bin

INTI UNIVERSITY COLLEGE

DIPLOMA IN INFORMATION AND COMMUNICATIONS TECHNOLOGY
MAT 1113: DISCRETE MATHEMATICS
ASSIGNMENT 3: MAY 2009 SESSION

Answer ALL Questions.

1. In the RSA public-key cryptosystem, to encrypt a, compute c = an mod z and send c to the holder of the public keys z and n, where z is chosen as the product of two primes p and q. Assume that we choose our primes to be p = 53 and q = 47, and n = 33, encrypt 1008 using the public keys z and n.
(7 marks)

2. A word is encoded using the parity check code and it is transmitted. For the following received word, decode the word using a single-error correcting code procedure.

0010100
(3 marks)

3. Consider the (2, 7) encoding function e:

e (00) = 0000000
e (01) = 1011010
e (10) = 0110010
e (11) = 1011001

(i) Find the minimum distance of e.
(3.5 marks)
(ii) How many errors will e detect?
(1 mark)

4. In the RSA public-key cryptosystem, to encrypt a, compute c = an mod z and send c to the holder of public keys z and n, where z is chosen as the product of two primes p and q. Assume that we choose our primes to be p = 37 and q = 41, and n = 34, encrypt 1001 using the public keys z and n.
(7 marks)

5. Consider the (7, 8) parity check code. For the received word, determine whether an
error will be detected.
11010101
(1 mark)


- THE END -