cs5158_hw5_2023

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University of Cincinnati, Main Campus *

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5137

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Computer Science

Date

Dec 6, 2023

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pdf

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1

Uploaded by AgentMeerkatMaster524

CS 5158/6058 Data Security and Privacy, Fall 2023 Homework 5 Instructor: Dr. Boyang Wang Due Date: 12/01/2023 (Friday), 11:59pm. Format: Please type your solutions and submit a pdf of your solutions in Canvas. Total Points: 7 points Problem 1 (2.5 points.) Given a group G , the order of this group p , and an element g of this group, please explain the following definitions 1. What is the definition of the order of element g ? 2. What is the definition of a generator of a group? 3. What is a cyclic group? 4. What is Discrete-Logarithmic Problem? Problem 2 (1.5 points). Given public parameter ( G, p, g ), where G is a cyclic group, p is the order of this group, and g is a generator of this group. Assume Alice chooses an integer a and Bob selects an integer b 1. Please explain the details of Diffie-Hellman Exchange Protocol. 2. (On additional question for CS6058) Assume there is a Man-In-The-Middle attack in Diffie- Hellman Exchange Protocol, and an attacker chooses an integer c , please explain the details of this Man-In-The-Middle attack. Problem 3 (1 point). In a Proof of Work (PoW) problem, assume the total number of bits in a hash value is 10 and the difficulty of this PoW is 8. In addition, we assume the outputs of a hash function are uniformly distributed. 1. What is the target of this PoW? 2. On average, how many hash operations do we need to find a solution given this target? Problem 4 (2 points). Assume the current blockchain in the Bitcoin network has 1 , 234 blocks, the next block will be added to the blockchain should be No. 1235. In addition, assume the hashing power of the entire Bitcoin network is 1 , 000 , 000 hashes per second. If Alice would like to mine bitcoins with her laptop, and she can compute 5 , 000 hashes per second with this laptop 1. What is the probability that both block No. 1235 and block No. 1236 in the blockchain will be added by Alice? 2. If Alice increases her hashing power to 10 , 000 hashes per second and the hashing power of the entire Bitcoin network increases to 2 , 000 , 000 hashes per second, will Alice have a higher probability to add the next block into the blockchain?
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