Quote from: jonald_fyookball on March 13, 2014, 12:38:44 AM

Dude...bro... You are STILL missing the freaking point!

No one is questioning the advancement of technology
or even our ability to predict...but its essentially
PHYSICALLY IMPOSSIBLE to make a computer that
would do 10^70 FLOPS.

Let's do the math, shall we:

1. size of atom is roughly 0.0000000000001 meters

...therefore...

2. Number of atoms in a meter = 10^13 not necessary but lets assume so
3. Number of atoms in a cubic meter = 10^39

...also...

4. speed of light = 299,792,458 metres per second

...thus...

5. time required for light to travel the distance of 1 meter =
1/299792458 seconds = .000000003335 seconds.
6. time required for light to travel the length of 1 atom =
0.000000000000000000003335 seconds.
7. If SOMEHOW, in this tiny timeframe,
a floating point operation could be
done using the space of a single atom,
you would get 2.99*10^20 FLOPS for each atom-size "bit".
(take the reciprocal of the above number)

8. So a cubic-meter sized computer filled with atoms
back to back, each calculating at the speed of light
would still only get you 2.99 *10^59 FLOPS.

9. to get to 10^70, you would need 33 billion of these
cubic meters sized computers. Stacked end to end, these cubes
would go to the moon and back 42 times.

See, it always comes down to the answer: 42.

I'm not going trough all the zeros not because it's not interesting, but because it hurt my eyes, please use Exponentiation.

Just to answer you claim above I just have one question : between the nucleus and and the electrons what do we have?, and inside the nucleus between Quarks what do we have? and what is the scale of this thing in comparison of real stuff there, maybe you understand what I'm getting at by now, because you made a hypothesis above about the possible number of atoms in cubic meter.

Also another thing that picked my attention which is 2.99 *10^59 FLOPS so for you this number seems to be fine right? You agree that this number is more than enough to brute force 128bit AES almost instantly right? ok do you know the link between 256bit ECDSA in private key and 128bit AES?

Quote from: DeathAndTaxes on March 13, 2014, 01:17:49 AM

No we won't. You seem to vastly underestimate how large 10^70, 2^128, and 2^160 are.

In 40 years Moore's law has provided roughly 1*10^6 improvement in transistor density and a roughly comparable improvement in cost per unit of computing power and power per unit of computing power. It is highly likely that Moore's law will not be sustained for another 40 years, Intel may actually slip below that "benchmark" for the first in this decade. The cost to build smaller and smaller process nodes is increasing exponentially and the time between process nodes (which should be no more than 24 months) is slowly inching upward. Lets not even get into the fact that there are only 8 maybe 9 process nodes before we get down to the transistors using 3 atoms a piece.

Still lets assume that an equivalent amount of improvement occurs over the next 4 decades. That is a ~10^6. Today top supercomputers are PFLOP scale. Lets ignore the fact that Integer performance is often a magnitude worse and that it takes tens of thousands of operations to complete a single keypair (and even more to perform lookups). Lets just naively assume that 1 ECDSA key generation and lookup can be done in 1 FLOP (which doesn't even make sense but trying to be ultra conservative). That would mean today a top super computer could do ~34 PK/s (peta keys per second). To keep the math simple lets just round up to 100 PK/s or 1*10^17 kps.

If we then assume a 1*10^6 factor improvement in relative performance in the next 40 years that would make a top SC something on the order of 1*10^23 kps. Now lets assume you build one for every man woman and child on the planet (estimated to be ~10 B in 2054). That would put world wide key breaking power at 1*10^33 kps. You aren't even within the same ballpark as 10^70.

In reality performance will probably slip below Moore's law, you can't process on key per clock cycle, and even if you could we are looking at an energy requirement greater than what is used by the entire human race for all other purposes.

I've already made a more precise calculus in my previous post about, but lets take your calculus for the moment

The 10^6 factor of improvement is wrong, is the minimum of current improvement is between 10^3 and 10^4 per decade (I'll invite you to check the list of the top supercomputers in the world and approve this fact by yourself (again we are talking about classical computing we aren't even considering QC for example) We also agree that Moors law in electronics has it limits due the Quantum effects at the small scale, let me just remind you that Flops != transistor count, it's one of many facture, such architecture, alghorithms and firmwires....ect ect but this is just a side note) .

10^17KPS is your initial point right? with a factor of improvement between 10^3 and 10^4 per decade, lets just say 2 decades of 10^4 and 2 others 10^3 in over the 4 decades you took as an example, we should have an improvement of 10^14 so we will have by then (if we assume only classic computing which is by then would be obsolete in my opinion anyway we are at 10^30+ (and this is something I've already mentioned in my initial comment, and this is goes with what I said in my previous comments and I'm pretty sure it was a reply to you "in the next few decades, we will reach 10^30-10^40Flops which is more than to crach 128Bit AES in a few seconds, and we will eventually reach 10^70+" And like I said before this just considering classical computing, which will become obsolete in the next decade or two, at least in terms of supercomputing