Practice Definition Of Discrete Logarithm (17.2.2) - More Applications of Groups

Practice: Definition of Discrete Logarithm

Lesson 17.2.2More Applications of Groups

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8 questions

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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 basic definition of a cyclic group?
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Think about how one element can generate all others.
Question 2.
What is the discrete logarithm of 1 to any base?
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Remember the property of logarithms.
3Question 3.
What is the discrete logarithm in a cyclic group?
- The base of the logarithm
- The exponent that generates an element
- The order of the group
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Think of which part of the equation represents the exponent.
4Question 4.
The logarithm of 1 in a cyclic group is always _____.
- True
- False
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Recall the property of logarithms.
Question 5.
Given a cyclic group of order 11 and generator g = 2, calculate the discrete logarithm of y = 8.
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Iterate powers of the generator until you match y.
Question 6.
Explain why it is computationally harder to determine the discrete logarithm in groups defined by multiplication modulo a prime compared to addition modulo a prime.
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Think about how the outputs of multiplication can change drastically with slight changes in the input.

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