1A.

For this question, use the following definitions.

- Let m be a message
- Let Ka+ be the public key for Alice, and Ka+(m) be the function
expression which indicates the message, m, is encrypted using
Alice's public key
- Let Ka- be the private key for Alice, and Ka-(m) be the
function expression which indicates the message, m, is encrypted
using Alice's private key
- Let Kb+ be the public key for Bob, and Kb+(m) be the function
expression which indicates the message, m, is encrypted using Bob's
public key
- Let Kb- be the private key for Bob, and Kb-(m) be the function
expression which indicates the message, m, is encrypted using Bob's
private key
- Let Ka+() be the inverse function of Ka-(), so
Ka+(Ka-(m))=Ka-(Ka+(m))=m
- Let Kb+() be the inverse function of Kb-(), so
Kb+(Kb-(m))=Kb-(Kb+(m))=m
- Let H() be a hash function

QUESTION: If Alice wants to send a message that only Bob can
read, what message does she send?

1B.

For this question, use the following definitions.

- Let m be a message
- Let Ka+ be the public key for Alice, and Ka+(m) be the function
expression which indicates the message, m, is encrypted using
Alice's public key
- Let Ka- be the private key for Alice, and Ka-(m) be the
function expression which indicates the message, m, is encrypted
using Alice's private key
- Let Kb+ be the public key for Bob, and Kb+(m) be the function
expression which indicates the message, m, is encrypted using Bob's
public key
- Let Kb- be the private key for Bob, and Kb-(m) be the function
expression which indicates the message, m, is encrypted using Bob's
private key
- Let Ka+() be the inverse function of Ka-(), so
Ka+(Ka-(m))=Ka-(Ka+(m))=m
- Let Kb+() be the inverse function of Kb-(), so
Kb+(Kb-(m))=Kb-(Kb+(m))=m
- Let H() be a hash function

QUESTION: If Alice wants to send a message that only Bob can
read, AND that Bob can know that the message must have come from
Alice, what message does she send?