17.2.3 - Computational Difficulty of Discrete Logarithm
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Practice Questions
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Define a discrete logarithm within a cyclic group.
💡 Hint: Think about how logarithms work in general.
What is the complexity of the brute-force algorithm for computing discrete logarithms?
💡 Hint: Consider how many elements are in a cyclic group.
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Interactive Quizzes
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What does the discrete logarithm measure?
💡 Hint: Relate it to the concept of logarithms you already know.
True or False: The difficulty of solving DLP is crucial for the security of cryptographic systems.
💡 Hint: Think about how secure communications depend on problem complexity.
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Challenge Problems
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Consider a cyclic group of order 7 generated by 3. What is the discrete logarithm of 6 to the base 3?
💡 Hint: Calculate powers of the generator one by one.
Explain how the difficulty of the DLP can lead to vulnerabilities in cryptographic protocols. Provide an example.
💡 Hint: Reflect on real-world implications of breaking encryption schemes.
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