17.2 - More Applications of Groups
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Practice Questions
Test your understanding with targeted questions
What is the definition of a discrete logarithm?
💡 Hint: Think about how traditional logarithms work.
In a cyclic group, what does a generator do?
💡 Hint: Recall the example of powers in mathematics.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the discrete logarithm represent in a cyclic group?
💡 Hint: Consider what exponent means in mathematics.
True or False: The Diffie-Hellman protocol allows two parties to establish a shared key without sharing their private keys.
💡 Hint: Think about the purpose of the protocol.
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Challenge Problems
Push your limits with advanced challenges
Suppose you have a cyclic group of order 7, with generator g = 3. Calculate the discrete logarithm of y = 5.
💡 Hint: List the powers of g until you reach y.
Explain and prove why the discrete logarithm problem remains hard in multiplicative groups modulo a large prime.
💡 Hint: Focus on the nature of cyclic groups and modular arithmetic!
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