It has been held as true in the context of copyright law, that RAM copies of data (programs/data from the hard disk) are not "copies", else you couldn't run a program without making copies of it. I think that ought to make data in RAM not documents by the same logic.
What are you jabbering on about? The ISS is *invaluable*. How else will we be able to know what the effect of microgravity is over the fermentation of bok choi kimchee. Which I believe is an experiment to be scheduled some time soon. You can't pull the plug. Not until after the kimchee experiment at least!
That would be a fantastic feature! If it had a 5 year warrantee, and was looking a bit shabby after 4, just set the date forwards a year, watch it fail, and take it back to the shop for a new one!
re your sig: 'The "Overrated" moderation exists only to facilitate abuse.'
What should I do when I see a post containing gross factual inaccuracies moderated as "informative"?
There really ought to be other downward moderations, but while there isn't a "just plain wrong", one _has_ to use "overrated". One might posit that for every type of moderation there ought to be an equal and opposite one.
Did you miss the bit where it was explained that the monitors in question were only capable of producing 262,144 unique colour triads, each approximating a different colour? Apple did wrong. It knew it was doing wrong, so it used deliberately inexact weasel wording so they could try and wiggle out of trouble if this kind of objection was raised.
If they do that, then they ought to halve the horizontal and vertical resolutions. Either claim 1280*1024 at 260K colours, or 640*512 at 16.2M colours.
No it's more like suing a car dealership that says they have hundreds of models of car to chose from, but in reality has only 64 cars to chose from but you can buy them pre-owned or new, and you can pay up front or get a credit deal.
This may be industry-wide, as it appears 6-bit displays are very common, but it certainly appears to be to be false advertising. 'millions of colours' has always implied 24-bit in the PC world.
I think the syntax used can be abominable, but the actual instruction sets are human friendly too most of the time, particularly on RISC architectures. x86 would have to be the ultimate totally-bollocksed-up architecture, yet funnily enough it's the one I most frequently asm in.
I've never understood the gcc -S or objdump output from HPPA, Spark, Power, or Alpha, but consider myself familiar enough with the workings of the processor that I'm a pretty nifty coder for them. (#registers, approximate latencies, load/store issues, existance of conditional operations, branch overheads - if you know those you can code very tight C, with just the right amount of loop unrolling etc..) No doubt a blackfin would look just as noisy to me!
Z80 was the last instruction set where it was bloody obvious what everything did (apart from the wacky nybble-based rotate/swap instruction).
Or simply: - translate into raw (unsafe) data that you can handle first - escape anything dodgy *last*
Given that different contexts require different escaping (such as parameters for a shell command versus characters intended for a regexp match, versus parameters for a SQL query, versus something to be used as a filename, etc.) it often makes most sense to try to store, in an encapsulated form, the dangerous raw string, and to request it to be rendered in the appropriate way on demand. That can alas come with a run-time overhead in some scenarios, and when it doesn't it can add to the memory footprint instead (as you'll be juggling both the raw and the ad-hoc escaped form(s) simultaniously).
The reporting of this story in the press and blogs is abysmal.
The composite they wanted to factor was 307 digits long, as a 7-digit factor was already known. However, it was easier for them to split the 313-digit composite than the 307-digit one, due to how SNFS works.
You can crack 3DES in O(2^168) time, and O(1) space, or O(2^112) time and O(2^64) space.
However, do not try to compare the key sizes of symmetric and asymmetric algorithms, they are not directly comparable.
There's no need for any secret-key crypto primitive to have a key length over 256 bits, as long as it passes all known tests and resists all known analyses. There isn't O(2^128) space in the universe in order to do a meet-in-the-middle or birthday attack, for example.
If it's ever considered that 256-bits of key isn't enough security, Rijndael was designed with other parametrisations with longer keys.
Anyway, for a direct answer to your question, QAES would be breakable in O(2^512) time using O(2^512) space. You'd need plenty of parallel universes in order for that number to be a risk.
This task is already the work-factor equivalent to just over 700-digits for GNFS, I think. So you can reduce your estimate by about a year, apart from that, your estimate is a very good one.
For similar sized numbers, Arjen Lenstra from the team that performed this crack, GNFS has traditionally lagged SNFS by 9 years. However, without giving any clues away, he implied that the 1024-bit GNFS crack might come sooner than that this time. So your secrets from 2007 could be potentially read by any sufficiently interested party before 2016.
The '40 quadrillion year', and patented, cryptosystem really hasn't lived up to what it originally promised.
How are you going to deal with the >60000000*60000000 matrix using distributed.net?
This is all about clever implementation, not about CPU power.
Having said that, NFSNet does run distributed factoring tasks very closely related to the one just cracked. However, for those, the matrix processing stage is all done centrally on one monster box after all of the individual drones have gathered all the source data for it.
Join up, I highly recommend it as a distributed computing project.
Re:How many people have the computing power ...
on
A Mighty Number Falls
·
· Score: 1
Many many corporations can do this, assuming they can get access to a high enough quality implementation of the software. There are probably 2 or 3 such implementations in the world. One of the stages may have had a new custom implementation, so it might be possible that there's only one actual implementation that would be capable end-to-end.
It was 'only' 300 GHz years on modern architecture processors.
You are missing the fact that there are two types of factoring algorithms.
Firstly there are factor-finding algorithms, whose difficulty is dependent on properties of the individual factors of the composite. Examples of these are trial-division, Pollard/Brent Rho, Pollard P-1, someone else's P+1, and Lenstra's ECM algorithms.
Secondly there are splitting algorithms, whose difficulty is dependent on the properties of the composite itself, not its factors.
The difficulty of finding an 80-digit factor using the first type of algorithm is more or less impossibility. It's never been done. The record is something like 70 digits just last year. Only about half a dozen people have ever even found 60+ digit factors.
So with that in mind, when you're pretty sure there are no <60-digit factors (by running Lenstra's ECM many thousand times), you have pretty much no option but hitting the second type of algorithm.
(If you're looking at a 100-digit composite, you would only run ECM until you were fairly sure there were no <30-digit factors, if looking at a 130-digit composite, you'd run ECM until sure there were no 40-digit factors. Approximately - I pulled those figures out of my arse.)
The reporting on this story has been _very_ garbled universally. You can tell none of the journalists or bloggers have a clue about what they're reporting on.
The 7 digit factor was already known, so there was a 307-digit composite that needed to be factored. The algorithm used (SNFS) works better with numbers with a simple algebraic form. So it was decided to factor the full 313-digit number, knowing that the 7-digit factor could be extracted trivially from the final result.
The difficulty of the factorisation computation was therefore best measured as 313-digits, even though the composite they wanted to factor was 307-digits.
For quite a while there have often been cases where instead of factoring N, you'll factor k*N for some small k, for various reasons. When it comes to use of the Number Field Sieve (NFS) making the number you want to factor have a very simple algebraic form, so you can use the Special NFS rather than the General NFS, is _enormously_ valuable.
Slashdot Mirror
It has been held as true in the context of copyright law, that RAM copies of data (programs/data from the hard disk) are not "copies", else you couldn't run a program without making copies of it. I think that ought to make data in RAM not documents by the same logic.
Completely OT - but have you seen /Blink/ yet?
/Blink/ is an absolute classic.
I'm too old for Bonnie Langford episodes, being a Tom Bakerite, but I have to say that the latest
I may disagree with you, but I fully support your right to demonstrate publically how utterly ignorant you are of quadrature aplitude modulation.
An(ti)gram:
Quadrature Amplitude Modulation = our ultra-antiquated dial-up modem
What are you jabbering on about? The ISS is *invaluable*. How else will we be able to know what the effect of microgravity is over the fermentation of bok choi kimchee. Which I believe is an experiment to be scheduled some time soon. You can't pull the plug. Not until after the kimchee experiment at least!
That would be a fantastic feature! If it had a 5 year warrantee, and was looking a bit shabby after 4, just set the date forwards a year, watch it fail, and take it back to the shop for a new one!
Sig - Fist of Fun reference?
re your sig: 'The "Overrated" moderation exists only to facilitate abuse.'
What should I do when I see a post containing gross factual inaccuracies moderated as "informative"?
There really ought to be other downward moderations, but while there isn't a "just plain wrong", one _has_ to use "overrated". One might posit that for every type of moderation there ought to be an equal and opposite one.
Informative <-> Wrong
Interesting <-> Tedious
Insightful <-> Well duh!
Funny <-> 3 Stooges
Did you miss the bit where it was explained that the monitors in question were only capable of producing 262,144 unique colour triads, each approximating a different colour? Apple did wrong. It knew it was doing wrong, so it used deliberately inexact weasel wording so they could try and wiggle out of trouble if this kind of objection was raised.
Nope, there's dark red, medium red, bright red, etc. The monitors are capable of displaying 64 levels of each (including black).
If they do that, then they ought to halve the horizontal and vertical resolutions.
Either claim 1280*1024 at 260K colours, or 640*512 at 16.2M colours.
Except that it's a 6-bit display. 2^(3*6) is a quarter of a million.
No it's more like suing a car dealership that says they have hundreds of models of car to chose from, but in reality has only 64 cars to chose from but you can buy them pre-owned or new, and you can pay up front or get a credit deal.
This may be industry-wide, as it appears 6-bit displays are very common, but it certainly appears to be to be false advertising. 'millions of colours' has always implied 24-bit in the PC world.
I think the syntax used can be abominable, but the actual instruction sets are human friendly too most of the time, particularly on RISC architectures. x86 would have to be the ultimate totally-bollocksed-up architecture, yet funnily enough it's the one I most frequently asm in.
.) No doubt a blackfin would look just as noisy to me!
I've never understood the gcc -S or objdump output from HPPA, Spark, Power, or Alpha, but consider myself familiar enough with the workings of the processor that I'm a pretty nifty coder for them. (#registers, approximate latencies, load/store issues, existance of conditional operations, branch overheads - if you know those you can code very tight C, with just the right amount of loop unrolling etc.
Z80 was the last instruction set where it was bloody obvious what everything did (apart from the wacky nybble-based rotate/swap instruction).
Or simply:
- translate into raw (unsafe) data that you can handle first
- escape anything dodgy *last*
Given that different contexts require different escaping (such as parameters for a shell command versus characters intended for a regexp match, versus parameters for a SQL query, versus something to be used as a filename, etc.) it often makes most sense to try to store, in an encapsulated form, the dangerous raw string, and to request it to be rendered in the appropriate way on demand. That can alas come with a run-time overhead in some scenarios, and when it doesn't it can add to the memory footprint instead (as you'll be juggling both the raw and the ad-hoc escaped form(s) simultaniously).
You evidently know nothing about distributed computing.
Read up on Amdahl's Law.
You might not even need to learn it - you could just replay it in some situations.
Read up on Kerckhoff's principle.
The reporting of this story in the press and blogs is abysmal.
The composite they wanted to factor was 307 digits long, as a 7-digit factor was already known.
However, it was easier for them to split the 313-digit composite than the 307-digit one, due to how SNFS works.
You can crack 3DES in O(2^168) time, and O(1) space, or O(2^112) time and O(2^64) space.
However, do not try to compare the key sizes of symmetric and asymmetric algorithms, they are not directly comparable.
There's no need for any secret-key crypto primitive to have a key length over 256 bits, as long as it passes all known tests and resists all known analyses. There isn't O(2^128) space in the universe in order to do a meet-in-the-middle or birthday attack, for example.
If it's ever considered that 256-bits of key isn't enough security, Rijndael was designed with other parametrisations with longer keys.
Anyway, for a direct answer to your question, QAES would be breakable in O(2^512) time using O(2^512) space. You'd need plenty of parallel universes in order for that number to be a risk.
This task is already the work-factor equivalent to just over 700-digits for GNFS, I think. So you can reduce your estimate by about a year, apart from that, your estimate is a very good one.
For similar sized numbers, Arjen Lenstra from the team that performed this crack, GNFS has traditionally lagged SNFS by 9 years. However, without giving any clues away, he implied that the 1024-bit GNFS crack might come sooner than that this time. So your secrets from 2007 could be potentially read by any sufficiently interested party before 2016.
The '40 quadrillion year', and patented, cryptosystem really hasn't lived up to what it originally promised.
Your final sentence is completely and utterly wrong. Read up on the differences between SNFS and GNFS.
They actually did factor the full number, and didn't remove the 7-digit factor. That's what made the job a hundred times easier for them.
Erm, RSA uses composites. That's the problem.
How are you going to deal with the >60000000*60000000 matrix using distributed.net?
This is all about clever implementation, not about CPU power.
Having said that, NFSNet does run distributed factoring tasks very closely related to the one just cracked. However, for those, the matrix processing stage is all done centrally on one monster box after all of the individual drones have gathered all the source data for it.
Join up, I highly recommend it as a distributed computing project.
Many many corporations can do this, assuming they can get access to a high enough quality implementation of the software. There are probably 2 or 3 such implementations in the world. One of the stages may have had a new custom implementation, so it might be possible that there's only one actual implementation that would be capable end-to-end.
It was 'only' 300 GHz years on modern architecture processors.
You are missing the fact that there are two types of factoring algorithms.
Firstly there are factor-finding algorithms, whose difficulty is dependent on properties of the individual factors of the composite. Examples of these are trial-division, Pollard/Brent Rho, Pollard P-1, someone else's P+1, and Lenstra's ECM algorithms.
Secondly there are splitting algorithms, whose difficulty is dependent on the properties of the composite itself, not its factors.
The difficulty of finding an 80-digit factor using the first type of algorithm is more or less impossibility. It's never been done. The record is something like 70 digits just last year. Only about half a dozen people have ever even found 60+ digit factors.
So with that in mind, when you're pretty sure there are no <60-digit factors (by running Lenstra's ECM many thousand times), you have pretty much no option but hitting the second type of algorithm.
(If you're looking at a 100-digit composite, you would only run ECM until you were fairly sure there were no <30-digit factors, if looking at a 130-digit composite, you'd run ECM until sure there were no 40-digit factors. Approximately - I pulled those figures out of my arse.)
The reporting on this story has been _very_ garbled universally. You can tell none of the journalists or bloggers have a clue about what they're reporting on.
The 7 digit factor was already known, so there was a 307-digit composite that needed to be factored.
The algorithm used (SNFS) works better with numbers with a simple algebraic form.
So it was decided to factor the full 313-digit number, knowing that the 7-digit factor could be extracted trivially from the final result.
The difficulty of the factorisation computation was therefore best measured as 313-digits, even though the composite they wanted to factor was 307-digits.
For quite a while there have often been cases where instead of factoring N, you'll factor k*N for some small k, for various reasons. When it comes to use of the Number Field Sieve (NFS) making the number you want to factor have a very simple algebraic form, so you can use the Special NFS rather than the General NFS, is _enormously_ valuable.