ISEC2000 First Semester Final Exam, June 2017
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1. (6 marks) In the revised Affine Cipher given below, if two numbers 0≤a,b≤30, are
the session key, where a is coprime to 31 and the message M is required to be
integers between 0 and 30 with the encryption and decryption procedure as follows:
C=(aM+b) mod 31.
M=a-1(C-b) mod 31.
If M is required to be an integer between 0 and 30, describe the encryption and
decryption process step by step for M=7 with a key=(a,b)=(3,7).
2. (6 marks)
i) Explain the two concepts, the minimum distance and information rate, for a designed
| code scheme in channel coding. | (3 marks) |
| ii) In the one-time Pad, what are the two important characteristics to guarantee the | |
| theoretical security? | (3 marks) |
3. (6 marks) Given an S-box in DES as below.
Derive the output step by step for an input p=[110101].
4. (6 marks) Given an initial state S0=(a0,a1,a2,a3)=(1010) for the following linear
feedback shift register and a plaintext P=(101011101) (The leftmost bit in bold is
defined as the first bit of input). Compute the corresponding cipher-text step by
step.
a
0 a1 a2 a3
Plain-text Cipher-text
ISEC2000 First Semester Final Exam, June 2017
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5. (10 marks)
i) State three approaches of message authentication and detail their differences.
(6 marks)
ii) Explain the meaning of NP and P in computational complexity. (4 marks)
6. (15 marks)
i) Describe the original Diffie-Hellman protocol in detail. (6 marks)
ii) Make your own assumptions on what is contained in a public key certificate. Based
on Diffie-Hellman protocol and public key certificate, design a protocol which
enables users A and B to share a secret session key. This protocol should also enable
authentication. Explain each step.
(9 marks)
7. (18 Marks) The RSA scheme can be stated as below.
Step 1 Set up
Select prime numbers p and q.
Calculate n=p*q.
Calculate Φ(n)=(p-1)*(q-1).
Select e such that gcd(e, Φ(n))=1, 1<e<Φ(n).
Calculate d= e-1 mod Φ(n). (1)
Public key: e,n
Private key d,n
Step 2 Encryption
| For M<n, C= M e mod n |
(2) |
Step 3 Decryption
M=C d mod n.
In the process, you are required to obtain d in (1) via the Extended Euclid
Algorithm (EEA). Answer all the following questions:
| i) Prove that d is co-prime with Φ(n). ii) Can p or p-1 be used as a public key? Explain your answer. |
(5 marks) |
(3 Marks)
iii) Given p=5, q=11, e=7, M=177, compute the private key d and outline step
by step the encryption and decryption process. (10 marks)
ISEC2000 First Semester Final Exam, June 2017
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8. (15 marks) The Fermat Theorem can be stated as follows:
If p is a prime number and a is a positive integer with a <p. Then
| a p-1 mod p = 1. | (3) |
| Using the same assumptions as in the Fermat Theorem, prove the following | |
| assertion (using the Fermat Theorem): a p a p x mod = x mod( p-1) mod |
(4) |
where x is any positive integer. Using formula (4), compute the following value
3 mod11 ?
8
3
=
9. (12 marks) Give the definitions of a one-way threshold function and one-way
function. Explain their differences using examples in encryption and hash
functions.
10. (6 marks) Given a prime number p>0, for any number of 0<a<p, the smallest
positive integer k satisfying is called the order of a. Calculate the
order of a in the following cases.
1. p=5, a=3
2. P=5, a=4
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a p k mod 1 =
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