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Student Number_____________
THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF COMPUTING AND I NFORMATION SYSTEMS
Quiz – Practice
COMP90043 Cryptography and Security
Duration: 45 minutes
Authorized materials:
The following items are authorized: writing materials (e.g. pens, pencils)
and non-electronic dictionaries are allowed.
Calculators and all other books are not allowed.
Instructions to Students:
PART I: True or False (Put an X in the appropriate column)
A) The Euclidean algorithm cannot be adapted to find the multiplicative inverse of a polynomial. B) True C) False X
D) A prime concern with DES has been its vulnerability to brute-force attack because of its relatively short key length. E) TrueX F) False
G) Confusion seeks to make the statistical relationship between the plaintext and ciphertext as complex as possible in order to thwart attempts to deduce the key. H) True I) False X
J) The way to measure the resistance of a hash algorithm to cryptanalysis is to compare its strength to the effort required for a brute-force attack. K) True X L) False
M) A recipient in possession of the secret key cannot generate an authentication code to verify the integrity of the message. N) True O) FalseX
PART II: Multiple Choice Questions (Please put an X for the correct answer)
A) An important quantity in number theory referred to as __________ , is defined as the number of positive integers less than n and relatively prime to n. B) CRT C) Miller-Rabin D) Euler’s totient function X E) Fermat’s theorem
F) __________ is when each plaintext element or group of elements is uniquely replaced by a corresponding ciphertext element or group of elements. G) Substitution X H) Diffusion I) Streaming J) Permutation
K) The __________ indicates that the subscriber identified in the certificate has sole control and access to the private key. L) OAEP M) Public Key Certificate X N) Digital Signature O) PKI
Calculate using modular arithmetic (Show your work)
- 2 123 mod 29 = ______18________
- -1298 mod 12 = ______10 _____________
- 5 31 mod 31 = _______5___________
There are multiple of ways simplifying it, refer to the workshop on this subject.
Calculate Euler's totient function for the following numbers (Show your work) :
- 1653 =3 * 19 * 29 Phi(1653) = 2 1828= ___1008 = _____________
2. 2 7 = _______2^6 = 64___________
Given the following RSA parameters, compute the missing parameters (Show your work) (1 * 3 = 3 marks):
Public Key = (3, 15), C = 2, M = _____17_____
Answer the following (Show your work if applicable) See the assignment 1 model solution.s
- Consider the following version of a classical cipher where plain text and cipher text elements are from integers from 0 to 25. The encryption function, which takes any plain text p to a cipher text c , is given by
c = E{a,b}(p) = (ap + b) mod 26, where a and b are integers less than 26.
a. What is the decryption function for the scheme?
b. How many different non-trivial keys are possible for the scheme?
