pmetzger@lehman.com said: (2^56)*8 = 576,460,752,303,423,488

(2^56)*8*1000/(10^9) = 576,460,752,303

I was originally assuming a one byte result per calculation and gave a hashing justification. (I glossed over the overhead for this approach, but we could analyze this, too, if anyone's interested.) You however are multiplying by 8 for no clear reason. Feel free to explain, but the way I see it, the calculation is: (2^56 calculations) * (1 byte per) * ($1000/disk) / (10^9 bytes/disk) ...which comes to 72 billion dollars. This is significantly larger than my first calculation, and the difference is purely due to roundoff error, because I said that 2^56 = 10^16, where it's actually 10^16.8576. 10^16 * $1000 / 10^9 does indeed equal my original figure of $10 billion, so it's just that I should have left another digit of precision in rounding the exponent. Now I agree that 72 billion dollars is a lot. Even 10 billion is a lot. But all I was trying to establish was that these numbers are not *completely* impossible, because you were giving Karl a hard time about this. Ridiculously expensive is a very different thing than *impossible*. There are schemes that result in figures like 10^9 billion dollars... *that* I call plainly impossible. I also projected forward 10 years to let prices come down by a factor of 10...that's another way of underscoring *possibility*. Over the last 10 years disk drive prices have fallen significantly more than a factor of 10 per megabyte, so I am being quite cautious here. A factor of 30 is justifiable, but I won't go that far, I'll continue to be conservative. Even your own figure of $576 billion becomes $57.6 billion in 10 years, which is merely too expensive, not *impossible*...if WW III were underway and such a project were of critical importance, it would happen... $50 billion would not be too much under *those* circumstances. That's the difference between "impossible" and "expensive".

Lets think for a moment, shall we? You are encrypting every possible block with DES, which results in lots of random blocks. You really want to search through the lot of them serially without any indexing whatsoever? Seems like you haven't thought this out.

If you want to critique this part of my back-of-the-envelope, its weakest part is the sorting, in which it is very hard to effectively serialize disk access. For the benefit of the doubt, let's give that a factor of 100 slowdown... so that 10 years from now we have an *average* disk transfer rate of 10^7 bytes per second for this algorithm rather than the 10^9 that I was assuming. I think it could be done faster, but even so, this increases the time from 1 hour to 4 days...still not an impossibility, just not as *nice* as 1 hour. Again, I need only establish possibility for the algorithm Karl related; I'm not saying the NSA *will* do this.

Oh, now I just realized -- you are going to have to store each source block with each output block. That means that even if you don't do any indexing, you are going to need twice the disk space I just mentioned, or over $1 TRILLION in disk for a very slow DES cracker.

Ok, so figures are doubled...my 72 billion becomes 144 billion. Pretty expensive. Not *impossible*.

Sorry, but you lose.

I never claimed this was likely...all I was after was to see whether it worked out to e.g. 10^9 trillion dollars...*that* I would call impossible.

Never designed a disk system, have you?

Actually, yes I have; I've been a hardware and software systems architect in all kinds of different subspecialties. The fact that we may disagree doesn't make me an idiot...hell, I may even make drastic mistakes and say things that *are* idiotic. It still doesn't make me an idiot...it would make me "someone who made a mistake". Considering that I was doing a quickie back-of-the-envelope, I'm not even embarassed about such mistakes. No one else did an estimate. 2^56 *sounds* ridiculously huge; I'm content to be within a factor of 100 in showing that it is merely quite expensive. I daresay that you yourself have a better feel for the expense now than you did when you first critiqued Karl's post. Flaming me is a poor way to win an inherently technical argument. Stick to the point.

Sorry, but you can't actually read a disk as fast as you can read RAM. Caching only works if you have frequently accessed blocks -- if you are reading a whole disk you can't go faster than the disk transfer rate no matter how many gods you pray to. Your technical credibility is rapidly plunging.

It is true that you can't do better than the average transfer rate, and here you have a valid point, I neglected this. It would be unrealistic given the other assumptions to assume better than 10^7 bytes per second transfer rate with technology 10 years hence. In fact even 100 megabytes per second might seem high to you, so let's call it 50Mb/s (surely a very conservative figure), for a total of 20 times slower than I estimated. That increases the 4 days to 80 days. Not very nice...but *possible*. You see the pattern here...you are raising valid technical objections, a whole series of good points that I glossed over with my back-of-the- envelope calculations. But even so, it doesn't change my basic point that the approach is *possible*. You need to find a factor of perhaps 1000 in cost and a factor of perhaps 1000 in time in order to demonstrate that this approach is inherently *impossible*. The fact that you spot flaws in my back-of-the-envelope also doesn't mean that it's called for to flame me. Again, let's stick to technical discussion.

Guess you can't read my calculations, can you?

Tsk, another flame.

...

Skip the sarcasm and pick a different quantity discount. If you don't like my 90% discount for quantity 1 million disk drives, pick another one.

Sort of like saying "if you don't like the laws of physics, pick different laws"?

Even for a flame, I don't get this. I said, if you think that a 90% discount for quantity-million is unrealistic, tell me what discount you think *is* realistic. That's a valid question. The $1000 per gigabyte drive is roughly accurate *today* in quantity *one*. The higher the quantity you buy, the better a discount you get; that's the way it works, and I'm sure you know that as well as I. So perhaps my 90% discount is overly optimistic...fine, I say...tell me a different figure. If you say 10% I'll argue. Anything between 10% and 90% is conceivable, so pick your figure. It still doesn't affect the bottom line argument as to whether the algorithm Karl mentioned will be possible in 10 years. It clearly would be very very expensive. It would also clearly *not* be completely impossible. Karl posted something which is theoretically reasonable but that is nontrivally expensive even ten years from now. He deserves credit for discussing a theoretical possibility which is even marginally conceivable. He does not deserve a harsh response...and I think you *were* harsh to him. Do me a favor and skip the flames in your future responses; they're not very much fun. Doug -- Doug Merritt doug@netcom.com Professional Wild-eyed Visionary Member, Crusaders for a Better Tomorrow (The above is a joke; the following are mailing lists:) Unicode Novis Cypherpunks Gutenberg Wavelets Conlang Logli Alife HC_III Computational linguistics Fundamental physics Cogsci SF GA VR CASE TLAs