17.2.7. Key Agreement Problem

Try these first

1. 1.

   What is a discrete logarithm?

   Hint

   Think about how logarithms work in basic mathematics.

2. 2.

   What is a cyclic group?

   Hint

   Consider how one number can generate multiple outcomes through exponentiation.

3. 3.

   What is the discrete logarithm?

   • The log of a number in base 2
   • The power needed to express an element as a generator's power
   • A type of encryption method

   Hint

   Think about the relationship between log and power.

4. 4.

   The Diffie-Hellman protocol allows for secure communication over public channels without prior secret exchange.

   • True
   • False

   Hint

   Recall the central purpose of the Diffie-Hellman method.

5. 5.

   Given a cyclic group of order 7, with a generator g=3, calculate the discrete log for y=5.

   Hint

   Calculate the powers of 3 and reduce modulo 7.

6. 6.

   Explain why the security of communications depends on the computational difficulty of discrete logarithms.

   Hint

   Think about the relationship between the group's structure and the challenge faced.