Computing and Information Systems/Creative
Computing
CO3326 Computer security
Coursework assignment 2 2018–19
IMPORTANT: all students have been allocated a unique set of
data to use for this coursework assignment. You can obtain this using
your Student Reference Number (SRN) from the following URL:
http://foley.gold.ac.uk/cw19/api/cw2/{srn}. For example, if your SRN is
877665544, you would obtain your data from http://foley.gold.ac.uk/cw19/api/
cw2/877665544. If you have difficulties obtaining your assignment data, please
email us at: intcomp@gold.ac.uk
This coursework assignment is designed to help you enrich your learning experience
and to encourage self-study and creativity. Chapter 9 (pages 95-103) of the
subject guide, including the suggested supplementary reading, will help you in
completing this assignment. You should read the coursework assignment very
carefully and pay particular attention to the Submission requirements.
You are expected to submit two files: a report and a results sheet. The
report counts as 60% of your coursework assignment mark, in which you are
expected to answer the questions below. The results sheet counts as 40% of your
mark, in which you are expected to summarise the results of your calculations in
a specific format. Please use the cipher text and keys provided when answering
the questions and when compiling the results sheet.
To complete the coursework assignment, it will make your life easier if you write
a program. You are welcome to use any programming language.
1
Coursework assignment 2
This coursework assignment takes a practical example for the El Gamal public
key cryptosystem. The notation is similar to the one used in your subject guide
(section 9.4, pages 99 – 101). IMPORTANT: To answer the questions below,
please use the coursework 2 assignment data that you obtained using your SRN.
Question 1 Verify whether p is an actual prime (i.e. not just a probable
prime). Provide a brief explanation and include the method from your code, as
well as the runtime.
Question 2 What is the computational complexity of your primality check?
Presumably, you have a loop; how many steps does it take relative to p? Include
the code where you calculate this.
Question 3 Discuss briefly how you can go about optimising the primality
check, including a code snippet.
Question 4 Verify whether g is a generator for p. Provide a brief explanation
and include the method from your code, as well as the runtime. Hint: As p is a
16-digit prime, the definition from your subject guide is not a practical way to
verify whether g is a generator. You will have to research on how El Gamal is
implemented in practice (for example in Open SSL) – you will find that p is a
special kind of prime.
Question 5 Considering that a is Alice’s private key and b is Bob’s private
key, compute their public keys and show how they can generate the same shared
key. Include a brief explanation and the relevant code snippet.
Question 6 Decrypt the provided cipher text which has been encrypted with
the shared key that you computed in Question 5. Include a brief explanation
and the relevant code snippet.
Question 7 Suppose Alice and Bob want to generate a new set of keys. They
decide that they should use a 17-digit prime instead. How would they go on
about generating a new p and a corresponding generator g? Provide a brief
explanation and include the relevant code snippet, as well as its runtime.
Question 8 Generate a new set of private and public keys for Alice and Bob,
using the p and g you generated in Question 7. Encrypt your SRN with the
shared key. Include a brief explanation and the relevant code snippet.
2
Submission requirements
REMINDER: It is important that your submitted coursework assignment is
your own individual work and, for the most part, written in your own words. You
must provide appropriate in-text citation for both paraphrase and quotation, with
a detailed reference section at the end of your coursework. Copying, plagiarism
and unaccredited and wholesale reproduction of material from books or from
any online source is unacceptable, and will be penalised (see our guide on how
to avoid plagiarism on the VLE).
You should upload two single files only. These must not be placed in a folder,
zipped, etc.
The report should be submitted as a PDF document following a strict naming
scheme: YourName_{srn}_CO3326cw2.pdf. For example, Steve Jobs with SRN
877665544 would submit SteveJobs_877665544_CO3326cw2.pdf.
The results sheet should be submitted as a JSON file with a strict
format and strict naming scheme. This summarises the results of your
calculations and will be automatically checked by an algorithm, so pay
particular attention to its format. The name of the file should be
YourName_{srn}_CO3326cw2.json; for example, Steve Jobs with SRN
877665544 would submit SteveJobs_877665544_CO3326cw2.json.
Example
You have obtained your coursework assignment data in the following format
(this is an example for illustration):
{
“srn”: “877665544”,
“name”: “Steve Jobs”,
“exercise1”: {
“p”: “2685735182215187”,
“g”: “2”,
“a”: “3628281929”,
“b”: “5915661551”,
“cipherText”: {
“encoded”: “65462432711955”,
“base64”: “O4mpDEUT”
}
}
}
3
For this, Steve Jobs would submit the following JSON, which reflects a correct
solution:
{
“srn”: “877665544”,
“name”: “Steve Jobs”,
“exercise1”: {
“p”: “2685735182215187”,
“g”: “2”,
“a”: “3628281929”,
“b”: “5915661551”,
“x”: “1611247168640770”,
“y”: “1057465508852156”,
“k”: “1133299385179611”,
“cipherText”: {
“encoded”: “65462432711955”,
“base64”: “O4mpDEUT”
},
“plainText”: {
“encoded”: “427071729268”,
“base64”: “Y291bnQ=”,
“text”: “count”
}
},
“exercise2”: {
“p”: “44685735181995023”,
“g”: “5”,
“a”: “4628273483”,
“b”: “6915587579”,
“x”: “3934012106049896”,
“y”: “6387156331543282”,
“k”: “16887845058447247”,
“cipherText”: {
“encoded”: “27261997930282270”,
“base64”: “YNqkhoB9Hg==”
},
“plainText”: {
“encoded”: “877665544”,
“base64”: “NFAdCA==”
}
}
}
4
Explanation
The srn and name fields are self-explanatory. exercise1 is relevant for questions
1 to 6 from the report. exercise2 contains the results of questions 7 and 8. The
notation is similar to the notation used in section 9.4, pages 99 – 101, in the
subject guide: p is the prime, g is the generator, a is Alice’s private key, b is
Bob’s private key, x is Alice’s public key, y is Bob’s public key, k is the resulting
shared secret key.
In Exercise 1 the plain text has been encoded with Base64, which has been
transformed to a number. If you are using Java, there are utilities provided by
Apache or Google, among others, to do these operations. Similar libraries exist
in other programming languages. If you struggle with these operations or you
would like to double-check your results, you can use the web API calls below.
For Base64 encoding/decoding you can use the following:
http://foley.gold.ac.uk/cw19/api/cw2/encode?text=count
http://foley.gold.ac.uk/cw19/api/cw2/decode?base64=Y291bnQ=
For text encoding/decoding to/from numbers, you can use the following:
http://foley.gold.ac.uk/cw19/api/cw2/toNumber?text=Y291bnQ=
http://foley.gold.ac.uk/cw19/api/cw2/toText?number=427071729268
obviously replacing count, Y291bnQ= and 427071729268 with the text or number
you want to encode/decode.
In both the plainText and cipherText, the encoded is a number, the text is an
English dictionary word and the base64 is a Base64-encoded text. As in exercise2
you have a number to encrypt (your SRN), the text field is irrelevant.
Final note
You can use the example solution above as a template, which is a well-formed
JSON, and replace the values with your data and calculation results. As the
JSON will be evaluated by an algorithm, every quote, comma, colon, curly
brace upper/lower case is crucial. Please pay attention to these. It would
be a shame to lose a potential 40% of the total marks for this coursework
assignment because of a misplaced comma or a missing quote. There are
online tools you can use for JSON formatting and validation (for example
https://jsonformatter.curiousconcept.com), so double-check that your JSON is
syntactically correct.
[END OF COURSEWORK ASSIGNMENT 2]
WX：codehelp