I think Schneier wrote this well before quantum computers were a reality - did he miss something fundamental in regards to them? Quantum computers are relatively new but the theory behind them is nearly a century old.

*One of the consequences of the second law of thermodynamics is that a certain amount of energy is necessary to represent information. To record a single bit by changing the state of a system requires an amount of energy no less than kT, where T is the absolute temperature of the system and k is the Boltzman constant. (Stick with me; the physics lesson is almost over.)

Given that k = 1.38×10-16 erg/°Kelvin, and that the ambient temperature of the universe is 3.2°Kelvin, an ideal computer running at 3.2°K would consume 4.4×10-16 ergs every time it set or cleared a bit. To run a computer any colder than the cosmic background radiation would require extra energy to run a heat pump.

Now, the annual energy output of our sun is about 1.21×1041 ergs. This is enough to power about 2.7×1056 single bit changes on our ideal computer; enough state changes to put a 187-bit counter through all its values. If we built a Dyson sphere around the sun and captured all its energy for 32 years, without any loss, we could power a computer to count up to 2192. Of course, it wouldn't have the energy left over to perform any useful calculations with this counter.

But that's just one star, and a measly one at that. A typical supernova releases something like 1051 ergs. (About a hundred times as much energy would be released in the form of neutrinos, but let them go for now.) If all of this energy could be channeled into a single orgy of computation, a 219-bit counter could be cycled through all of its states.

These numbers have nothing to do with the technology of the devices; they are the maximums that thermodynamics will allow. And they strongly imply that brute-force attacks against 256-bit keys will be infeasible until computers are built from something other than matter and occupy something other than space.*

I’m not a physicist but quantum particles were still considered to be matter the last time I checked.

You probably don’t even need quantum for this, one day someone’s gonna figure out a clever trick for primes. It’s not mathematically provable to be “hard” and if you look on a radial graph there’s a visible pattern. I’ll worry when people are breaking decent sized elliptic curves.

Chinese researchers break 22-bit RSA encryption.

It’s still important news but that headline is deliberately missing that crucial little bit of scope.

Cracking encryption is one of the things we expect quantum computers to be extremely good at, so I’m not particularly surprised by this development.

Funny, neither the article nor the paper seem to mention Shor’s Algorithm. I’m going to read up more on this in the morning.