December 2003 - cypherpunks-legacy

Re: Representations of Pi, etc.
by tcmay＠got.net 17 Dec '03

17 Dec '03

At 3:19 AM 1/5/96, jim bell wrote: >But BTW, isn't it interesting, that news item from a few weeks ago, on an >algorithm for determining individual bits in Pi, regardless of whether >you've calculated all the previous ones. Only problem is, it only works in >hexadecimal (and, obviously, binary, etc, not decimal. ^^^^^^^^^^^ ??? I didn't see this result you mention, but it surprises me. The part about how it works in some bases, but not in decimal. The "hand-waving" (motivational/informal) explanation for why I am surprised is that "Nature doesn't care about bipeds with 10 digits vs. bipeds, or whatever, with 2 digits or 16 digits." That is, results applicable in base 16, hexadecimal, should be easily applicable in base 10. And there is are interesting properties about the distribution of digits in "random" numbers. Pi is of course not random by many definitions, but shares certain important properties with random numbers. (Or sequences, if you wish.) One of these is properties is that of _regularity_, the frequency of digits. A regular number is one whose expansion has in the limit the same frequency for all digits, and this is so in any base. Thus, a regular number has an equal frequency (in the limit, blah blah) of 0s, 1s, 2s, 3s, etc. And switching to another base will not change this. I recollect that pi has been proved to me regular, i.e., that pi has an equal frequency of all digits, in the limit, in all bases. (This is the sense in which we can argue that pi is "random." in the sense that there are no correlations, no dependence of the n+1th digit on the nth digit, and "no apparent order." Furthermore, there is no effective compression of pi, except by some tricks, such as _naming_ it (a dictionary compression, of sorts) or by specifying a program which computes it. Lots of interesting issues about the real meaning of randomness and compressability, about the "logical depth" of certain computations, etc. I recommend "The Universal Turing Machine" (ed. by Haken, as I recall) for a nice set of articles on these fascinating issues.) In summary, I would be surprised to find that a method for calculating the Nth digit of pi works for base N but not for base M (modulo some minor efficiency factors related to machine architecture, etc.). Any pointers to this result would be appreciated. --Tim May (By the way, randomness and regularity, real or only apparent, are some of my favorite topics. Numbers which _appear_ to be regular, but which actually aren't, are said to be "cryptoregular" (hidden regular). The connection with cryptography is more than tangential: a text block or number which _appears_ to be random or regular (the same frequency definition applies to letters as well as digits) may be transformed by application of a key to a nonrandom or nonregular thing. The connection with entropy and randomness is right there, of course, and is left for the interested folks to think about.) We got computers, we're tapping phone lines, we know that that ain't allowed. ---------:---------:---------:---------:---------:---------:---------:---- Timothy C. May | Crypto Anarchy: encryption, digital money, tcmay(a)got.net 408-728-0152 | anonymous networks, digital pseudonyms, zero W.A.S.T.E.: Corralitos, CA | knowledge, reputations, information markets, Higher Power: 2^756839 - 1 | black markets, collapse of governments. "National borders aren't even speed bumps on the information superhighway."

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Three recent posts on usenet about getting far hex digits of pi.
by Jay Sulzberger 17 Dec '03

17 Dec '03

For Timothy C. May and all the cypherists on this list: Here are three recent posts to usenet on the beautiful, and partly new results on getting digits far out in pi, without explicitly getting all the nearer to the heximal point digits. > From sci.math Wed Dec 20 05:16:17 1995 > Path: panix!news.denver.eti.net!imci3!imci2!newsfeed.internetmci.com!uwm.edu!msunews!netnews.upenn.edu!red.seas.upenn.edu!jimmosk > From: jimmosk(a)red.seas.upenn.edu (Jim J Moskowitz) > Newsgroups: sci.math > Subject: nth digit of pi calculable? > Date: 18 Dec 1995 03:29:08 GMT > Organization: University of Pennsylvania > Lines: 29 > Message-ID: <4b2n64$s27(a)netnews.upenn.edu> > NNTP-Posting-Host: red.seas.upenn.edu > Status: RO > X-Status: > > I've seen the recent reports about the discovery of a formula for pi > of the form > infinity > ----- > \ (- n) / 4 2 1 1 \ > ) 16 (------- - ------- - ------- - ------- ) > / \8 n + 1 8 n + 4 8 n + 5 8 n + 6 / > ----- > n = 0 > > which is said to tell you in a simple manner what the nth digit in the > hexadecimal expansion of pi is. I don't see why. Yes, the ith term of > this series does include 16^-i, which is the ith place in said expansion, > but the term in parentheses (sorry; they look more like angle brackets) > isn't an integer, so it's not giving you the value of the number in that > ith place. Instead, it gives you several digits which are in places further > along in pi, with no guarantee that other terms in this sigma won't also > include digits in those places, forcing you to calculate and add up many > terms.... > > Taking an incautious plunge into the world of computational math, > Jim > > > -- > ----------------------------------------------------------------------------- > Jim Moskowitz (jimmosk(a)eniac.seas.upenn.edu) > Visit the Unknown Composers Page: > http://www.seas.upenn.edu/~jimmosk/TOC.html > > >From sci.math.pi Fri Jan 5 04:08:06 1996 > From sci.math Wed Dec 20 05:16:57 1995 > Path: panix!cmcl2!oitnews.harvard.edu!purdue!lerc.nasa.gov!magnus.acs.ohio-state.edu!math.ohio-state.edu!howland.reston.ans.net!newsfeed.internetmci.com!EU.net!peer-news.britain.eu.net!lyra.csx.cam.ac.uk!cet1 > From: cet1(a)cus.cam.ac.uk (Chris Thompson) > Newsgroups: sci.math > Subject: Re: nth digit of pi calculable? > Date: 18 Dec 1995 15:21:18 GMT > Organization: University of Cambridge, England > Lines: 46 > Message-ID: <4b40te$r02(a)lyra.csx.cam.ac.uk> > References: <4b2n64$s27(a)netnews.upenn.edu> > NNTP-Posting-Host: grus.cus.cam.ac.uk > Status: RO > X-Status: > > In article <4b2n64$s27(a)netnews.upenn.edu>, jimmosk(a)red.seas.upenn.edu > (Jim J Moskowitz) writes: > |> I've seen the recent reports about the discovery of a formula for pi > |> of the form > |> infinity > |> ----- > |> \ (- n) / 4 2 1 1 \ > |> ) 16 (------- - ------- - ------- - ------- ) > |> / \8 n + 1 8 n + 4 8 n + 5 8 n + 6 / > |> ----- > |> n = 0 > |> > |> which is said to tell you in a simple manner what the nth digit in the > |> hexadecimal expansion of pi is. I don't see why. Yes, the ith term of > |> this series does include 16^-i, which is the ith place in said expansion, > |> but the term in parentheses (sorry; they look more like angle brackets) > |> isn't an integer, so it's not giving you the value of the number in that > |> ith place. Instead, it gives you several digits which are in places further > |> along in pi, with no guarantee that other terms in this sigma won't also > |> include digits in those places, forcing you to calculate and add up many > |> terms.... > > You certainly have to add up a large number of terms. It is the ease with > which these terms can be computed that has attracted interest to this and > similar formulae. > > Think in terms of trying to find the fractional part of 16^N * pi to reasonable > accuracy, which is what is really meant by "finding the (N+1)'th hexadecmal > digit" here -- you might always get unlucky and find only that this fractional > part was between .2fffff and .300001, say. The terms with n >= N are of > absolute value less than 1, and form a rapidly converging series, so their > contribution is easy to compute. The term with n < N contribute terms of > the form > > fractional part ( 16^a(i) * b(i) / i ) > > where i < 8N, a(i) < N, and the b(i) are small integers. So it is sufficient > to compute 16^a(i) mod i. If you don't already know, you can find out how to > do this in time logarithmic in a(i) in, say, Knuth ACP Vol 2. > > This is all explained in detail in the Borwein/Borwein/Plouffe paper, available > from http://www.cecm.sfu.ca/~pborwein/PAPERS/P123.ps, which should be pretty > comprehensible even by an amateur. > > Chris Thompson > Email: cet1(a)cam.ac.uk > > >From sci.math.pi Fri Jan 5 04:08:06 1996 > From sci.math Wed Dec 20 05:17:20 1995 > Path: panix!bloom-beacon.mit.edu!gatech!psuvax1!news.math.psu.edu!chi-news.cic.net!uwm.edu!lll-winken.llnl.gov!apple.com!apple.com!not-for-mail > From: rjohnson(a)apple.com (Robert Johnson) > Newsgroups: sci.math > Subject: Re: nth digit of pi calculable? > Date: 19 Dec 1995 13:01:28 -0800 > Organization: Apple Computer, Inc., Cupertino, California > Lines: 57 > Message-ID: <4b7978$cj1(a)apple.com> > References: <4b2n64$s27(a)netnews.upenn.edu> > NNTP-Posting-Host: apple.com > Status: RO > X-Status: > > > In article <4b2n64$s27(a)netnews.upenn.edu>, > Jim J Moskowitz <jimmosk(a)red.seas.upenn.edu> wrote: > >I've seen the recent reports about the discovery of a formula for pi > >of the form > > infinity > > ----- > > \ (- n) / 4 2 1 1 \ > > ) 16 (------- - ------- - ------- - ------- ) > > / \8 n + 1 8 n + 4 8 n + 5 8 n + 6 / > > ----- > > n = 0 > > > >which is said to tell you in a simple manner what the nth digit in the > >hexadecimal expansion of pi is. I don't see why. Yes, the ith term of > >this series does include 16^-i, which is the ith place in said expansion, > >but the term in parentheses (sorry; they look more like angle brackets) > >isn't an integer, so it's not giving you the value of the number in that > >ith place. Instead, it gives you several digits which are in places further > >along in pi, with no guarantee that other terms in this sigma won't also > >include digits in those places, forcing you to calculate and add up many > >terms.... > > The full article can be found in PostScript form at > > http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P123.ps > > and a text announcement can be found at > > http://www.mathsoft.com/asolve/plouffe/scimath.txt > > Yes indeed, you have to add up many terms. However, the amount of > computation to find the n^th digit is on the order of n. Whereas, > to compute n digits would require computation on the order of n^2. > > The idea that drastically reduces the work here is that it is very easy > to compute the n^th hex digit of 1/k. This is accomplished by raising > 16 to the n-1^st power modulo k. Dividing the remainder by k gives the > hex expansion of 1/k starting at the n^th hex digit. Raising 16 to the > n-1^st power modulo k is done by squaring and multiplying based on the > binary expansion of n-1 (the method of repeated squaring). > > Thus, to get 16^{-k} 4/(8k+1) starting at the nth hex digit, > compute 4*16^(n-1-k) mod 8k+1. Divide this remainder by 8k+1. > For example, take n = 1000000000 and k = 1257894: > > 4*16^998742105 mod 10063153 = 4894450 > > and 4894450/10063153 = .7C82F7B089CCA729... (hex) > > It will still entail around billion terms to compute the billionth > digit of pi, but that's better than computing a quintillion digits. > > Rob Johnson > Apple Computer, Inc. > rjohnson(a)apple.com > > >

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ZAP_law
by John Young 17 Dec '03

17 Dec '03

1-5-96. W$Jaw: "High Tech Zaps German Privacy Laws. CompuServe Case Shows Difficulty of Enforcement." The growing popularity of the Internet and other multimedia services poses a major challenge to Germany's tough data-protection legislation. The personal information that is freely given and used for marketing purposes in the U.S. is off limits in Germany. The CompuServe case demonstrates just how difficult it is becoming for national regulators to control the flow of information. This is particularly true in Germany, where a raft of legislation is in force designed to avoid-any repeat of the Nazi-era abuse of data, as well as the dissemination of pornography and extremist propaganda. The nation's internal security services are already struggling to combat the sophisticated use of computers by neo-Nazi groups. Following a recent ban on several such organizations, right-wing extremists have been sending coded messages of racial hatred to one another through a system of computer mailboxes known as the Thule network. "CompuServe Seeks a High-Tech Answer To Fracas Over Bar on Adult Material." Industry executives said the move sets a bad precedent that could invite still more countries to demand their own diverging standards of what is acceptable. Critics further maintained that the approach simply won't work. In addition, critics voiced concern that CompuServe's efforts will lead to on-line services being forced to take responsibility for information they didn't create. 1-5-95, WashPo: "Worldwide Net, Worldwide Trouble" [Editorial] The borderless quality of the Internet, one of its great strengths, can now be seen also as a source of unprecedented and unnerving international liability. Just as "community standards" were used in Tennessee to prosecute two California-based bulletin board operators on obscenity charges a few years back, big commercial providers like CompuServe or America Online could find themselves facing charges based on the very different legal systems of a Germany or France or, for that matter, an Iran. Trio: ZAP_law

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ISD_eny
by John Young 17 Dec '03

17 Dec '03

1-5-96. NYP: "2 Large Phone Companies Seek Higher Digital Rates. Critics See Damage to a Fast Internet Link." The proposal has angered people who use the ISDN service to work from home. Phil Karn, an engineer at Qualcomm, argued that the new tariff would cost him about $100 more a month. He said he was upset by the proposal to lift rates and was anxious to switch to cable service when it became available. ISD_eny --------- On cable modems: the 12-27 W$J reported on a test at Boston College, and provided comparisons with other systems. GEY_ser

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Market Earth Wins Another
by Duncan Frissell 17 Dec '03

17 Dec '03

NEW YORK (Reuter) - AT&T Corp. said Thursday that its embryonic online service AT&T Interchange Online Network would become part of the Internet's World Wide Web within a year instead of being a proprietary system. ``The Interchange platform as we know it will phase out over a year or so. That platform will be dissolved into the World Wide Web,'' Michael Kolowich, president of AT&T New Media Services told journalists on a conference call. AT&T said it would be able to take advantage of the best electronic commerce and navigation software for the Internet, most of which are not compatible with Interchange. In doing so AT&T is taking a leaf out of Microsoft Corp.'s book which in December changed tack to open its online service for free to Internet users. The move may be replicated in other online companies, analysts say. ****************** Now if Microsoft and AT&T can't fight open market information networks, what chance do the Feds have to impose their proprietary system on the Net? The Feds are even worse at marketing than AT&T. DCF "If AT&T owned KFC they'd advertize that they are selling 'hot, dead, chicken'. No, I'm afraid they'd advertize 'lukewarm, dead, chicken'." -- Stolen from Jerry Pournelle

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Re: Windows Eudora and PGP
by Bill Stewart 17 Dec '03

17 Dec '03

>>>1) Use cut-and-paste into Private Idaho. Private Idaho will allow you to >>>paste back into Eudora. (Or you can send out from Private Idaho directly.) >>>This option is useful becuase it supports nyms and chaining of remailers. ... >>[sigh] Just what I thought, no easy solutions. Private Idaho's pretty easy - if you're replying to a message, you'll need to do a cut&paste to move the original into PI, but it follows all the standard Windows cut&paste clipboard stuff, and after that you can send the message directly (from newer versions of PI) or pick a menu item that hands it back to your mailer (Eudora or several others are supported) for delivery. Inside PI, you can pick menu items to call PGP, add remailer headers, etc. At 07:46 PM 1/3/96 -0500, "Douglas F. Elznic" <delznic(a)storm.net> wrote: > I have also heard that ViaCrypt is a good alternative. But I am not sure. >Has anyone else out there heard anything good/bad about ViaCrypt? I've got the ViaCrypt Windows package, as well as their DOS versions. It's really nice for key management (which Private Idaho doesn't do much of), though some of the other PGP Windows frontends also do that. Its encryption/decryption/signing functions are mainly oriented towards files rather than Clipboards - the big advantage of this is that there aren't any silly 64KB or 640KB limits anywhere, but it's a bit clumsier. I usually use Private Idaho as a front-end to ViaCrypt as well; it's faster and prettier to have ViaCrypt handling the Windows interfaces than to have PI pop up a DOS window to run Real PGP in. The PGP 3.0 stuff, when it comes out, will help the process a lot. #-- # Thanks; Bill # Bill Stewart, stewarts(a)ix.netcom.com, Pager/Voicemail 1-408-787-1281 # # "The price of liberty is eternal vigilance" used to mean us watching # the government, not the other way around....

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Internet Gateway for Bletchly Park Trust
by pjb＠ny.ubs.com 17 Dec '03

17 Dec '03

I am trying to setup an Internet gateway for BP Trust. I will either convience Sun to donate a SparcStation for this purpose, or I will donate one myself. What I need is a contact in the UK for some ISPs, or a University or somesuch that would consider hosting their domain/address. Will anyone having any information that might be of use to me in this endevour please email me at: pjb(a)ny.ubs.com and/or pjb(a)23kgroup.com. I have just returned from a trip to BP, and there are many new and exciting things going on there. I will (RSN) post an article re: the current state of affairs at BP. Cheers, paul

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Re: Representations of Pi, etc.
by stevenw＠best.com 17 Dec '03

17 Dec '03

Tim May wrote: >In summary, I would be surprised to find that a method for calculating the >Nth digit of pi works for base N but not for base M (modulo some minor >efficiency factors related to machine architecture, etc.). > >Any pointers to this result would be appreciated. See Peter Borwein's home page: http://www.cecm.sfu.ca:80/personal/pborwein/ under _Calculating Pi and Other matters_. ------------------------------------------------------------------------- Steven Weller | "The Internet, of course, is more | than just a place to find pictures | of people having sex with dogs." stevenw(a)best.com | -- Time Magazine, 3 July 1995

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Re: Compuserve grovels to foreign censors
by Gordon Campbell 17 Dec '03

17 Dec '03

At 12:56 AM 1/5/96 -0500, Larry Sudduth wrote: >Attachment Converted: C:\WORK\WINMAIL.DAT What, pray tell, is this? ----- Gordon R. Campbell, Owner - Mowat Woods Graphics P.O. Box 1902, Kingston, Ontario, Canada K7L 5J7 Ph: (613) 542-4087 Fax: (613) 542-1139 2048-bit PGP key available on request.

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Re: US cryptographic patents, 1995
by thad＠hammerhead.com 17 Dec '03

17 Dec '03

lull(a)acm.org (John Lull) said: > This data was extracted from a free database maintained by the > EDS Shadow Patent Office at http://www.spo.edo.com/ That's really http://www.spo.eds.com thad -- Thaddeus Beier thad(a)hammerhead.com Technology Development 408) 286-3376 Hammerhead Productions http://www.got.net/~thad

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