Suppose Alice and Bob are using a shared secret key encryption algorithm in which the cost to do encryption and decryption is linear in the length of the key. Suppose they decide to start using $256-$bit keys instead of $128-$bit keys. How much longer will encryption and decryption take them?

Now suppose evil Trudy is doing brute$-$force search to decrypt Alice and Bob$$s conversation. How much more computation will Trudy need to use with $256-$bit keys than when they were using $128-$bit keys?