Exercise 1: DES vs. AES-128 Keyspace Comparison — Possible Solution
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DES keyspace:      2^56  = approximately 7.2 x 10^16
AES-128 keyspace:  2^128 = approximately 3.4 x 10^38

Ratio: 2^128 / 2^56 = 2^72 = approximately 4.7 x 10^21

So the AES-128 keyspace is roughly 4.7 x 10^21 times larger than
DES's -- not a modest increase, but multiple orders of magnitude
beyond it. To put the scale in perspective, that ratio (~10^21) is
comparable to the difference between one second and roughly 150,000
times the current age of the universe.

What this implies about brute-forcing AES-128 with similar hardware:

If a purpose-built machine like 1998's Deep Crack could exhaust the
entire 56-bit DES keyspace in under a day, exhausting the AES-128
keyspace with a similarly-scaled machine would take on the order of
4.7 x 10^21 days -- a number of days many orders of magnitude larger
than the current age of the universe in years. Even accounting for
decades of hardware improvement since 1998 (including GPUs, ASICs, and
theoretical quantum speedups discussed in Chapter 12), no realistic
or foreseeable computing advance closes a gap of that size. This is
exactly why the chapter describes AES-128 brute force as "utterly
infeasible" rather than merely "difficult."

WHY THIS WORKS AS AN ANSWER
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This directly extends the chapter's own DES/AES numbers using the
same order-of-magnitude reasoning the chapter itself uses (comparing
7.2 x 10^16 against 3.4 x 10^38). Each additional key bit doubles the
keyspace, so the extra 72 bits between DES's 56 and AES's 128 doesn't
add security linearly -- it multiplies the difficulty by 2^72, which
is the concrete, calculable reason DES's real-world 1998 defeat says
nothing at all about AES's practical safety today.