17.2.1. Discrete Logarithm and the Discrete Logarithm Problem

Try these first

1. 1.

   Define the term 'generator' in the context of cyclic groups.

   Hint

   Think about how you can create all elements using one element.

2. 2.

   What is the unique integer in the discrete log definition?

   Hint

   Look at the equation we discussed.

3. 3.

   What is the discrete logarithm of y=81 if the base g=3?

   • 2
   • 4
   • 3
   • 5

   Hint

   Think of powers of 3.

4. 4.

   The discrete logarithm of the identity element is always 0.

   • True
   • False

   Hint

   Recall the property of identity operations.

5. 5.

   Given g = 5 and y = 25 in a cyclic group of order 6. Compute the discrete log.

   Hint

   Start checking powers of 5.

6. 6.

   In a secure key exchange between two parties, explain how knowledge of the discrete logarithm can compromise security.

   Hint

   Consider how public information can lead to discovering private details.