The Diffie-Hellman-Merkle key exchange involves the following steps to calculate the value you send to Rachel:

Given:

• Generator ($g$) = 2
• Prime ($p$) = 19
• Your secret number ($a$) = 13

Formula:

The value sent to Rachel is: $A = g^a \mod p$

Substituting the values: $A = 2^{13} \mod 19$

Calculation:

1. Compute $2^{13}$: $2^{13} = 8192$

2. Take the modulo with 19: $8192 \mod 19$

Perform the division: $8192 \div 19 = 431 \text{ remainder } 15$

Thus: $8192 \mod 19 = 15$

Final Answer:

The value you send to Rachel is 15.

---

Do you want me to explain modular arithmetic in detail or verify this computation?
Here are 5 related questions for further exploration:

1. What value will Rachel send to you if her secret number is $b = 7$?
2. How do you compute the shared secret once you receive Rachel's value?
3. Why is the Diffie-Hellman-Merkle key exchange considered secure?
4. What happens if $g$ or $p$ is poorly chosen in the Diffie-Hellman scheme?
5. How does modular arithmetic ensure secrecy in key exchange?

Tip: Always double-check the primality of $p$ in Diffie-Hellman to ensure the security of the key exchange.