Assignment: The Secure Channel, Random Number Generation, Primes and Modular Arithmetic
1. In our definition of a secure channel, what are the two things that an eavesdropper is "allowed" to learn? Why do our constructions allow the eavesdropper to learn them?
2. You are placing an order with an online retailer. To complete a purchase, your web browser sends a single encrypted, authenticated message to the web site, consisting only of the following information: a) your credit card information, b) the item number and quantity being ordered.
a. Sayan adversary is sitting between you and the retailer, with the ability to intercept traffic and send messages. Describe an attack the adversarycould carry out to "max out" your credit card. What type of attack is this?
b. What could the retailer do to prevent this attack, simply by changing what data is sent in the single encrypted, authenticated message?
3. The followingsentence describes steps that are used to generate a ciphertext c and authentication tag t.
"The message number i is concatenated with the message and encrypted with key Kenc to produce the ciphertext. The key Kauth is concatenated with i and the message and hashed with SHA-384 to produce the tag."
Write these definitions of c and t in the symbolic notation that is used in class and the textbook.
4. If an adversary knows the process by which a 128-bit key is generated, and this process is known to includeonly 86 bits of entropy, what is the probability of guessing it correctly with a single guess?
5. When using physical phenomena (mouse movements, etc.) as a source of entropy for random number generation, why is it unwise to use the measurements directly as random bits?
6. Consider the Debian Linux RNG bug described in class, which potentially allowed all SSL traffic coming from the system to be decrypted. Search online and give the time span between the bug's introduction and when the vulnerability was announced publicly.
7. Perform the following modular exponentiations using the decomposition method shown in class.
a. 265 (mod 5)
b. 317 (mod 7)
c. 419 (mod 11)
8. Compute the value of the totient function φ for each of the following numbers.
a. φ(7)
b. φ(15)
c. φ(16)
d. φ(18)
9. Is 4 a generator for the group of multiplication modulo 7? Show why this is or is not the case.
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also include a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also Include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.