Question 4. (25 points) The purpose of this question is to investigate the situation resulting from the following policy (that we assume to be applied system-wide) All emails are required to satisfy the following requirement: If M is the email (in cluding all its headers) then the leftmost k bits of H(M) must all be 1 (the same k is used system-wide); an email that satisfies this requirement is said to be compliant. A non-compliant email is automatically rejected - it is neither forwarded nor delivered. To help make emails compliant, they include a special count header that is an integer whose sole purpose is to be modified by the sender until the email becomes compliant. To send an email, the sender's software first tries a value of 0 for the count header, then it tries 1, .. .etc until she finds a value that makes the email compliant: It is this compliant version of the email that is sent Answer the following questions about such an email scheme. I. Let c be the smallest value of the count header that makes a given email compliant. Compute, as a function of k, the expected value of c. 2. There are obvious drawbacks to such an email scheme (e.g., it slows down the sending of emails, it is a drain on cell phone and laptop batteries, etc). Give at least one advantage to using such an email scheme. Briefly Justify your answer. Question 4. (25 points) The purpose of this question is to investigate the situation resulting from the following policy (that we assume to be applied system-wide) All emails are required to satisfy the following requirement: If M is the email (in cluding all its headers) then the leftmost k bits of H(M) must all be 1 (the same k is used system-wide); an email that satisfies this requirement is said to be compliant. A non-compliant email is automatically rejected - it is neither forwarded nor delivered. To help make emails compliant, they include a special count header that is an integer whose sole purpose is to be modified by the sender until the email becomes compliant. To send an email, the sender's software first tries a value of 0 for the count header, then it tries 1, .. .etc until she finds a value that makes the email compliant: It is this compliant version of the email that is sent Answer the following questions about such an email scheme. I. Let c be the smallest value of the count header that makes a given email compliant. Compute, as a function of k, the expected value of c. 2. There are obvious drawbacks to such an email scheme (e.g., it slows down the sending of emails, it is a drain on cell phone and laptop batteries, etc). Give at least one advantage to using such an email scheme. Briefly Justify your
