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Re: Lucky's 1024-bit post [was: RE: objectivity and factoringanalysis]
Lucky Green wrote: [Written originally in response to a post on Cryptography. --Lucky] Enzo wrote: Further to Lucky's comments: in the last few days I have discussed keysize issues with a few people on a couple of mailing lists, and I have encountered a hostility to large keysizes of which, frankly, I don't understand the reasons. On the client side at least, performance is not an issue: PGP 7.0.3 with my new 4096-bit PGP key appears to be as snappy as it was with 1024-bit keys, and the table at http://www.mccune.cc/PGPpage2.htm#Speed looks quite reassuring. In particular, none of the naysayers explained me clearly why it should be reasonable to use 256-bit ciphers like AES with 1024-bit PK keypairs. Allow me to shed at least some light on the strange phenomenon that you experienced for I have experienced the same phenomenon and was able to glean at least a few of the reasons why application authors and maintainers have proven so reluctant to increase RSA key sizes or mandate minimum key sizes in their applications. 1) Very, very few applications, and no cryptographic libraries that I am aware of, that currently employ RSA perform any kind of sanity check on the size of the keys. The current release version of various programs that I looked at will happily accept a 4-bit RSA client key that anyone could factor in their head. VeriSign not too long ago signed a 384-bit SSL server key that may readers of this list could break with the old computers in their home. Such certificate signing practices, or their lack thereof, are nothing short of irresponsible. OpenSSL allows you to specificy acceptable ciphersuites, and this does, in fact, consitute a check on size both on the PK and the symmetric cipher (and if it isn't working, I'd like to know!). I have not tested the following hypothesis and am not willing to spend the required $125 on the experiment, but I would not be in the least surprised if many public CA's would readily sign a certificate for a 4-bit RSA key. C.f. the being caught with one's pants down observation in my previous post. If somebody want to perform this experiment, better do it quick, since the CA vendors read this mailing list. :-) Actually, ISTR its impossible to generate a certificate request below some size in the hundreds of bits (I forget exactly what, but there's some bit of stuff that has to be asymmetrically crypted that is that long). 2) One frequently voiced argument against increasing key sizes is the resultant decrease in performance. Yes, it is absolutely true that increasing the size of an RSA key leads to a decrease in performance. However, larger keys decrease performance less than naive experiments may seem to indicate. For many applications, generating a 2048-bit key and comparing the performance with that of a 1024-bit key will lead to numbers that differ widely, much more so than can be attributed to the larger key size. The reason for this phenomenon is that RSA algorithm performance is highly dependent on optimizations that are both key size and processor specific. The same optimization strategy that will give you blazingly fast performance with a 1024-bit key will absolute kill performance with a 4096-bit key, for which a different optimization strategy is needed. Similarly, optimizations are highly processor specific. An optimization designed specifically for a Pentium III processor will run slower on a Pentium IV than your basic Pentium optimized code would. Coo. Do you have more details on what optimisations these might be, because clearly the test: if(keysize 1024) optimise_this_way(); else optimise_that_way(); is exceedingly cheap. And one I'd be happy to add to OpenSSL. Some applications offer the correct optimizations for each key size. Others just optimize for 1024-bit keys, thus leading to abysmal performance with some larger keys. Example: PGP appears to offer excellent performance optimizations across all key sizes. The performance difference between a 1024-bit RSA key and a 4096-bit key can't be much more than a second. (I didn't directly time this, but I can hear when the outgoing mail from my laptop hits the mail spool on my SMTP server; the increase in lag is insignificant from a user perspective). OpenSSH with 4096-bit keys on both ends on a 450 and 333 MHz machine respectively is noticeably slower than with 1024-bit keys, perhaps by a couple of seconds, but still well within user tolerance. I suspect additional optimizations are possible which would decrease the lag further. Numbers like a couple of seconds would kill HTTPS stone dead, of course. 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: Two ideas for random number generation
At 09:42 AM 4/23/02 -0700, Tim May wrote: And even if the world were Newtonian, in a classical billiard ball sense, with Planck's constant precisely equal to zero, predictability is a chimera. Consider a game of billiards, with perfectly spherical billiard balls, a perfectly flat table, etc. Trajectories depend on angles to a precision that keeps going deeper and deeper into the decimals. For example, predicting the table state after, say, 3 seconds, might require knowing positions, speeds, and angles (in other words, the vectors) to a precision of one part in a thousand. Doable, one might say. Predictability gets much worse if one of the walls of a pool-table is curved, then the uncertainty in a perfectly-round ball's momentum is magnified after reflection, compared to a pool-table of 3 or more flat walls. You may have meant to imply this --if spherical balls hit other balls the uncertainty is similarly magnified-- but its worth noting the difference in predictability between flat and curved-wall abstract billiards. There is a fascinating demo-photograph that shows reflections off 4 stacked steel balls is a classical fractal. But after 30 seconds, any errors that are greater than one part in a billion would lead to substantially different table states. Fail to know the mass or position or elasticity or whatever of just one of the billiard balls to one part in a billion and the outcome is no longer predictable. Exactly. This is why some of us severe quantum skeptics still accept atomic-level generated uncertainty (resistor, junction, radioactive) and the entropy harvested therefrom. --- Lorentz' weather-sim was deterministic, but screwing up a small decimal fraction as he retyped something totally hosed his expected results ---that's the concept.
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Re: Two ideas for random number generation
[EMAIL PROTECTED] wrote: On 24 Apr 2002 at 17:41, David Howe wrote: its probably a better (if much slower) stream cypher than most currently in use; I can't think of any that have larger than a 256 internal state, and that implies a 2^256 step cycle at best; for pi to be worse, it would have to have less than 2^256 digits. This is putting sillines on top of silliness. It's true that in principle that the decimal expansion of pi has an infinite number of digits, but any practical implementation of a PRNG based on pi would still have to have a finite number of accessable states. Indeed my point (the mentioned hardware implimentation limitations) - however, you don't need an infinite pi - a prng based on a subset that has 2^257 bits of the sequence has by definition a longer cycle time than a 256 state prng. Conversely, a PRNG whose cycle is only 2^256 bits long will never repeat itself during the lifetime of the device, or the lifetime of the universe for that matter. which is why a subset is sufficient.
Re: Two ideas for random number generation
Major Variola (ret) wrote: There is a fascinating demo-photograph that shows reflections off 4 stacked steel balls is a classical fractal. Topology in chaotic scattering - DAVID SWEET, EDWARD OTT JAMES A. YORKE http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v399/n6734/abs/399315a0_fs.html 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
RE: Two ideas for random number generation
Sandy Harris[SMTP:[EMAIL PROTECTED]] Jim Choate wrote: PRNG output is fixed/repeatable too - that is a properly you *want* from a PRNG. No it isn't. You -want- a RNG but you can't have one. Nobody -wants- a PRNG, they -settle- for it. That is nearly true for crypto applications, but it certainly isn't for some others. e.g. If you're debugging simulation software, you may need to be able to make the PRNG produce repeatable output by giving it the same seed on every run. For crypto, it absolutely clear that you need a true RNG for some things, if only seeding and re-seeding a PRNG, and that using a PRNG introduces one more thing that could contain dangerous weaknesses. Given a well-designed PRNG, though, it is not clear that there's any real benefit to using a true RNG instead. If you're generating 128-bit session keys, there is no practical difference between using the true RNG directly and using a good PRNG with, say, 256-bit key. Here we've sort of come full circle. My first post mentioning a pi based PRNG was to call out Jim's nonsense. In his post of Monday, April 22, 6:38 PM, jim had written: 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. Peter (that's me) responded on April 23, 10:29 AM As usual, Jim is wrong. There are deterministic systems which never repeat. For example, there is an algorithm which will give you the nth digit of pi. If I use this as my PRNG (one way I could seed it would be to use key to pick a starting point) how long does Jim think it will run before it repeats?? Exactly what is the Choatian definition of a PRNG which requires it to repeat, anyway? --- My point, I hope it is clear, was to prove that there are deterministic algorithms which do not repeat. When Jim realized what an fool he'd made of himself, he decided to change the subject; first by claiming this would be a pretty lousy PRNG to use for a cipher (of course it is - my point concerned repeated sequences, not making a good cipher), and then to blather about k-distribution (which may be a characteristic of a good PRNG, but is irrelevant to my point). I suspect the if Jim were correct, he might actually have a solution to the Halting Problem Of particular humor is his repeated insistance that anywhere one might use a PRNG, a RNG would be better. Jim, try implementing SSL with a true RNG instead of RC4. The ciphertext may be quite secure, but it's not very useful. Peter Trei
Re: Quantum mechanics, England, and Topos Theory
[EMAIL PROTECTED] wrote: [...] For example, when a sheep dies you get more grass for the remaining sheep, which gets you more sheep again, so you can do a reasonable job of predicting sheep population without knowing anything about the fates of individual sheep. Actually as the cycle time for the sheep population the cycle time for the grass are not the same or multiples of each other, what you get from a deterministic continuously variable model is wild oscillations of sheep and grass populations that make it nigh on impossible to predict the sheep population at any given time in the future. Things get more steady if you introduce predators that eat the sheep, but never completely predictable in the long run. The only way to know how the model system would stand at any time in the future beyond the typical cycle time is to do the sums. And there is no guarantee that the real world analogue of the model would be in a similar state at that time. One of the classic examples of what is now called chaos (a word that I don't like in this context). The exact trajectory taken by simple models of predator-prey systems is often very sensitively dependent on initial conditions. Of course in real life these things are stochastic anyway so the variables in your model should actually be probability distributions, which makes the sums much harder and leads to considerable handwaving. Known about since the 1920s, pretty exhaustively described by Robert May, John Maynard-Smith others in the 1970s, but still argued about today. Whether or not more complex systems (more species, more levels of predation, more kinds of resource) are more stable is still a moot point, opinions tending to depend (sensitively) on what the opinionated one actually means by stable. And on whether they have a background in maths, or physical sciences, or molecular biology, or real biology. This kind of thing has implications for economics technology markets of course (cf Santa Fe, ad infinitum). People who think like ecologists tend to assume that a more complex market, with more participants, and more kinds of interaction between them, will be in the long run more stable - perhaps because that is what they think they see in nature. People who think like engineers may disagree and talk of excessive market volatility, and the dangers of new forms of trading so on, and they need for regulation, looking for a few global variables to track and control. Apologies for off-topicness, but this is probably the only subject that's come up here about which I suspect I'm better read than the list in general. I'm working towards a doctorate in which I intend to argue (in effect) that for many kinds of investigation (such as the relationship between complexity and stability of the whole system) you do need to know about the fates of the individual sheep. (Or, in my case, imaginary protobacteria, to keep it simple :-) Similarly, if i cut a fart in an elevator, there's no telling where an indvidual stink molecule will go, but in not too long they'll be more or less uniformly spread throughout the elevator. I suspect they probably won't, not unless you spend a lot more time in the lift than is healthy for you. Whiffs will be whisked about chaotically, some being lost every time the door is opened or anyone walks around. So some poor guy on the 3rd floor will get a noseful, but someone else standing next to him might miss out entirely.
Re: Two ideas for random number generation
On Thursday, April 25, 2002, at 07:45 AM, Major Variola (ret) wrote: At 09:42 AM 4/23/02 -0700, Tim May wrote: And even if the world were Newtonian, in a classical billiard ball sense, with Planck's constant precisely equal to zero, predictability is a chimera. Consider a game of billiards, with perfectly spherical billiard balls, a perfectly flat table, etc. Trajectories depend on angles to a precision that keeps going deeper and deeper into the decimals. For example, predicting the table state after, say, 3 seconds, might require knowing positions, speeds, and angles (in other words, the vectors) to a precision of one part in a thousand. Doable, one might say. Predictability gets much worse if one of the walls of a pool-table is curved, then the uncertainty in a perfectly-round ball's momentum is magnified after reflection, compared to a pool-table of 3 or more flat walls. Yes, of course. There are many sources of divergence, and curved walls certainly add divergence. But, as you acknowledge, the curvature of the spherical balls is a source. In fact, the radius of curvature of a ball is much smaller than that of curved side walls, so of course they are huge sources of divergence. And it's important for people not to think that the curved walls or curved balls are important to the phenomenon: if all surfaces were nominally flat (say, to a sixteenth wavelength, about the best a telescope mirror is ground to), the divergences would _still_ occur. Tiny alternations in temperature would affect dimensions, friction, speeds, and hence would alter arrival times. At some point, objects in one history would bounce and in another history would miss...the changes at this point are _huge_. (I actually did a project at Intel which exploited this. I devised a scheme whereby known good microprocessors would be imaged by an electron microcope, state by state (using beam blanking to only illuminate the chip during a specific state), and then would be digitally subtracted or otherwise compared to the internal states of chips having some speed problem, or some voltage problem, or just plain failing. By examining the time evolution of divergent states, especially by running the history backwards, we could pinpoint the first divergence, the first state where voltage levels differed noticeably. This was usually a place where a design needed to be tweaked, or where a marginality was present, or a flaw, etc. This machine, the Dynamic Fault Imager, was used to get speeds up on the 80286 and later processors.) You may have meant to imply this --if spherical balls hit other balls the uncertainty is similarly magnified-- but its worth noting the difference in predictability between flat and curved-wall abstract billiards. And it's also useful for people to understand, deeply, that the divergences may enter at the fourth decimal place, or the sixth, or the twelfth. But they enter, and enter quickly, and the cascade of divergences doesn't much involve issues of flat vs. curved walls. The divergences are at a much more profound level. BTW, someone was speculating about history healing itself (this is my term for it, a familiar trope in SF). A look at the billiard ball model will show how this cannot conceivably happen: as soon as one ball misses another, all of the later trajectories are radically different. If this is not immediately clear, spend several minutes drawing pictures. If the writer was talking about conserved quantities (I think he mentioned vapors in an elevator, for example), this is not at all what we are talking about. Yes, the total energy of the billiard balls will remain roughly the same in both histories, though divergences will occur even in total energy, just more slowly. Yes, the earth's overall climate is not dramatically affected by butterflies. But the point here is that the positions and veocities of the billard balls are unpredictable after some time t, where t is probably on the order of tens of seconds, even if Planck's constant were zero and there were no quantum effects whatsoever. --Tim May To those who scare peace-loving people with phantoms of lost liberty, my message is this: Your tactics only aid terrorists. --John Ashcroft, U.S. Attorney General
Re: Two ideas for random number generation
Trei, Peter wrote: [...] Exactly what is the Choatian definition of a PRNG which requires it to repeat, anyway? Possibly confusion between 2 common English meanings of repeat. (1) repeatable, so if someone else runs the same algorithm on similar hardware with the same initial conditions they get the same results, which a program to calculate pi will be. (2) repetitive, so that if you run the algorithim for long enough a given sequence comes round again. Which pi isn't. Of course of pi will have repeats, in the trivial sense that any given sequence will many times in a sufficiently long enough rendition. But there is no cycle there, just randomness. The decimal digits 12 will occur many times, and 123 will occur rather fewer times, and so on, but it is not repetitive in this sense because seeing 1 followed by 2 gives you no clue that 3 comes next. And seeing 9863770323499906322 gives you no clue that next time you see 986377032349990632 you will get 2 next. (I think - I make no pretence to know much about maths) Ken
Re: Lucky's 1024-bit post [was: RE: objectivity and factoring analysis
Lucky Green writes: Given how panels are assembled and the role they fulfill, I thought it would be understood that when one writes that certain results came out of a panel that this does not imply that each panelist performed the same calculations. But rather that that the information gained from a panel (Ian: math appears to be correct, Nicko: if the math is correct, these are the engineering implications of the math) are based on the combined input from the panelists. My apologies if this process of a panel was not understood by all readers and some readers therefore interpreted my post to indicate that both Ian and Nicko performed parallel engineering estimates. What he wrote originally was: : The panel, consisting of Ian Goldberg and Nicko van Someren, put forth : the following rough first estimates: : : While the interconnections required by Bernstein's proposed architecture : add a non-trivial level of complexity, as Bruce Schneier correctly : pointed out in his latest CRYPTOGRAM newsletter, a 1024-bit RSA : factoring device can likely be built using only commercially available : technology for a price range of several hundred million dollars to about : 1 billion dollars : Bernstein's machine, once built, ... will be able to break a 1024-bit : RSA or DH key in seconds to minutes. It's not a matter of assuming parallel engineering estimates, but rather the implication here is that Ian endorsed the results. In saying that the panel put forth a result, and the panel is composed of named people, it implies that the named people put forth the result. The mere fact that Ian found it necessary to immediately post a disclaimer makes it clear how misleading this phrasing was. Another problem with Lucky's comment is that somewhere between Nicko's thinking and Lucky's posting, the fact was dropped that only the matrix solver was being considered. This is only 1/2 the machine; in fact in most factoring efforts today it is the smaller part of the whole job. Neither Nicko nor Ian nor anyone else passed judgement on the equally crucial question of whether the other part of the machine was buildable. It was not until at least a week after FC that I contacted Nicko inquiring if he still believed that his initial estimates were correct, now that that he had some time to think about it. He told me that the estimates had not changed. It is obvious that in fact Nicko had not spent much time going over his figures, else he would have immediately spotted the factor of 10 million error in his run time estimate. Saying that his estimates had not changed is meaningless if he has not reviewed them. Lucky failed to make clear the cursory nature of these estimates, that the machine build cost was based on a hurried hour's work before the panel, and that the run time was based on about 5 seconds calculation during the panel itself. It's not relevant whether this was in part Nicko's fault for perhaps not making clear to Lucky that the estimate stood in the same shape a week later. But it was Lucky who went public with the claim, so he must take the blame for the inaccuracy. In fact, if Lucky had passed his incendiary commentary to Nicko and Ian for review before publishing it, it is clear that they would have asked for corrections. Ian would have wanted to remove his name from the implied endorsement of the numeric results, and Nicko would have undoubtedly wanted to see more caveats placed on figures which were going to be attached to his name all over the net, as well as making clear that he was just talking about the matrix solution. Of course this would have removed much of the drama from Lucky's story. The moral is if you're going to quote people, you're obligated to check the accuracy of the quotes. Lucky is not a journalist but in this instance he is playing one on the net, and he deserves to be criticized for committing such an elementary blunder, just as he would deserve credit for bringing a genuine breakthrough to wide attention. For example, Bruce has been quoted in a widely-cited eWeek article that I don't assume that someone with a massive budget has already built this machine, because I don't believe that the machine can be built. Bruce shortly thereafter stated in his Cryptogram newsletter that I have long believed that a 1024-bit key could fall to a machine costing $1 billion. Since these quotes describe mutually exclusive view points, we have an example of what can happen when a debate spills over into the popular media. ... http://www.eweek.com/article/0,3658,s=712a=24663,00.asp They are not mutually exclusive, and the difference is clear. In the first paragraph, Bruce is saying that Bernstein's design is not practical. To get his asymptotic results of 3x key length, Bernstein must forego the use of sieving and replace it with a parallel ECM factoring algorithm to determine smoothness. Asymptotically, this is a much lower cost approach for finding relations,
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Politech archive on ongoing dispute over Radikal site: http://www.politechbot.com/cgi-bin/politech.cgi?name=radikal And: German nat'l railroad readies linking-suit against Google, Yahoo http://www.politechbot.com/p-03406.html Some Radikal mirror sites: http://web.archive.org/web/20020208065004/http://www.xs4all.nl/~tank/radikal/ http://www.cyberpass.net/radikal http://www.ecn.org/radikal/ http://www.contrast.org/radikal/ --- Date: Thu, 25 Apr 2002 16:48:37 +0200 To: [EMAIL PROTECTED] From: Maurice Wessling [EMAIL PROTECTED] Subject: Indymedia threatened by German Railroads [The German Railroads are threatening Indymedia in the Netherlands with a lawsuit to remove links to mirrors of the magazine Radikal. Previously the Railroad company succeeded in forcing ISP xs4all.nl to remove the original Radikal site and threatened Google with a lawsuit to remove the links from their database.] http://www.indymedia.nl/2002/04/3508.shtml Indymeda.nl refuses to remove links to Radikal site despite being summoned indymedia.nl, 24.04.2002 21:39 Press release Indymeda.nl refuses to remove links to Radikal site despite being summoned to do so by Deutsche Bahn (German Rail) Tuesday 23 april the newsmedium Indymedia NL has received a letter from a lawfirm representing Deutsche Bahn AG demanding the removal of an internet page. The page in question contains some links to mirrors of the -long defunct- german periodical Radikal. Two articles contained in those mirrors have been the subject of a lawsuit last week. DB objects to these articles because these contain instructions on how to obstruct the heavily critized German nuclear transports. By way of a judicial procedure, Internet provider XS4ALL has been ordered to remove these pages from the homepage of one of its subscribers. After this removal, many mirrors have sprung up all over the world. If the Indymedia page containing links to th7ese mirrors is not removed immediately, DB will sue, their letter states. Indymedia NL adamantly refuses to comply with DB4s demand to remove the links for the following three reasons: Firstly the links in question do not directly lead to the disputed articles, but to mirrors in which the articles are contained. The articles therefore are at least three clicks away (from indymedia to the mirror and from the mirror to the content page of the Radikal editions and from there to the articles). Complying with this request would mean jeopardizing the fundaments of the internet, since links are the esence of this medium. Secondly, Indymedia NL is part of a worldwide independent news network, entirely produced by volunteers. Using the open publishing system, anyone can freely publish his or her news in the form of text, audio, video or photos. Principally Indymedia.nl does not want to censor or prevent people from placing links to news sources. We believe that everyone has the right to place links, notwithstanding the content available through these links. Thirdly, Indymedia NL thinks that conforming to the demand would jeopardize the national and international freedom of the press, which is the basis of every democratic system. The possibility for censorship of hyperlinks in this way would have severe negative consequences for relevant provision of information in all layers of society (media, education, etc). Indymedia NL therefore calls for support in this very fundamental issue. Indymedia stresses that the issue is about references to freely available pages which are outside of Indymedia4s responsibility. Updates on this case will be posted on http://www.indymedia.nl The disputed webpage is at http://www.indymedia.nl/2002/04/3281.shtml Monetary donations can be directed to Dutch bank account 56.03.59.349 on behalf of Stichting SBIP, Amsterdam. Any form of legal expertise is also very welcome. More information: [EMAIL PROTECTED]
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