代做CS5285: Information Security for eCommerce Problem Set 1 Autumn, 2024代做Prolog

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CS5285: Information Security for eCommerce

Autumn, 2024

Problem Set 1 (Due Date: October 18)

Questions:

1. Security Services and Mechanisms (10):Find a news article about any security-related incident that has been reported in the press since the start of August 2024 (e.g. large hack, data breach, malware, etc.). The even could have taken place before August 2024, but it must have been ﬁrst reported afterwards. Write a short essay (maximum 400 words) explaining in your own words what has happened. You must mention the type of attackers involved, what the main security services are that were compromised, and what services and mechanisms you think could have been used to mitigate this event. Provide one link to the incident article you are discussing.

2. Modes of Operation and ’shift cipher’ (5-5-5-5-5): Suppose that we use a shift cipher that has a 4-bit input and 4-bit output as a block cipher. Let the shift cipher key be k = 3, i.e. Ek(A(0000)) = D(0011) and the plaintext be P = BOBALICE (P0 is B). The conversion between the letters and binary strings are given in the table below. Note that this alphabet only has 16 letters as shown, e.g. Ek(O) = B.

A	B	C	D	E	F	G	H
0000	0001	0010	0011	0100	0101	0110	0111

I	J	K	L	M	N	O	P
1000	1001	1010	1011	1100	1101	1110	1111

(a) Encrypt the plaintext P using CBC mode with IV = 0011.

(b) Encrypt the plaintext P using CBC mode with IV = 1010. How does your ciphertext compare to that in 2(a).

(c) Encrypt the plaintext P using CTR mode with P0 being encrypted with counter starting at 0 (you can use online/calculator to do decimal to binary conversion, e.g. 1 is 0001, 2 is 0010).

(d) Use your answer from 2(a). If the MSB bit of C3 becomes an error, what is the recovered plaintext?

(e) Use your answer from 2(a). If the block C3 is lost (receiver does not realise it is missing and process C4 as C3), what is the recovered plaintext?

3. Number Theory (5-5-5-5-5-5 points): Show your steps in the following calculations (you can use a calculator but you need to show how you approached to problem - you cannot give me only the answer). Let X be your 8-digit student ID (e.g. 12345678) and Y be the least signiﬁcant 4-digits of your student ID (e.g. 5678), and consider X and Y to be an integer.

You must use your student ID, other values will be marked incorrect.

(a) Compute 41Y mod 18865 using the square-and-multiply method. (b) Calculate φ(Y).

(d) Find integers x and z such that x · X + z · 928374827 = gcd(X, 928374827). (e) Compute 108809-1 mod 291452.

(f) Choose any prime number Z that is smaller than X . Calculate XX mod Z.

4. El-Gamal (2-3-3-2) Consider the El-Gamal encryption scheme and let p = 13 and g = 3

(a) Suppose the private key is x = 5. Compute the public key y.

(b) Encrypt the message M = 6 using the public key above and r = 7.

(d) What security services can you provide using the El-Gamal algorithm shown in the class notes?

5. Di e-Hellman(2-2-2-6) Consider a Diffie-Hellman key exchange with p = 13 and g = 7.

(a) Alice picks x = 5, what is the public key A will send to Bob? (b) Bob picks y = 11, what is the public B he will send to Alice?

(d) One weakness of DH is that it is vulnerable to Man-in-the-Middle attack. How could you modify the exchanged messages in DH to prevent this attack? Clearly state all your assumptions (including any additional cryptographic algorithm or material needed) and the notation you used.

6. HMAC (10)

(a) You are the owner of an online software vendor. Your clients purchase and download programs from you over the Internet. To prevent attackers from adding malware at the end of you programs you decide to use an HMAC to provide data origin authentication. Your chief programmer tells you that they will implement the HMAC as follows:

HMAC =h(Kjjdata)

Explain why this is not a secure HMAC implementation. How would you suggest they implement an HMAC?