Question

Alice and Bob are using the Diffie-Hellman key exchange protocol to agree on a key for a shift cipher. Suppose the public prime p = 31 and the public base g = 3.

1. Alice picks a = 14 as her secret number. What number A does she send to Bob?

Answer 1

Alice calculates the number A to send to Bob using the expression 3^14 mod 31, which simplifies to A = 25.

Step-by-step explanation:

The student is asking about the Diffie-Hellman key exchange protocol, which is a method of securely exchanging cryptographic keys over a public channel. In this scenario, the public prime p is given as 31 and the public base g is given as 3. Alice's secret number is a which equals 14. To calculate the number A that Alice sends to Bob, we need to compute ga mod p. Hence, A is 314 mod 31. To find A, we perform the calculation:

A = 314 mod 31 = (4782969 mod 31)

Now, we find the remainder of 4782969 when divided by 31, which gives:

A = 25

Hence, Alice sends the number 25 to Bob.