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:

1. Verify that h(3) = h(53) and h(9) = h(59).
2. Explain why they have the same hash values.
3. 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.

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