17.2.2 - Definition of Discrete Logarithm
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Practice Questions
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What is the basic definition of a cyclic group?
💡 Hint: Think about how one element can generate all others.
What is the discrete logarithm of 1 to any base?
💡 Hint: Remember the property of logarithms.
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Interactive Quizzes
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What is the discrete logarithm in a cyclic group?
💡 Hint: Think of which part of the equation represents the exponent.
The logarithm of 1 in a cyclic group is always _____.
💡 Hint: Recall the property of logarithms.
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Challenge Problems
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Given a cyclic group of order 11 and generator g = 2, calculate the discrete logarithm of y = 8.
💡 Hint: Iterate powers of the generator until you match y.
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.
💡 Hint: Think about how the outputs of multiplication can change drastically with slight changes in the input.
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