17.2.6. Applications of Discrete Log Problem in Cryptography

Try these first

1. 1.

   Define the discrete logarithm.

   Hint

   Think about the structure of logarithms in general.

2. 2.

   What is a cyclic group?

   Hint

   Consider what defines group structure in mathematics.

3. 3.

   What does the discrete logarithm problem involve?

   • Calculating the order of a group
   • Finding the exponent x in g^x = y
   • Determining the generator of a group

   Hint

   Focus on the relationship between operations and exponents.

4. 4.

   True or False: The Diffie-Hellman protocol allows two parties to create a shared secret key using DLP.

   • True
   • False

   Hint

   Think about what the protocol aims to achieve.

5. 5.

   Given g = 5 in a cyclic group of order 11, calculate the discrete logarithm of y = 3.

   Hint

   Calculate the powers of g step by step until you find the matching value.

6. 6.

   Assess the security implications of using a widely known DLP where algorithms exist to solve it efficiently.

   Hint

   Research any known vulnerabilities in popular cryptographic systems.