# Maths and Computing Sample Assignment

**Assessment**

The questions are based on the book 'Network Security, Second Edition, private Communication in a public World- Charlie Kaufman, Radia Perlman, Mike Speciner'.

- Using Euclid's algorithm, produce public and private keys from the following two prime numbers: p = 41 and q = 67. Show your working (at a minimum, you should show your working for n, F(n), your reason for the selection of e and the completed table for Euclid's algorithm).
- In an RSA system, the public key of a given user is (e=179, n=1457). Using Euclid's algorithm, determine the private key for this user. Show your working (at a minimum, you should show your working for p, q, F(n) and the completed table for Euclid's algorithm).
- Assume Eve has captured a message from Alice and that she knows it is an encrypted salary figure in the range 10,000 to 1,000,000. Further assume the figure is encrypted with Bob's public key using a direct implementation of the RSA algorithm (i.e., with no PKSC applied).
- Explain how Eve can learn what the encrypted figure is.
- Explain in detail how PKCS (Public-Key Cryptography Standard), when combined with the RSA algorithm, can thwart Eve's attempt at discovering the encrypted figure.

- Again assume a direct implementation of RSA (i.e., no PKCS). Alice encrypts the number 8 with her public key (e=3, n=1081). What is wrong with this approach and how would PKCS fix it?
- Is the Lamport hash protocol vulnerable to server database disclosure? Explain indetail why or why not.

**Rationale**

- To demonstrate your understanding of:
- The RSA encryption and decryption algorithm;
- Euclid's algorithm;
- The Public Key Cryptography Standard (PKCS)
- Strengths and weaknesses of various cryptographic protocols;
- Lamport's hash; and
- Kerberos V4.
- Marking criteria

**Question 1**

- Correct calculation (and working) for n
- Correct calculation (and working) for Fn
- Choice of a suitable value for e and the reason for doing so
- Correct working (complete table) for Euclid's algorithm
- Correct choice of d based on Euclid's algorithm
- Correct identification of complete private key

**Question 2**

- Correct calculation (and working) for p and q
- Correct calculation (and working) for Fn
- Correct working (complete table) for Euclid's algorithm
- Correct choice of d based on Euclid's algorithm
- Correct identification of complete private key

**Question 3**

- Easiest method by which Eve can discover the ciphertext
- Identification of the section in the PKCS standard that will prevent this and the reasons why
- Correct spelling and grammar
- Use of at least one supporting reference
- Correct APA referencing style

**Question 4**

- Identification of the obvious flaw with this approach and how it can be exploited
- Identification of the section in the PKCS standard that will prevent this and the reasons why
- Correct spelling and grammar
- Use of at least one supporting reference
- Correct APA referencing style

**Question 5**

- Identification whether or not the given protocol is secure
- The reason why/why it is not secure
- Correct spelling and grammar
- Use of at least one supporting reference
- Correct APA referencing style

**Question 6**

- Creation of a valid protocol that achieves the objectives
- Explanation explaining why the protocol is security
- Correct spelling and grammar
- Use of at least one supporting reference
- Correct APA referencing style

**Question 7**

- Identification whether or not Lamport's hash is vulnerable to database disclosure
- Correct spelling and grammar
- Use of at least one supporting reference
- Correct APA referencing style

**Question 8**

- One (1) reason why the authenticator offers no security benefit when requesting a ticket
- Two (2) reasons why the authenticator offers a security benefit when logging into Bob
- Correct spelling and grammar
- Correct APA referencing style

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