Assuming shared parameters: prime p base g
Alice's private key is a and her public key is A, which is g ^ a mod p
Calcuating A requires g * g * g... a times. Modulus is applied whenever necessary.
If an attacker knows A, p, and g, why is it hard to calculate a? Would he not just keep multiplying on g and seeing if he's achieved A?
I am not seeing what is fundamentally different between Alice's computation to create A from a, and Eve's computation to brute force a knowing A. Can anyone provide some insight here?