A block cipher E is a symmetric$-$key encryption scheme that encrypts an L$-$bit plaintext message m

with an $`-$bit secret key k and produces an L$-$bit ciphertext c $=$ Ek$($m$).$ When performing exhaustive

key search $($also known as brute force search$)$ on E to find k$,$ you can assume that you are given

two plaintext$-$ciphertext pairs $($m$1,$ c$1)$ and $($m$2,$ c$2),$ and that there is a unique key k which satisfies

c$1=$ Ek$($m$1)$ and c$2=$ Ek$($m$2).$

$($a$)$ Let E$1$ be a block cipher with $64-$bit keys and $64-$bit plaintexts and ciphertexts. Suppose that

today you begin performing exhaustive search for an E$1$ secret key k on a MacBook Pro M$1$

that has one $10-$core $3\mathrm{.}2$ GHz CPU. What is the probability that you will find the secret key k

before you die?