Practice Easy Computation in Certain Cyclic Groups - 17.2.4 | 17. More Applications of Groups | Discrete Mathematics - Vol 3
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Easy Computation in Certain Cyclic Groups

17.2.4 - Easy Computation in Certain Cyclic Groups

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the discrete logarithm of the identity element in a cyclic group?

💡 Hint: Recall the properties of group elements.

Question 2 Easy

Explain why every integer except zero can be a generator in Z_p.

💡 Hint: Think about prime properties.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the discrete logarithm of an element in a cyclic group?

An integer x where g^x = y
An element in the group
The order of the group

💡 Hint: Consider the definition provided earlier.

Question 2

True or False: The discrete logarithm can be computed easily in any cyclic group.

True
False

💡 Hint: Recall the discussion about groups that complicate these calculations.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Analyze the discrete log problem in both easy and hard cyclic groups. Provide examples for each and explain the underlying properties.

💡 Hint: Focus on properties of prime moduli versus composite structures.

Challenge 2 Hard

Given a cyclic group defined by a prime number p, devise a method for securely exchanging keys using the discrete log approach.

💡 Hint: Reflect on the practicality of sending public values openly.

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