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Re: A Math problem related to cryptography
by phelix＠vallnet.com 17 Dec '03

17 Dec '03

On 19 Oct 1997 18:36:26 -0500, Jeffery Walker <jeff(a)beol.net> wrote: > > I have been working on some math and C++ code to implement it. The >problem relates to a possible new means of factoring. However, I have run >into a problem which I cannot solve. Indeed it maybe impossible. The >problem is this: > > Find and equation using only multiplication, division, GCD, LCM and >powers (not addition or subtraction) in terms of a and b which is equal to >a+b for all Integers. If so desired it can be assumed that a and b are >relative primes with a>b. Note that equivalent problems include but aren't >limited to finding a similar equation for a+1. If other functions such as >logs are required they may be allowed but I would have to look into it. > > To encourage people to answer I am offering $20 for a solution and >$10 for a proof that it is impossible. I will judge all answers as to the >validity both in terms of actually being correct (or in the case of a proof >a valid argument) and in that they do not use functions such as addition or >subtraction which are not allowed. > (why do I get the feeling that I'm doing somebody's homework assignment) Claim: In the realm of Integers, There does not exist a formula using only multplication,division,GCD,LCM,and powers such that f(a,b)=a+b for all integers a,b Proof (by contradiction): I assume that a,b are primes > 2. Lets also define x,y,z,w,m,n and any integer >=0 and C,D,E as any integer > 0. Now let's look at the operations available to us: multiplication and powers: C=C*(a^0)*(b^0) CD=E(a^0)*(b^0) where E=CD a=1*(a^1)*(b^0) a^2=1(a^2)*(b^0) Cab^2=C*(a^1)*(b^2) well , all results can be expressed in the following form: C*(a^x)*(b*y) division: a !| b and b !| a (here !| means "does not divide") (From here on out, lets assume that a !| C,D,E and b !| C,D,E. it makes things simpler) Ca/a=C*(a^0)*(b*0) Ca/D=E*(a^1)*(b^0) assuming that E | C I won't go through all this. It should be obvious that for all allowed divisions, the result can be expressed as C*(a^x)*(b*y) GCD: gcd(a,b)=1 gcd(a,C)=1 gcd(Ca,Da)=max(a,gcd(C,D)) gcd(Ca,Db)=gcd(C,D) gcd(C(a^x),C(a^y))=C(a^(min(x,y))) gcd(C(a^x)*(b^y),D(a^z)*(b^w))=gcd(C,D)*(a^(min(x,y)))*(b^(min(z,w)))) =E(a^m)*(b^n) for E=gcd(C,D) m=min(x,z) and n=min(y,w) so, all results of GCD can be expressed in the form: C(a^x)(b^y) LCM: LCM(C,D)=CD/gcd(C,D) LCM(C(a^x)*(b^y),D(a^z)*(b^w)) =CD*(a^(x+z))*(b^(y+w))/gcd(C(a^x)*(b^y),D(a^z)*(b^w)) =( CD/gcd(C,D) * (a^(|x+z-min(xz)|)) * (b^(y+w-min(yw)) = E(a^m)*(b^n) where E=CD/gcd(C,D)=lcm(C,D), m=x+z-min(x,z) , n=y+w-min(y,w) so, all results of LCM can be expressed in the form: C(a^x)(b^y) Now, as you can probably tell by now, I don't remember a damn thing about groups, rings, and fields. If i did, I could have done all of the above in one paragraph. SO, what I'm trying to say is that all the numbers you can operate on here will be of the form C(a^x)(b^y). SO you really have to prove at least the following C(a^x)(b^y)=a+b for some C>0, x,y>=0 integers Now, you could probably say that C=a+b, x,y=0, but that's a cop out and is probably not allowed. Now, watch while I cop out and provide an easy counterexample: assume some formula exists such that f(a,b)=a+b with f only using *,/,gcd,lcm,^ operators let a=5, b=7 Since I know that ultimately anything I do with constants and the operators 8,/,gcd,lcm,^ will result in something in the form of C(a^x)(b^y), I won't even mess with the formula there must exist some C>0, x,y>=0 that makes: C(5^x)(7^y)=5+7=12 of x>=1 and y>=1 then C(5^x)(7^y)>12 for all C>0 if x=0 and y=0, C=12 (this works) if x=1,y=0 then 5C=12. there is no C which satisfies this. if x=0,y=1 then 7C=12. there is no C which satisfies this. so, the only solution is C=12, or more generally, C=a+b oops, that can't be the formula since we're not allowed to do that. QED. Well, that was pretty sloppy, so lets be more general about this: C(a^x)(b^y)=a+b Now, I'm sure that somewhere in the history of mathematics somebody has proven that for primes a and b where a,b>2 that a*b>a+b. So, for any x,y,C>0, C(a^x)(b^y)>a+b. C, of course, cannot be negative, or zero, so all were left with is x or y being zero. Let y=0. we have: C*a^x=a+b C*a^x - a = b a*(C*a^(x-1) - 1 ) = b a*E=b Now, a and b are primes and a!=b. From the fundamental theorem of algebra, every number can be represented by a series of primes such as: p1^a1 * p2^a2 * p3^a3 * ... In a*E=b, if we factor each side down to its primes, we find that the right hand side does not contain the prime 'a' which is on the left hand side, so a*E != b. A similar argument can be used for the case x=0. This leaves the only solution to C(a^x)(b^y)=a+b being x=0,y=0 C(a^0)(b^0)=C=a+b which isn't allowed. QED Now, If you're like me, you've probably read the above and don't have a f*cking clue what I meant (I sure wouldn't if I read all that crap). So here's the executive summary. With the operators you've defined on the number set you want to work with, no matter how complicated or crazy your formula is, I can express the result at C(a^x)(b^y). And hopefully, I've shown that C(a^x)(b^y) cannot equal a+b except in the trivial case of C=a+b (with x,y=0) which is what you don't want. >Thanks, >Jeff >P.S. I am very interested in joining the coderpunks list as I do program >and am interested in cryptography as related to programming. If someone >would be kind enough to recommend me I thank you. > I wasn't aware that you had to be invited to the coderpunks list. Just send a message to majordomo(a)toad.com with the following in the body: subscribe coderpunks -- Phelix, who really should have been able to give a better proof (especially since one of my degrees has the word 'Mathematics' on it)

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RC5 encryption
by vcarlos35＠juno.com 17 Dec '03

17 Dec '03

Forgive this seemingly naive question, but.... Where does RC5 derive its security from? I know about the ROTL stuff and the key expansion methods (I have the RSA Cryptobytes, HAC, AC, etc.) However, I personally can't see how it would work. I know its supposedly secure because of the data-dependent rotations, and other features. Correct me if I'm wrong, but a ROTL assembler command shifts all bits to the LEFT one and moves the "overflow" bits back into the right end of the register: 0100111011 to 0011101101 if it rotates left by 2 How does this make it hard to decrypt? The round function seems MUCH weaker than IDEA's, CAST's, or even GOST and Blowfish. Vincent Carlos

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Re: consensus on pgp? can we consolidate for action?
by nobody＠REPLAY.COM 17 Dec '03

17 Dec '03

Lucky Green wrote: > I encrypt both my SMTP and POP links using SafePassage Secure Tunnel. > 128 bit SSL v3 with client certs. You can download a free eval copy of > SPST at http://www.c2.net/products/spst/ Without the certs, it shouldn't > take longer than 15 min. to set this up at your site. > > Disclaimer: I work for C2. Will these constant lies from C2Nut employees never stop? I've been at C2 for three months, now, and I haven't seen Lucky do any work, yet. CorporateSpyMonger

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Your "RIGHT" to Speak to Big Brother
by Eric Cordian 17 Dec '03

17 Dec '03

Today Janet "The Bitch of Waco" Reno held a news conference announcing that, in her not-so-humble opinion, Microsoft Corporation was in violation of a consent decree by virtue of bundling Internet Explorer with Windows '95, and that she was asking for a $1 million a day fine. Ho Hum. However, one tiny item in her news conference caught my attention. It wasn't related to IE or Windows, but to company secrets protected by non-disclosure agreements. Even though Microsoft has indicated that it does not intend for its non-disclosure agreements to be binding in a way which prevents persons from disclosing anything they like to the DOJ in a criminal investigation, the Feds apparently want the concept of non-disclosure to the government scrapped. Everyone, they claim, has a "right" to speak to the government on any subject whatsoever, which cannot be abrogated by anything as flimsy as a contract or agreement, designed to protect anothers secrets. After all, the government is your friend, and is here to help you. This was made clearer when The Bitch of Waco introduced her minion, Assistant Attorney General Joel Klein. "We're asking the court to order Microsoft to tell everyone who has signed or who in the future will sign a non- disclosure agreement, that it doesn't apply to the government, period. We won't allow anyone to interfere with the people's right to provide information to their government." And there you have it. The people's right to provide their neighbor's proprietary information their government shall not be infringed. How Constitutional-Sounding. -- Eric Michael Cordian 0+ O:.T:.O:. Mathematical Munitions Division "Do What Thou Wilt Shall Be The Whole Of The Law"

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RE: Impeachment of Janet Reno -- was Justice Department Sues Micr
by Robert Hettinga 17 Dec '03

17 Dec '03

--- begin forwarded text Date: Mon, 20 Oct 1997 22:20:09 -0400 Reply-To: com-priv(a)lists.ecosystems.net Originator: com-priv(a)lists.psi.com Sender: com-priv(a)lists.psi.com Precedence: bulk From: Com-Priv <com-priv(a)lists.ecosystems.net> To: Multiple recipients of list <com-priv(a)lists.psi.com> Subject: RE: Impeachment of Janet Reno -- was Justice Department Sues Micr X-Comment: Commercialization and Privatization of the Internet All right, I will justify (again) my position. Re: the bundling of a software with an Operating System. I will not say that I agree that there should be any restrictions or regulations regarding what applications can be "bundled" with an operating system. I will say that I vehemently disagree that the government should legislate what constitutes an operating system and what applications may be included. But I will concede that there is an ethical question regarding of bundling of any product with that of another in an effort to make bundled product competitive on something other than its merits. But please do not insult my intelligence. This is not the core issue at hand. Microsoft has been bundling IE since before it even had a version number when Windows 95 was originally released more than two years ago. I just took a close look at Windows 95 OEM Service Release 2, and you cannot not install IE -- that was released last summer. So I ask, why is this coming up now? The answer was given in the letter to the DOJ that Ralph Nadar's organization posted to this very list not more than one month ago. "Microsoft should not be permitted to...integrate the MSE with the operating system in ways that are unavailable to other firms." This is not the consumer public via DOJ against Microsoft, this is Netscape via DOJ against Microsoft. This is not about Windows 95 and IE 3.0, this is about Windows 98 and NT 5.0. Windows 98 and NT 5.0 have evolved the core operating system interface and functionality to be seamlessly integrated with and based upon Internet standards CIFS, LDAP, HTTP, HTML/XML, etc. This is what Netscape is attacking. There is a natural progression and market pressure to natively integrate Internet-based standards into both OS's and applications -- to legislatively prevent that is absolutely ridiculous and harmful to consumers. It would be the equivalent in my mind if the Australian maker of the Trumpet Winsocket (the most popular TCP/IP stack for Windows 3.1) had sued Microsoft for bundling TCP/IP with Windows 95/NT. All I can say about Netscape is the ability to successfully build and market software that complements or enhances another software package is dependent on a good relationship with that software vendor -- this is self-evident in the market. To self-proclaim yourself the destroyer of that vendor and then except that vendor to support you is utterly moronic -- they get what they deserve. For our mercenary government to pull out their guns in service of Netscape and force Microsoft to permit their existence is criminal. To proclaim Microsoft a monopoly and use that as justification to completely disregard reason, objectivity and rights of property, and disrupt the free market with subjective law and reason of guns is repulsive. I have trouble calling myself an American. Matt "You'd better get it straight that it's not a bunch of boy scouts you're up against -- then you'll know that this is not the age for beautiful gestures. We're after power and we mean it. Your fellows were pikers, but we know the real trick, and you'd better get wise to it. There's no way to rule innocent men. The only power any government has is the power to crack down on criminals. Well, when there aren't enough criminals, one makes them. Once declares so many things to be a crime that it becomes impossible for men to live without breaking laws. Who wants a nation of law-abiding citizens? What's there in that for anyone? But just pass the kind of laws that can neither be observed nor enforced nor objectively interpreted -- and you create a nation of law-breakers---and then you cash in on guilt. Now that's the system...that's the game, and once you understand it, you'll be easier to deal with." _Atlas Shrugged_ --- end forwarded text ----------------- Robert Hettinga (rah(a)shipwright.com) Philodox e$, 44 Farquhar Street, Boston, MA 02131 USA "... however it may deserve respect for its usefulness and antiquity, [predicting the end of the world] has not been found agreeable to experience." -- Edward Gibbon, 'Decline and Fall of the Roman Empire' The e$ Home Page: http://www.shipwright.com/ Ask me about FC98 in Anguilla!: <http://www.fc98.ai/>

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YOUR LISTING ON YAHOO!
by brian＠firstgear.com 17 Dec '03

17 Dec '03

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Cypherpunks Related (?) or merely about DC in general?
by nobody＠REPLAY.COM 17 Dec '03

17 Dec '03

Q. How did Sir Alexander Fleming change Spain's bullfighting? A. Before he invented penicillin, countless toreros died of infected wounds. After, even the smallest arenas were equipped with penicillin syringes. And the performances became much more exhilarating. Said one cape artist: "Now I can stand closer to the bull." http://www.LMBoyd.com/postscript.htm

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I am a homosexual!@#$!@#@!!
by Bronc Buster 17 Dec '03

17 Dec '03

Hi, my name is Bronc Buster and you all know me. but what you donot know is that I AM A HOMOFAGGOT who likes lil' boys cocks and stuff. you all have to email me here cuz some body email bombed my other adress and then my new one. i also want to see pics of your cocks but please wtrie my name on your dick before you mail them to me so i know You love me. off to spank my small monkey, Bronc Buster ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com

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French GAK
by nobody＠REPLAY.COM 17 Dec '03

17 Dec '03

Wall Street Journal, October 20, 1997: French Proposal For Encryption Is Worrying EC By Jennifer L. Schenker A proposed French law ensuring government access to corporate electronic communications is setting off alarm bells in the business community and on the European Commission. France, presenting the law as a liberalization of its current policy, is the only Western country that bans any domestic use of cryptography - technology that encodes data for protection against prying eyes. France also places strict controls on the export of encryption tools, a restriction imposed by certain other countries, including the U.S. The new rules, submitted to the European Commission on Thursday, allow businesses operating in France to encode their corporate secrets but require that keys to unlock the code be given to a French government-approved entity in which the majority of the capital or votes is retained by French nationals. Microsoft Corp., Netscape Communications Corp. and the Business Software Association have raised objections to the French proposal. The BSA represents major international software publishers and high-tech companies, including Novell Inc., Compaq Computer Corp., Apple Computer Inc. and Lotus, a unit of International Business Machines Corp. The proposal also requires companies selling products with embedded encryption software in France to reveal "source code" - the rough equivalent of asking Coke to reveal its secret formula. Some believe that such a key-recovery system would make it easier for competitors to gain access to a company's secrets. The BSA's European chapter is expected to release a public statement this week supporting the European Commission's decision earlier this month to reject the key-recovery approach to encryption, which is championed by both the U.S. and France. The commission, which will formally comment on the French proposal by month's end, is concerned partly because the French ownership requirements may violate internal market rules. "I do not say this is the best system. It is the least bad in trying to find a balance between national-security interests, economic interests and the protection of personal privacy," said Gen. Jean-Louis Desvegnes, chief of France's Central Service for the Security of Information Systems, a civilian agency that reports directly to the French prime minister's office. He indicated that France might be flexible on the ownership requirements. -----

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everybody wants a piece of Microsoft's monopoly
by Zooko Journeyman 17 Dec '03

17 Dec '03

If you thought Microsoft and Bill Gates were bad for the evolution of our precious technology, you'll _love_ the new "Guvsoft", lead by everyone's favorite businesswoman Janet Reno. The race to see who can play "Little Mister Gates" best and earn a cut of the action is accelerating. Pundits are already taking bets on Scott "Now Selling Licenses For 100% Pure Anything-Non-Microsoft" McNealy, Steve "Competition Is Great As Long It Doesn't Actually Affect Us" Jobs, and Janet "I've Already Demonstrated My Grasp Of Tactics And Tact" Reno. I mean, _sure_ Microsoft is an oppressive monopoly, but then what the hell is the USG? Zooko

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