SIT 281代写留学生、Matlab编程代做、帮写Matlab、Matlab设计帮写

日期：2018-09-28 09:55

SIT 281 TRIMESTER 2 2018

ASSIGNMENT 2

DUE: By 12 NOON (Australian Eastern Standard Time), Monday 1st October

2018.

Submit a single file to the unit Cloud. The cover page is in the Assignment folder

on the unit Cloud and also available at

http://www.deakin.edu.au/__data/assets/word_doc/0003/954021/SEBEAssignment-Coversheet.docx

It should be incorporated at the beginning of your submission.

Marks are given for explanations.

NO EXTENSIONS allowed without medical or other certification.

LATE ASSIGNMENTS will automatically lose 10% per day up to a maximum of

three days, including weekends and holidays. Assignments submitted 4 or more days

late will not be marked and are given zero. NO EXTENSIONS FOR ANY

REASONS, INCLUDING THOSE BASED ON DISABILITY PLANS, PAST

FRIDAY OCTOBER 5

METHOD OF SUBMISSION: Complete the cover sheet with your unit code, your

full name, campus enrolled at (B, G or X) and ID; please underline your family name

as recorded with Deakin.

1. Alice and Bob want to establish a common key pair using the Diffie-Hellman key

exchange protocol and then use it in to send each other messages using a symmetric

cipher. They agree by email on a prime p=877 and a primitive root (generator) a=

453; these are public knowledge). Then Alice chooses secret x=25 while Bob chooses

secret y=13.

Alice is in Australia while Bob is in Brazil. Carl, a Canadian friend of Alice, has been

tracking the email received and sent by Alice and decides that he wants to listen in on

conversations between Alice and Bob. Carl therefore sets up a man-in-the-middle

attack as follows.

Carl sees the set-up agreed to by Alice and Bob and he chooses secret z = 17.

Using the primitive root and her secret, Alice computes 45325 (mod 877) and sends it

to Bob; however, Carl intercepts this email (which Bob never receives). Similarly,

Carl intercepts Bob’s e-mail containing 45313 (mod 877) (which Alice never

receives).

Determine what common key Carl sets up with Bob, and his common key with Alice.

4 marks

2. Tony selects the prime p = 2357 and a primitive root g = 2 (mod 2357). Tony also

chooses the private key a = 1751 and computes ga

mod p which is 21751 (mod 2357) ≡

1185. Now Tony’s public key is (p = 2357; g = 2; ga

= 1185).

To encrypt a message m = 2035 to send to Tony, Bai selects a random integer k =

1520 and computes u = 21520 (mod 2357) ≡ 1430 and v = 2035 * 11851520 (mod

2357) ≡ 697, and sends the pair ( 1430, 697) to Tony. Tony decrypts to retrieve the

message 2035.

Bai then sends a second message m’ = 1339 to Tony, using the same value of random

integer k: he computes u = 21520

(mod 2357) ≡ 1430 and v = 1339 * 11851520 (mod

2357) ≡ 2145, and send the pair (1430, 2145) to Tony.

Oscar, works with Tony and has seen the pair (1430, 697) and m = 2035. Oscar is

now keen to obtain m' without Tony knowing. He sees the second pair (1430, 2145)

on Tony’s laptop. Show how he derives m’. 4 marks

3. Use a Maple procedure to find all points on the elliptic curve y

2 = x3 + 295x + 2891

over Z3137.

Capture from Maple and copy into your assignment answer all points with xcoordinate

less than 50. 5 marks

4. This is an RSA factoring question. In order to do the question, you need to read and

understand the preliminary part.

PRELIMINARY PART: If you know the modulus n, and can steal phi(n), then you

can calculate the two primes p and q such that n=pq as follows:

n – phi(n) + 1 = n – (p-1)(q-1) + 1 = n – pq +p + q -1 +1 = p+q.

This tells you the sum of p and q.

Suppose p > q (one has to be larger than the other). Then

p – q = √[(p-q)2

] = √[p2 +q2

+2pq – 4pq] = √[p2 +q2

+2pq – 4pq] = √[(p +q)2

-4n].

Since we know p+q, we now obtain p-q from this last equation. This gives us the

values of p and q using the following formulas:

p = ? [(p+q) + (p-q)] and q = ? [(p+q) - (p-q)].

(a) Verify that using these formulas p*q = n. 4 marks

(b) You bribe someone in the lab to give you the phi value for the current RSA

scheme being used. You now know that n = 7863043 and phi(n) = 7855120. Compute

the values of the factors of n using the formulas above. Show your work. 3 marks

TOTAL: 20 marks