Question

Which of the following is the key exchange that Eve and Mel might use to simultaneously agree on a large prime number and integer?

A. Quantum Prime

B. Prime-Curve

C. Diffie-Hellman

D. Elliptic Curve Diffie-Hellman

Answer 1

Here, as per the question,

Diffie-Hellman is the key exchange that Eve and Mel might use to simultaneously agree on a large prime number and integer.

Let's see, what is Diffie-Hellman key exchange and how things work.

• The premise of the Diffie-Hellman key exchange is that two people, Eve and Mel, want to come up with a shared secret number.

1. Eve and Mel agree, publicly, on a prime number P, and a base number N. Eve will know these two numbers, and it won't matter.
2. Eve chooses a number A, which we'll call her "secret exponent." She keeps A secret from everyone, including Mel.
3. Mel, likewise, chooses his "secret exponent" B, which he keeps secret from everyone, including Eve (for subtle reasons, both A and B should be relatively prime to N; that is, A should have no common factors with N, and neither should B).
4. Then, Eve computes the number and sends J to Mel. Similarly, Mel computes the number.
   J = N^A (mod P)
   K = N^B (mod P)
5. The final mathematical trick is that Eve now takes K, the number she got from Mel, and computes
   K^A(mod P)
6. Mel does the same step in his own way, computing
   J^B (mod P)
7. With this number as a key, Eve and Mel can now start communicating privately using some other cipher.

Please let me know in the comments in case of any confusion. Also, please upvote if you like.