Practice More Applications Of Groups (17.2) - More Applications of Groups

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the definition of a discrete logarithm?
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Think about how traditional logarithms work.
Question 2.
In a cyclic group, what does a generator do?
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Recall the example of powers in mathematics.
3Question 3.
What does the discrete logarithm represent in a cyclic group?
- The base of the logarithm
- The exponent that satisfies g^x = y
- The value of y
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Consider what exponent means in mathematics.
4Question 4.
True or False: The Diffie-Hellman protocol allows two parties to establish a shared key without sharing their private keys.
- True
- False
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Think about the purpose of the protocol.
Question 5.
Suppose you have a cyclic group of order 7, with generator g = 3. Calculate the discrete logarithm of y = 5.
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List the powers of g until you reach y.
Question 6.
Explain and prove why the discrete logarithm problem remains hard in multiplicative groups modulo a large prime.
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Focus on the nature of cyclic groups and modular arithmetic!

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