Maths and Computing Sample Assignment

Assessment

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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

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