. First, Alice tells Bob what secret matrix she is going to use. To send a message, she replaces each letter by its corresponding order in the alphabet and puts a zero for a space. This yields a vector of integers which encodes the message. The 3-by-3 matrix is applied to the first three entries of the vector, then the next three entries, etc. This yields a new vector which carries the encrypted text. Alice then sends the encrypted vector in an email.
1. How can Bob decrypt the message?
Eve is eavesdropping the conversation. Although she doesn’t know what the matrix is, she happens to know that the message (1,0,4,0,1,0,1,0,1) yields the encrypted vector (2,0,0,0,1,0,0,0,3).
2. Can Eve decrypt the message without finding the inverse of the secret matrix?
3. What is the decrypted message corresponding to (2,23,3)? (Write it as a text.)
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