17.2.4 - Easy Computation in Certain Cyclic Groups
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Practice Questions
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What is the discrete logarithm of the identity element in a cyclic group?
💡 Hint: Recall the properties of group elements.
Explain why every integer except zero can be a generator in Z_p.
💡 Hint: Think about prime properties.
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Interactive Quizzes
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What is the discrete logarithm of an element in a cyclic group?
💡 Hint: Consider the definition provided earlier.
True or False: The discrete logarithm can be computed easily in any cyclic group.
💡 Hint: Recall the discussion about groups that complicate these calculations.
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Challenge Problems
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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.
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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