Question: Let H be a collision resistant hash function, MT be the Merkle hash tree construction we saw during the class (Lecture 16). 1. (5 points)

Let H be a collision resistant hash function, MT be the Merkle hash tree construction we saw during the class (Lecture 16). 1. (5 points) Prove that MT is collision resistant if the number of elements on the leaves, t, is fixed. 2. (5 points) If t is not fixed, show how to find two sets of inputs with the same root hash. 6

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Merkle-trees is a "mode of operation" for hash functions. They allow to construct a hash function that takes as input a value a large value using a hash function that accepts much smaller input:s...

Problem 7 Hash functions (15 marks) In class, we encountered three properties for hash functions in the context of cryptography: pre- image resistance, weak collision resistance and strong collision...

4. (40 points) General hash function properties. In this exercise, we discuss the preimage, second preimage, and collision resistance properties of hash functions. (a) Show that collision resistance...

Assume that you have N bins and M balls, and you are randomly placing each of the balls in some bin (several balls might be placed in the same bin. Let pN,M denote the probability of a collision,...

3 Hash Functions Let f, g and h be hash functions that each map binary strings of length 2n to binary strings of length n. Suppose that h(x) f(g(x)g(x)), where allb means a concatenated with b. Prove...

Suppose that in the Merkle - Damgard construction, we drop the requirement that the padding block encodes the message length. Let h be the compression function, let H be the resulting hash function,...

Please help! 81. 81. Ill Careful measurements have been made of Olympic sprinters in the 100 meter dash, A simple but reasonably accurate model is that a sprinter accelerates at 3.6 mfs2 for 3% s,...

If H is a collision resistant hash function, will H ' ( m ) = H ( m ) | | m also be collision resistant? A . Yes, H ' is collision resistant as long as H is collision resistant. B . It depends on the...

Hashing functions: Let A be a set with r elements, let B be the set {1, 2, 3, ..., 200000}, and assume that we have a randomly generated hashing function h: A -> B. In other words, we are aiming to...

Merkle - Damg ard ( 1 0 points ) Let h : { 0 , 1 } n + t - > { 0 , 1 } n be a fixed - length compression function. Suppose we forget a few of the important features of the Merkle - Damg ard...

Find the gradients of the following scalar fields: a) f(x, y) = y ln(x) + x sin(2x + y) b) g(x, y, z) = x + y + z

Explain why sunk costs should not be included in a capital budgeting analysis, but opportunity costs and externalities should be included.

4 5 Multiple Choice 1 0 points What action does NOT protect against the Sequence of Returns risk? Withdrawal from your retirement account at any time. Consider working past normal retirement age....

The following information concerns production in the Forging Department for November. All direct materials are placed into the process at the beginning of production, and conversion costs are...