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'.

1. 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).
2. 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).
3. 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.
4. 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?
5. 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