FIN553 Group-Based Assignment Group Formation and Submission Instructions Form a group of up to 4 members from your seminar group. Upload a single report via the seminar group site in Canvas. The group leader is responsible for the submission. Ensure equitable work distribution among group members. If there are issues, contact your instructor promptly. Submission …
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FIN553 Group-Based Assignment

Group Formation and Submission Instructions

Form a group of up to 4 members from your seminar group.
Upload a single report via the seminar group site in Canvas.
The group leader is responsible for the submission.
Ensure equitable work distribution among group members.
If there are issues, contact your instructor promptly.

Submission Format: Use Microsoft Office Word (.docx) and include the course code, title, SUSS PI number, name, and submission date.

Use of Generative AI Tools

Proper attribution is required for generative AI tool usage.
Include a table detailing the tool, prompts, outputs, and adapted parts.
The University may exercise a viva voce option for authorship verification.
Refer to the Student Handbook and TLC website for guidelines on academic integrity.

Assignment Questions

Question 1

Part 1: Collision Detection (5 Marks)

Using the hash function h(x)=(x² + 52x + 51) mod 100:

Verify that h(3) = h(53) and h(9) = h(59).
Explain why they have the same hash values.
Find two more distinct integers x and y such that h(x) = h(y).

Part 2: Nonce Discovery with SHA-256 (5 Marks)

Using the SHA-256 hash function, find a nonce n such that the string "FIN553" + n produces a hash with at least three leading zeros.

Part 3: Compare and Explain (10 Marks)

Compare the process of finding collisions in h(x) vs SHA-256.
Discuss why collisions in SHA-256 are more difficult to find.
Explain properties of secure hash functions.

Question 2

Part 1: Construct a Merkle Tree (10 Marks)

Compute hash values for 8 transactions using ASCII sum modulo 100.
Construct a Merkle Tree and show the hashes at each level.

Part 2: Verification Using the Merkle Root (5 Marks)

Calculate the Merkle Root.
Verify the inclusion of T3 in the Merkle Tree.

Part 3: Analysis and Explanation (5 Marks)

Explain why the provided hash function is unsuitable for real-world Merkle Trees.
Discuss the benefits of Merkle Trees in blockchain systems.

Question 3

Part 1: Digital Signature Creation (10 Marks)

Generate a digital signature using RSA for the message "Secure message for verification":

Hash the message using ASCII sum modulo 97.
Use RSA with p=7, q=11, e=5 to compute the signature.

Part 2: Digital Signature Verification (10 Marks)

Verify the signature using the public key (e, n).
Demonstrate message integrity verification.

Part 3: Analysis and Explanation (10 Marks)

Discuss the security aspects of RSA and potential weaknesses of a simplified RSA algorithm.
Explain real-world applications of digital signatures.

Question 4

Part 1: Understanding PBFT Phases (6 Marks)

Describe the pre-prepare, prepare, and commit phases of PBFT.
Explain the role of primary and honest nodes during these phases.

Part 2: Scenario Analysis (12 Marks)

Analyze the actions of honest and Byzantine nodes during each PBFT phase.
Explain the impact of Byzantine nodes on consensus.

Part 3: Analysis and Conclusion (12 Marks)

Illustrate why PBFT fails with 3 Byzantine nodes in a 7-node network.
Assess potential consequences of consensus failure.

— END OF ASSIGNMENT —

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