Econ1061 Secure Wireless Communication Answers Assessment Answers
You are a secret agent tasked to send and receive information related to national security. As a specialist in cryptography, you have decided to use matrix inverses to provide a simple and effective method for encoding and decoding messages.The numbers 1 – 26 have been assigned to letters of the alphabet as shown below. Additionally, the number 0 has been assigned to a blank to provide space between words.
|
Blank |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
M |
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
|
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z |
|
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
You have chosen to use the following (3 x 3) encoding matrix to encode messages:
A counterpart in Berlin has recently sent you the following confidential message. Let B represent a (3 x 14) matrix containing this original message. The coded message is therefore derived by multiplying A and B, i.e. coded message = AB. The coded message is as follows:
- Find the inverse of the encoding matrix [Use Gauss Jordan and show full working out].
- What is the original (decoded) message?
- Encode an appropriate response to this nationally sensitive message. The message must be between 21 and 42 characters (i.e. your matrix cannot be more than 14 columns) and be encoded by the same matrix. In your answer please include:
- Your secret message presented as a full sentence and without
- Your encoded message with encoding (that is after multiplying by ). This should be performed using the same methodology as matrix and be presented in 3 rows by
- Briefly describe three industries in which cryptography still play an important role today. Your explanation should also include a description of how cryptography is used by this industry. Keep this section short (half page maximum).
Question Two
You are a statistical consultant for the treasury department. You have been tasked to provide an input-output analysis on the Australian sector. In particular you are to analyse the interdependence of 32 industries based on the Leontief Input-Output model. The data required for this problem can be found in the ‘Assignment Data’ excel file[1].
You have been tasked with the following questions: Assume for questions a) to d) that all production is consumed by the industries inside this economy (this is known as a closed economy).
- Calculate and present the technology matrix. You will need to use the industry codes (under the sheet ‘Extra data’) in order to fit the whole table on one page.
- What is the total production (or consumption) and expenditure in dollars for the ‘Machinery and equipment, nec’ industry?
- Which industry has the highest consumption of its own resources? Which industry represents a significant importance to other industries? Note both industries may not necessarily be the same. Explain this finding and its consequences to the economy (in general), if this industry(s) was to experience poor performance.
For the remaining questions assume this economy is now ‘open’ and thus has an external demand (e.g. from the government, export demand etc.) of the following dollar amounts for each respective industry (this information can be found under the sheet ‘Extra data’). Also assume the technology matrix developed in the prior section applies for the remaining questions.
- Write the equation to represent the internal and external demands for ‘Basic metals’. In this equation do not include industries with zero dependency (when rounded off to 1 decimal place). Comment on this equation and particularly the coefficients contained within.
- How much output does each industry need to produce in order to satisfy the external demands as described? Which industry has the highest dollar output Which industry has the lowest dollar output? Present all solutions for each respective industry in a table.
- In the latest budget the government has declared significant cuts to the ‘Transport and storage’ industry. In fact, they have decided to cut the external demand of this industry by half! Calculate the new output for this industry. Which industry outside ‘Transport and storage’ will be most heavily impacted by this change? Express this change both in dollars and percentage.
Answer:
- “From the way that it used to be, yeah”
- Military service
In order to have secure wireless communication in the battlefield, satellite phones are equipped with cryptography technology. The cryptography technology is significant because it enables the military men and women to communicate without the fear of interception of their secrets by their enemies.
Telecommunication industry
Through cryptography, the telecommunication industry is able to secure the voice and text messages that their customers pass among them. The data passed can be in electronic, print etc. through cryptography, confidentiality and integrity of information conveyed is guaranteed. Any unauthorized person cannot have access to the information.
Micro-finance and banking sector
Financial institutions handle large volumes of data which are very sensitive since they involve monetary exchange between different parties. For this reason, they require high level of security and confidentiality. Through cryptography, these institutions are able to secure monetary transactions, protect access to individual sensitive data and passwords.
Question 2
- The amount used in production for wholesale and retail trade; repairs is $152,280.10 whereas the expenditure is $87,615.40. the expenditure is lower than the production hence we can deduce a profit of $64,664.70. By dividing % we obtain the profit margin.
- From the excel file and calculated values, the health and social work industry gets the highest loss as compared to other industries. They make a loss of $16405.8 which is -131.52% profit margin. The pulp, paper, paper products, printing and publishing industry register the best profit margins. A profit of $26,249 which is 66.4% profit margin. The assumptions involved are that the obtained values are of the entire economy.
- Looking at the construction industry, 65% of its resources are used in production. 63% of the resources used by Other non-metallic mineral products are from the construction industry. This reliance means that a downward shift in construction industry will result to losses in other non-metallic mineral products.
- Take the following;
X to represent construction
Y to represent financial intermediation
Z – real estate activities
Q – other businesses
Y = 0.2X+0.3Y+0.2Z+0.1Q+4660
Reference
Ekert, A.K., 1991. Quantum cryptography based on Bell’s theorem. Physical review letters, 67(6), p.661.
Katz, J., Menezes, A.J., Van Oorschot, P.C. and Vanstone, S.A., 1996. Handbook of applied cryptography. CRC press.
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