Part III: Code Project

Objective: To apply theoretical knowledge through practical coding exercises using a Jupyter notebook.

Exercises: Use jupyter notebook to do the coding problems.

Merkle Tree Implementation

Implement Merkle trees using SHA$256$ or another hashing algorithm. Utilize existing crypto

packages for hashing functions.

Each leaf node should reference a plaintext file.

Conduct a test with four leaf nodes, displaying the tree structure and hashes.

Conduct a second test with six leaf nodes, displaying the tree structure and hashes.

Root Hash Observation

Modify the content of one text file in the four$-$leaf$-$node scenario and compare the root hashes.

Discuss your observations.

Hash Collision

Define a hash function using SHA$256$ but take only $4$ bits as hash output.

Use the implementation in step $1($Merkle Tree Implementation$)$ with this hash function.

Attempt to generate multiple text files with identical meanings but different hashes by altering

file contents $($e$.$g$.,$ adding spaces$).$

Find a hash collision among the text files. Discuss how many such files need to be generated.

Discuss strategies for finding collisions with hashes ranging from $4-$bit to $160-$bit in length.

Hash Puzzle

Using the chosen hashing algorithm $(4$ bits output$),$ solve hash puzzles by finding hashes with a

leading $1$ zero bit, and then $2$ zero bits.

Briefly discuss the workload involved in solving a puzzle requiring a $20-$bit zero prefix for the

SHA$256.$