To determine the shared secret key, we use the Diffie-Hellman key exchange algorithm.
Your Calculation:
You raise Marc's value (3) to the power of your secret number (7), modulo the prime number (23).
So, 37mod 2337mod23.
Performing the calculation: 37mod 23=2187mod 23=1637mod23=2187mod23=16
Your calculated value is 16.
Marc's Calculation:
Marc raises your generator value (5) to the power of his secret number, modulo the prime number (23).
So, 5Marc’s secret numbermod 235Marc’s secret numbermod23.
However, we don't know Marc's secret number.
Shared Secret Key:
Both of you exchange your calculated values. Marc sends you 3, and you send him 16.
You raise Marc's value (3) to the power of your secret number (7), modulo the prime number (23).
Marc raises your calculated value (16) to the power of his secret number.
The resulting values should be the same, i.e., the shared secret key.
37mod 23=16Marc’s secret numbermod 2337mod23=16Marc’s secret numbermod23
Since we can't directly determine Marc's secret number, we can't calculate the exact shared secret key.
So, the shared secret key would be the result of the calculation where both of your calculated values are raised to each other's secret numbers, modulo 23.
