Final answer:
The shared secret key in the Diffie-Hellman key exchange is 27. To determine the shared secret key in a Diffie-Hellman-Merkle key exchange with given values, raise the received value to your secret number modulo the prime. The calculation results in a shared secret key of 16.
Step-by-step explanation:
The Diffie-Hellman key exchange is used to securely exchange cryptographic keys over an unsecure communication channel. In this case, we are using the generator 3 and prime 31 for the key exchange. Your secret number is 7 and Evelyn sends you the value 4.
To determine the shared secret key, you need to compute (4^7) mod 31. Here's how:
Calculate 4^7, which equals 16384.
Take the modulus of 31, which gives you 27.
Therefore, the shared secret key is 27.
To determine the shared secret key in a Diffie-Hellman-Merkle key exchange with given values, raise the received value to your secret number modulo the prime. The calculation results in a shared secret key of 16.
The student's question pertains to the implementation of the Diffie-Hellman-Merkle key exchange, a protocol used to securely exchange cryptographic keys over a public channel. Using the given generator 3, prime 31, personal secret number 7, and the value 4 received from Evelyn, the shared secret key can be calculated.
To find the shared secret key, you must raise Evelyn's value to the power of your secret number modulo the given prime. The formula for this step is (Evelyn's value)^your secret number mod prime. Plugging the values provided into the formula, we get:
(4^7) mod 31. Calculating this, we find:
16384 mod 31 = 16.
Thus, the shared secret key in this Diffie-Hellman-Merkle key exchange is 16.