Exercise Steps:

Important Note: Some steps will be time$-$consuming and may take considerable

amount of time to finish. Some steps may fail to find preimages as well.

Task $1$: Birthday Attack

$1.$ Introduction to Birthday Attack:

o Explain the birthday attack and how it exploits the birthday paradox to find

collisions in hash functions.

$2.$ Generate Random Messages and Hash Them:

o Provide the following code to find a collision using the birthday attack:

$3.$ Discussion:

o Discuss the results and the implications of finding a collision in hash functions.

Task $2$: Finding the First Preimage

$1.$ Introduction to First Preimage Attack:

o Explain the concept of a first preimage attack where an attacker tries to find a

message that hashes to a given hash value HHH$.$

$2.$ Given Hash Value:

o Use your own python code or the following code to find a message that hashes to

the given value in the code using brute force:

$3.$ Discussion:

o Discuss the difficulty and time complexity of finding a first preimage.

Task $3$: Finding the Second Preimage

$1.$ Introduction to Second Preimage Attack:

o Explain the concept of a second preimage attack where the attacker finds another

message that has the same hash value as a given message M$1.$

$2.$ Hashing your name

o Use the following code as a guideline to hash your name and try to find a second

preimage.

$3.$ Discussion:

o Discuss the challenges of finding a second preimage and how it compares to

finding a first preimage.