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http://unisci.com/stories/20022/0422022.htm -- The law is applied philosophy and a philosphical system is only as valid as its first principles. James Patrick Kelly - "Wildlife" [EMAIL PROTECTED] www.ssz.com [EMAIL PROTECTED] www.open-forge.org
Re: Two ideas for random number generation
On Mon, 22 Apr 2002, Trei, Peter wrote: > The defining difference between the two is that if you know the > algorithm and seed, the output of a PRNG can be reproduced, > at a different time, place. or both. There are circumstances in > which this is very much a desired quality. Actually you left something out, the PRNG by definition must have a modulus of repetition. At some point it starts the sequence over. In general, this is -never- a desired quality and is the primary distinction between the cost-utility of PRNG's versus RNG's. And on another statement by somebody about hardware v software RNG's: If you can't develop a RNG in software (ie you'd be in a state of sin), what makes you think you can do it using -only- digital gates in hardware? You can't. -- The law is applied philosophy and a philosphical system is only as valid as its first principles. James Patrick Kelly - "Wildlife" [EMAIL PROTECTED] www.ssz.com [EMAIL PROTECTED] www.open-forge.org
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Re: Re: Two ideas for random number generation: Q for Eugene
hi, I get the point.Thanx for all the replies. regards Data. --- Joseph Ashwood <[EMAIL PROTECTED]> wrote: > > - Original Message - > From: "gfgs pedo" <[EMAIL PROTECTED]> > > > > > Oh surely you can do better than that - making > it > > > hard to guess the seed > > > > is also clearly a desirable property (and one > that > > > the square root "rng" > > > > does not have). > > U can choose any arbitrary seed(greater than 100 > bits > > as he (i forgot who) mentioned earlier.Then > subject it > > to the Rabin-Miller test. > > Since the seed value is a very large number,it > would > > be impossible to determine the actual value.The > > chances the intruder find the correct seed or the > > prime number hence generated is practically verly > low. > > You act like the only possible way to figure it out > is to guess the initial > seed. The truth is that the number used leaves a > substantial amount of > residue in it's square root, and there are various > rules that can be applied > to square roots as well. Since with high likelihood > you will have a lot of > small factors but few large ones, it's a reasonable > beginning to simply > store the roots of the first many primes, this gives > you a strong network to > work from when looking for those leftover > signatures. With decent likelihood > the first 2^32 primes would be sufficient for this > when you choose 100 bit > numbers, and this attack will be much faster than > brute force. So while you > have defeated brute force (no surprise there, brute > force is easy to defeat) > you haven't developed a strong enough generation > sequence to really get much > of anywhere. > > > > Of course, finding the square root of a 100 > digit > > > number to a > > > precision of hundreds of decimal places is a lot > of > > > computational > > > effort for no good reason. > > Yes the effort is going to be large but why no > good > > reason? > > Because it's a broken pRNG, that is extremely > expensive to run. If you want > a fast pRNG you look to ciphers in CTR mode, or > stream ciphers, if you want > one that's provably good you go to BBS (which is > probably faster than your > algorithm anyway). So there's no good reason to > implement such an algorithm. > > > > BTW, the original poster seemed to be under the > > > delusion that > > > a number had to be prime in order for its square > to > > > be irrational, > > > but every integer that is not a perfect square > has > > > an irrational > > > square root (if A and B are mutually prime, > A^2/B^2 > > > can't be > > > simplified). > > > > Nope ,I'm under no such delusion :) > > Just the delusion that your algorithm was good. > Joe > __ Do You Yahoo!? Yahoo! Games - play chess, backgammon, pool and more http://games.yahoo.com/
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Re: Re: Two ideas for random number generation: Q for Eugene
- Original Message - From: "gfgs pedo" <[EMAIL PROTECTED]> > > > Oh surely you can do better than that - making it > > hard to guess the seed > > > is also clearly a desirable property (and one that > > the square root "rng" > > > does not have). > U can choose any arbitrary seed(greater than 100 bits > as he (i forgot who) mentioned earlier.Then subject it > to the Rabin-Miller test. > Since the seed value is a very large number,it would > be impossible to determine the actual value.The > chances the intruder find the correct seed or the > prime number hence generated is practically verly low. You act like the only possible way to figure it out is to guess the initial seed. The truth is that the number used leaves a substantial amount of residue in it's square root, and there are various rules that can be applied to square roots as well. Since with high likelihood you will have a lot of small factors but few large ones, it's a reasonable beginning to simply store the roots of the first many primes, this gives you a strong network to work from when looking for those leftover signatures. With decent likelihood the first 2^32 primes would be sufficient for this when you choose 100 bit numbers, and this attack will be much faster than brute force. So while you have defeated brute force (no surprise there, brute force is easy to defeat) you haven't developed a strong enough generation sequence to really get much of anywhere. > > Of course, finding the square root of a 100 digit > > number to a > > precision of hundreds of decimal places is a lot of > > computational > > effort for no good reason. > Yes the effort is going to be large but why no good > reason? Because it's a broken pRNG, that is extremely expensive to run. If you want a fast pRNG you look to ciphers in CTR mode, or stream ciphers, if you want one that's provably good you go to BBS (which is probably faster than your algorithm anyway). So there's no good reason to implement such an algorithm. > > BTW, the original poster seemed to be under the > > delusion that > > a number had to be prime in order for its square to > > be irrational, > > but every integer that is not a perfect square has > > an irrational > > square root (if A and B are mutually prime, A^2/B^2 > > can't be > > simplified). > > Nope ,I'm under no such delusion :) Just the delusion that your algorithm was good. Joe
Re: Re: Two ideas for random number generation
- Original Message - From: "Eugen Leitl" <[EMAIL PROTECTED]> > On Mon, 22 Apr 2002, Tim May wrote: > > > What real-life examples can you name where Gbit rates of random digits > > are actually needed? > > Multimedia streams, routers. If I want to secure a near-future 10 GBit > Ethernet stream with a symmetric cypher for the duration of a few years > (periodic rekeying from a RNG might help?) I need both lots of internal > state (the PRNG can't help leaking information about its state in the > cypher stream, though the rate of leakage is the function of smarts of the > attacker) and a high data rate. Actually that's not necessarily the case. Let's use your example of a Multimedia stream server that is filling a 10GBit/s connection. Right now the current minimum seems to be 56kbit/s. So that means that if every available connection is taken in the same second, the server would only need a rate of 2.2 million bits/sec from it's RNG to build a 128-bit key for each. A good design for this though has the client doing most of the random number choosing, where the only purpose of the server random number is to prevent the client of biasing the result, so 128-bits is more than sufficient. So 2.2 Mbit/sec seems to be the peak for that. Finding situations where a decent design will yield a need for an RNG to run about 1 Gbit/sec is extremely difficult. With poor designs it's actually rather easy, take a RNG that is poor enough (or a situation where that is a basic assumption) that it has to be distilled to 1 billionth it's size, obviously to support that multimedia stream server would require 2.2 million Gigabits per second (approximately). > > In any case, if someone wants Gbits per second of random numbers, > > it'll cost 'em, as it should. Not something I think we need to worry > > much about. > > Maybe, but it's neat trying to see how the constraints of 2d and 3d layout > of cells, signal TOF and fanout issues influence PRNG design if lots of > state bits and a high data rate are involved. It is not very useful right > now, agreed. I think it would be a good process to go through to develop a design for one, or at least a basic outline for how it could be done, but the basic idea that comes to mind looks a lot like /dev/random, but run in parallel collecting from several sources including a custom hardware pool similar to the Intel RNG. Joe
RE: Two ideas for random number generation
On Mon, 22 Apr 2002, Trei, Peter wrote: > So my suggestion is that while hardware accelaration of PRNGs may have > some usefulness, true RNGs need not have the same performance. I'd > rather see people work on making the true RNGs *trustworthy*, which is > a much more difficult problem. Out of curiosity, does anyone know what kind of data rates one can get from the RNG built into those oh-so-commodity i8xx motherboards? I don't have one, else I would just go time a read loop. And has anyone ever done an analysis of the output? Last I heard (~2.5 years ago?) Intel was refusing to release the design for inspection. Has that changed since? -Jack
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Re: Two ideas for random number generation: Q for Eugene
Ben Laurie wrote: > > gfgs pedo wrote: > > > > hi, > > > > --- [EMAIL PROTECTED] wrote: > > > On 22 Apr 2002 at 0:08, Ben Laurie wrote: > > > > > > Oh surely you can do better than that - making it > > > hard to guess the seed > > > > is also clearly a desirable property (and one that > > > the square root "rng" > > > > does not have). > > U can choose any arbitrary seed(greater than 100 bits > > as he (i forgot who) mentioned earlier.Then subject it > > to the Rabin-Miller test. > > Since the seed value is a very large number,it would > > be impossible to determine the actual value.The > > chances the intruder find the correct seed or the > > prime number hence generated is practically verly low. > > Uhuh - and how do you choose this large seed? Suppose an attacker knows some of your outputs. The whole sitiuation can be written as three numbers: x = integer part of root plus unknown "random" bits previously generated y = "random" bits attacker knows z = future "random" bits Shift everything left until you get: root*10^a = x*10^b + y + z with z < 1 We may not know a since that depends on the number of x bits, but we do know b since that depends only on the number of y bits. squaring to find the prime: prime*10^2a = x^2 * 10^2b + y^2 + z^2 + 2xy*10^b + 2xz*10^b + 2yz which is obviously zero mod 2a, so all bits to the right of that are zero. So it's also zero mod 10^b, since b < 2a, and we get: mod 10^b 0 = y^2 + z^2 + 2yz with z^2 < 1 so for bits to the left of the decimal, we have: y^2 + 2yz = 0 mod 10^b and since y and b are known, this is easliy solved for some z bits. Iterate with y' = y + discovered z bits. Methinks this is a fatal weakness, irrespective of the size of the prime.
Biometrics helping privacy: excerpt from Salon article on forensics
Occasionally a new piece of hardware comes along that initially stumps investigators. Stenhouse mentions one of the newer Thumb Drives. "There's one that requires a thumbprint onto the Thumb Drive itself. They have a pad where you actually have to put your thumb on it when you plug it in. Well, right now if you gave me one I would have to ponder how to forensically gather the data off it." Lee Tydlaska has been pondering Thumb Drives, too. "In the porn area, where are they gonna store their pictures? Well, they can store them on these and not even have to have it in their computers. They're easily destroyed and easily overlooked." [Combine this with built-in disk encryption/ autowiping and the ability to use good passwords.. and you've got a nice Cypherpunk Labs (tm) -approved project.] http://www.salon.com/tech/feature/2002/04/22/computer_forensics/index.html
RE: Two ideas for random number generation
> [EMAIL PROTECTED][SMTP:[EMAIL PROTECTED]] wrote: > > Why would one want to implement a PRNG in silicon, when one can > easily implement a real RNG in silicon? > RNGs and PRNGs serve somewhat different purposes in current cryptographic systems. Both are useful, but it's not clear to me that the Gbit true RNGs are needed. The defining difference between the two is that if you know the algorithm and seed, the output of a PRNG can be reproduced, at a different time, place. or both. There are circumstances in which this is very much a desired quality. For example, in communications using a stream cipher, is it neccesary that both ends be able to produce that same pseudorandom bitstream. You could not replace RC4 in SSL with an RNG, since both ends need to generate the same sequence. True RNGs are needed for much more limited purposes: generating session keys, initialization vectors, candidate RSA prime numbers, etc. The only high volume use I can think of for a true RNG is the mass production of OTP key material. So my suggestion is that while hardware accelaration of PRNGs may have some usefulness, true RNGs need not have the same performance. I'd rather see people work on making the true RNGs *trustworthy*, which is a much more difficult problem. Peter Trei
Re: Two ideas for random number generation: Q for Eugene
gfgs pedo wrote: > > hi, > > --- [EMAIL PROTECTED] wrote: > > On 22 Apr 2002 at 0:08, Ben Laurie wrote: > > > > Oh surely you can do better than that - making it > > hard to guess the seed > > > is also clearly a desirable property (and one that > > the square root "rng" > > > does not have). > U can choose any arbitrary seed(greater than 100 bits > as he (i forgot who) mentioned earlier.Then subject it > to the Rabin-Miller test. > Since the seed value is a very large number,it would > be impossible to determine the actual value.The > chances the intruder find the correct seed or the > prime number hence generated is practically verly low. Uhuh - and how do you choose this large seed? Cheers, Ben. -- http://www.apache-ssl.org/ben.html http://www.thebunker.net/ "There is no limit to what a man can do or how far he can go if he doesn't mind who gets the credit." - Robert Woodruff
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Re: 'Enigma' reviewed in Salon.
Marc de Piolenc wrote: >Ultra originated in Poland, not Britain. The wartime decryption work was >of course carried out in Britain, but without the prewar "seed" work of >the Poles it would probably have been futile. And not only Ultra is rightfully based on the Poles' original work, but the computer itself. The latter credit is almost never given to the three young Polish mathematicians who pointed the way for using math to reverse engineer mechancial crypto machines. No doubt that the far greater British human and material resources developed the Polish ideas behind Ultra and the bombe and grew them into a giant wartime cracking machine, that machine was and would have been a far different enterprise without the Polish initiative. Wartime industries and their succeeding commercial and governmental inheritors have a way of bestowing credit on organizations, with a bit of slathering of praise on exceptional individuals to gild the tin, but what endures are institutional histories to buttress investments while the individuals wither and dies, in person and in credit, at least until they are so long dead they cannot remind the history writers of what is truth and what bullshit. Once time comes it's then all bullshit for making movies. A movie about public key crypto is not far away, and might be made before all the developers die and are canonized for institutional portraiture. What a hoot Sun's PR release about Whit's elevation to a poster boy for corporate security. And, not to be overlooked in the rush to commercial, institutional grade exploitation, fuck Bruce Schneier for saying PGP will endure for a niche market. What the smell of money will do, slathered with personal envy of the genuine creators outside the world's beltway.
Slashdot | GPL's Strength
http://slashdot.org/articles/02/04/21/0152239.shtml?tid=117 -- -- The law is applied philosophy and a philosphical system is only as valid as its first principles. James Patrick Kelly - "Wildlife" [EMAIL PROTECTED] www.ssz.com [EMAIL PROTECTED] www.open-forge.org
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Need help on x mod m
hi, Here is a query frm my friend- I wondered if anyone knows a solution for my problem... x mod m = a x mod n = b Let's say i choose small number... m=5 n=3 a=3 b=1 then it's x mod 5 = 3 x mod 3 = 1 after trying a but you will now that x=13 but how can i solve it easier than trying all kinds of number. I mean a non-trivial solution. I think the effort gets too huge for larger numbers like: x mod 739631974298624487 = 403861151213590046; x mod 898793745643687546 = 206683840814855797; x=37658765832565679345651 And I want to use it at least with 128bit numbers. what would be a non-trivial method of solving x in the above example. Thank u Regards Data _ __ Do You Yahoo!? Yahoo! Games - play chess, backgammon, pool and more http://games.yahoo.com/
Re: Two ideas for random number generation: Q for Eugene
hi, --- [EMAIL PROTECTED] wrote: > On 22 Apr 2002 at 0:08, Ben Laurie wrote: > > Oh surely you can do better than that - making it > hard to guess the seed > > is also clearly a desirable property (and one that > the square root "rng" > > does not have). U can choose any arbitrary seed(greater than 100 bits as he (i forgot who) mentioned earlier.Then subject it to the Rabin-Miller test. Since the seed value is a very large number,it would be impossible to determine the actual value.The chances the intruder find the correct seed or the prime number hence generated is practically verly low. > > > > Of course, finding the square root of a 100 digit > number to a > precision of hundreds of decimal places is a lot of > computational > effort for no good reason. Yes the effort is going to be large but why no good reason? > BTW, the original poster seemed to be under the > delusion that > a number had to be prime in order for its square to > be irrational, > but every integer that is not a perfect square has > an irrational > square root (if A and B are mutually prime, A^2/B^2 > can't be > simplified). Nope ,I'm under no such delusion :) > George > > Cheers, > > > > Ben. > > > > -- > > http://www.apache-ssl.org/ben.html > http://www.thebunker.net/ > > > > "There is no limit to what a man can do or how far > he can go if he > > doesn't mind who gets the credit." - Robert > Woodruff > __ Do You Yahoo!? Yahoo! Games - play chess, backgammon, pool and more http://games.yahoo.com/
Re: CDR: 'Enigma' reviewed in Salon.
Ultra originated in Poland, not Britain. The wartime decryption work was of course carried out in Britain, but without the prewar "seed" work of the Poles it would probably have been futile. Marc de Piolenc matthew X wrote: > > It's not the great movie yet to > be made on the subject, but I'm sure I'm not the only one grateful to the > makers of "Enigma" for placing the credit for breaking the German code back > it belongs: with the British. After the cultural theft perpetrated two > years ago by "U-571," this modest restoration feels like an act of decency. -- Remember September 11, 2001 but don't forget July 4, 1776 They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety. - Benjamin Franklin
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Re: Two ideas for random number generation
On Mon, 22 Apr 2002, Tim May wrote: > What real-life examples can you name where Gbit rates of random digits > are actually needed? Multimedia streams, routers. If I want to secure a near-future 10 GBit Ethernet stream with a symmetric cypher for the duration of a few years (periodic rekeying from a RNG might help?) I need both lots of internal state (the PRNG can't help leaking information about its state in the cypher stream, though the rate of leakage is the function of smarts of the attacker) and a high data rate. > In any case, if someone wants Gbits per second of random numbers, > it'll cost 'em, as it should. Not something I think we need to worry > much about. Maybe, but it's neat trying to see how the constraints of 2d and 3d layout of cells, signal TOF and fanout issues influence PRNG design if lots of state bits and a high data rate are involved. It is not very useful right now, agreed.
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Re: Two ideas for random number generation (h/w comments)
At 08:09 AM 4/22/02 +0200, Eugen Leitl wrote:
>> And if one is implementing a PRNG in software, it is trivial to
>> have lots of internal state (asymptotically approaching one-time
>> pad properties).
>
>Yes, but software is too slow to be able to handle >GBit data rates.
It's
>inefficient use of CPU silicon real estate.
Comment on the latter: There is a lot of (high-margin) hardware made
which does something
that software can do, but much faster. This sounds obvious, but figure
out how long you
have to make a routing decision if your bits are coming in 10^10 / sec
and a new packet is every 2400 bits. Your basic Linux/486+2NICs
hobbyist router
does not have a chance :-) though its a perfectly viable solution at
lower rates.
Neither does your latest bleeding-edge general purpose Pentium-whatever.
So a general-purpose CPU is not just 'inefficient' ---its also
'insufficient'. Also,
they tend to burn a lot more watts than an ASIC would.
Comment on the former:
If you *really* had a reason and money for a hardware PRNG *and* you
needed
a lot of state, you'd just synthesize up a block of memory on your chip,
or an interface
to whatever kind of external D/SRAM you preferred.
\begin{understatement}
Software is a lot easier than h/ware if you don't need performance.
\end{understatement}
Re: Two ideas for random number generation
On Sunday, April 21, 2002, at 11:09 PM, Eugen Leitl wrote: > On Sun, 21 Apr 2002 [EMAIL PROTECTED] wrote: > >> Why would one want to implement a PRNG in silicon, when one can >> easily implement a real RNG in silicon? > > Both applications are orthogonal. PRNG != entropy. > >> And if one is implementing a PRNG in software, it is trivial to >> have lots of internal state (asymptotically approaching one-time >> pad properties). > > Yes, but software is too slow to be able to handle >GBit data rates. > It's > inefficient use of CPU silicon real estate. > What real-life examples can you name where Gbit rates of random digits are actually needed? Even high-bandwidth transfers of MPEGs, for example, will be done with conventional ciphers using only a tiny fraction of this bandwidth for the random number parts of the ciphers. Speaking of real world issues, it's been half a dozen years since Goldberg and Wagner broke the Netscape "time of day random number generator." I've heard of no serious attacks when a PRNG is used properly. Not to say it can't happen, or won't happen, or hasn't already happened. In any case, if someone wants Gbits per second of random numbers, it'll cost 'em, as it should. Not something I think we need to worry much about. --Tim May "As my father told me long ago, the objective is not to convince someone with your arguments but to provide the arguments with which he later convinces himself." -- David Friedman
