Chapter 4.6, Problem 32E

In Exercises 31-32 suppose that Alice and Bob have these public keys and corresponding private keys: $(n_{Alice},e_{Alice})=(2867,7)=(61.47,7),d_{Alice}=1183$ and $(n_{Bob},e_{Bob})=(3127,21)=(59.53,21),d_{Bob}=1149$ . First express your answers without carrying out the calculations. Then, using a computational aid, if available, perform the calculation to get the numerical answers.

Alice wants to send Bob the message “BUY NOW” so that he knows that she sent it and so that only Bob can read it. What should she send to Bob, assuming she signs the message and then encrypts it using Bob’s public key?