17.1. Discrete Mathematics

Try these first

1. 1.

   What is the definition of a discrete logarithm?

   Hint

   Think about the relationship between exponents and logarithms.

2. 2.

   What is the order of a cyclic group?

   Hint

   Remember, it's all about how many unique elements can be generated.

3. 3.

   What is the discrete logarithm of y if g = 5 and y = 25?

   • 1
   • 2
   • 3
   • 4

   Hint

   Think of what power of g results in y.

4. 4.

   True or False: The brute-force method is the most efficient way to calculate discrete logarithms.

   • True
   • False

   Hint

   Think about the amount of time it would take as the group size increases.

5. 5.

   Given g = 7 and y = 1 (the identity), what is the discrete logarithm?

   Hint

   Think about the properties of exponents and identity in groups.

6. 6.

   Demonstrate how the difficulty of discrete logarithms can impact security in a cryptographic protocol.

   Hint

   Consider the relationship between computation time and security.