The quantum speed limit told us that a system's energy caps its rate of computation. Hans Bremermann, in 1962, took that idea and asked the boldest possible follow-up: what if you converted an object's entire mass into computational energy? Einstein says a mass m is worth E = mc^2 of energy, and c^2 is an enormous number. Feed that into the speed limit and you get the maximum computational rate of a lump of matter of a given mass — a limit set only by m, c and \hbar. This is the limit that makes 256-bit encryption safe until the end of time.

Mass is a computational resource

Bremermann's reasoning is one line. A mass m carries energy mc^2; the speed limit says energy E allows at most about 2E/\pi\hbar distinguishable state changes per second; therefore

Bremermann's own 1962 estimate used a slightly different constant — he wrote the limit as roughly mc^2/h, giving

The two differ only by a small numerical factor (2/\pi versus 1, and h versus \hbar); both land near 10^{50} operations per second per kilogram. We will honour both: Bremermann's historical {\sim}1.36 \times 10^{50}\ \mathrm{Hz\,kg^{-1}} and the modern, Margolus–Levitin-tightened {\sim}5 \times 10^{50}. The order of magnitude is what matters, and it is staggering: a one-kilogram lump of "computronium" — matter organised into the ultimate computer — could perform some 10^{50} operations every second.

Why 256-bit keys are safe forever

Here is where an abstract cosmic limit does real cryptographic work. To break a cipher by brute force — trying every key — you must search a keyspace of 2^{n} keys for an n-bit key. For n = 256,

Now unleash the ultimate one-kilogram computer on it. At 5 \times 10^{50} operations per second, run it for a billion years ({\sim}3.2 \times 10^{16}\ \mathrm{s}):

That falls short of 2^{256} \approx 10^{77} by a factor of ten billion. A perfect computer the mass of a bag of sugar, running since ten times the age of the universe, would not have made a dent. This is the visual below: the demands of a 256-bit search tower over everything a kilogram of matter can ever deliver.

The lesson is not that our computers are weak — it is that exponential growth beats polynomial resources. Every bit added to the key doubles the search; the keyspace climbs a ladder that mass-energy simply cannot follow. Brute force loses to combinatorics, and it loses by cosmic margins. (This says nothing about clever attacks — a mathematical weakness in the cipher, or a quantum algorithm — only that blind exhaustive search is hopeless.)