December 2003 - cypherpunks-legacy

Re: infinity & set membership (fwd)
by Jim Choate 17 Dec '03

17 Dec '03

> What could be the problem here? One problem might be that an integer > (not including infinity) divided by "infinity" should be 0. This ratio has one of 3 outcomes in my system depending on the rate of approach to infinity of the defining functions, oo/oo = 0 if the denominator grows faster than the numerator oo/oo = oo if the numerator grows faster than the denominator oo/oo = 1 if the two functions grow at equal rates Jim Choate CyberTects ravage(a)ssz.com

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Re: Sandy and the Doc
by Toto 17 Dec '03

17 Dec '03

Bill Frantz wrote: > I hope if such a system is set up, people who use it will realize that > email is not 100% reliable. Just because algebra.com sent mail to > toad.com, doesn't mean that toad.com actually received it. A small > fraction of a percent of these messages will be lost. Are there any critereon established, yet, as to what type of content will be necessary for a letter to get 'lost'?

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Re: GSM crypto upgrade? (was Re: Newt's phone calls)
by Adam Back 17 Dec '03

17 Dec '03

Bill Frantz <frantz(a)netcom.com> writes: > At 4:39 AM -0800 1/16/97, Adam Back wrote: > >- PIN for phone's RSA signature keys > > It is not clear you need signatures in the secure phone case. Eric > Blossom's 3DES uses straight DH for key exchange with verbal verification > that both ends are using the same key. How does Eric's box display the negotiated key to the user? (I don't recall the pair I saw having displays). > As long as the man in the middle can't imitate a familiar voice, > this procedure is reasonably secure. This is the approach taken by PGPfone also. If the value of the conversations was high (>$100,000?) passable voice imitation wouldn't be that hard I suspect. Also I thought it would be kind of cute if there were some way for phones to exchange their signature keys `face to face' as well. > I agree that signatures of some kind are needed to identify the phone to > the cell company to prevent an all too familiar technique of stealing phone > service. But this protection would not be a 3rd party cell phone upgrade. It's about time something was done about that problem. Adam -- print pack"C*",split/\D+/,`echo "16iII*o\U@{$/=$z;[(pop,pop,unpack"H*",<> )]}\EsMsKsN0[lN*1lK[d2%Sa2/d0<X+d*lMLa^*lN%0]dsXx++lMlN/dsM0<J]dsJxp"|dc`

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Re: GSM crypto upgrade? (was Re: Newt's phone calls)
by Adam Back 17 Dec '03

17 Dec '03

Steve Shear <azur(a)netcom.com> writes: > For voice calls, it is not possible to merely insert a more secure crypto > function (e.g., IDEA) inside the less secure A5 crypto, unless the GSM base > station's protocol is aware the subscriber unit is using the more secure > crypto. Otherwise, when the GSM base station unwraps the A5 encrypted data > stream, which it assumes will contain digitized voice packets in the clear, > it will not find what its looking for and will be unable to convert the > packets to a circuit-switched voice signal. The circuit-switched voice signal is digital also, and the voice packet payload is transferred byte for byte into the circuit switched link right? So to insert IDEA encryption inside the A5 layer, you'd need to packetize the IDEA ciphertext so that it conforms to the voice packet spec (to fool the unwrapping the GSM station performs into thinking the packets are voice packets). Is that possible? Is the packet switched protocol non-error corrected? (ie Is packet dropping expected?) If so you need to use an IDEA mode which does not rely on previous packets. > If, as I have previously stated, the subscriber instead uses the data port > of his instrument and establishes a data link with his payload protected by > the more the secure crypto this is entirely feasible. If the above is infeasible. Probably this is a more practical approach anyway, as the data port has been already engineered to solve some of problems that would be encountered, and you would be duplicating effort. Adam -- print pack"C*",split/\D+/,`echo "16iII*o\U@{$/=$z;[(pop,pop,unpack"H*",<> )]}\EsMsKsN0[lN*1lK[d2%Sa2/d0<X+d*lMLa^*lN%0]dsXx++lMlN/dsM0<J]dsJxp"|dc`

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Re: [Math Noise] (fwd)
by Mike Duvos 17 Dec '03

17 Dec '03

Jim Choate <ravage(a)EINSTEIN.ssz.com> writes: > In short you are saying there are Reals which can not be > expressed in the format: > AmEm + Am-1Em-1 + ... + A0E0 . B0E-1 + B1E-2 + ... + BnE-n+1 > where m and n -> infinity. Another way of saying this is > that there are Reals for which membership in a set of Reals, > because they are uncountable and therefore unrepresentable, > is not possible. From a set perspective this means, Again, we may speak of a representation for the Reals within a formal system, although we may not speak of "The Representation of X" for every single Real X. We cannot assign to every Real a finite representation, but we can talk about the infinite representation all Reals have within a formal system without running out of space. The inability of a formal system to talk about each Real individually, or equivalently, that there are Real numbers which are not finitely denumerable, does not mean that there are Reals which do not have an representation as a non-ending sequence of symbols. > R = [[-infinity, ..., m] [n, ..., 0] [0, ..., p] [q, ..., +infinity]] > such that there are uncountable numbers between m,n or p,q; etc. Infinity does not have a predecessor, so it makes no sense to count back from it a finite number of steps. > Clearly in contradiction with the base axioms of > mathematics as described by Euclid in defining a line. This point completely escapes me. > And I contend that ANY number which is Real can be > expressed by the decimal expansion above. Which clearly > qualifies as a formal system. Useful formal systems employ finite strings from some alphabet. The set of all possible such strings is countable. The set of all sequences from the same alphabet is uncountable, but not particularly useful for theorem-proving, at least in a finite amount of time. > To say there are Reals for which there is no linear > representation is the same as saying there are lengths which > can't be measured. Now since a line is nothing but a set of > points, which don't have size, but only position this > obviously holds no water, unless you are saying it is not > possible to place two points arbitrarily close together, > which would imply that points have some sort of width, > clearly against the definition of a point. No. Points do not have width. > This all goes back to what I said in a earlier post, the > problem comes from our axiomatic (ie taken on faith, > unprovable) use of infinity. Without a clear and precise > dilineation of those axioms prior to the proof such > conclusions are worthless. In Axiomatic Set Theory, it is necessary to postulate (either implicitly or explicitly) the existance of one infinite set. This is an act of faith. Whether any infinities really exist is a matter for philosophy. > Several of you have said "infinity is not a number", this > is an axiom. Change the axioms and the whole structure > changes. I am simply saying that perhaps we should look at > the "infinity is not a number" axiom, much as geometers look > at Euclids Fifth Postulate. There is nothing inherent in > nature that prefers one axiomatic expression of infinity > over the other. If one constructs the Ordinals, which are isomorphism classes of well-ordered sets, and the Cardinals, which are equivalence classes of equipotent sets, one will automatically end up with all sorts of transfinite numbers. We normally don't include infinities when we build the rationals, the reals, or the complex numbers, unless we need them for a particular application, such as in using the extended real number line in defining measures. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd(a)netcom.com $ via Finger. $

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RE: THIS IS THE FIRST MESSAGE TO THE MODERATED CYPHERPUNKS LIST
by Butler 17 Dec '03

17 Dec '03

John Gilmore wrote: > >>Welcome to (what I hope is) a more useful and less confrontative >>cypherpunks list. Now, can we get back to talking about cryptography? > > "can we get 'BACK' to talking about cryptography?" You seem to have misspelled START. >Scott

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Re: [Math Noise] (fwd)
by Paul Foley 17 Dec '03

17 Dec '03

On Sun, 19 Jan 1997 22:34:05 -0600 (CST), Jim Choate wrote: Forwarded message: > Yes, the Reals can be constructed from the Rationals. No, the > Reals are not a subset of the Rationals. An arbitrary Real can be constructed from the Rationals. If we accept the proposition, as posed apparently by you and others, of uncountable Reals then your 'assumption' fails, otherwise the 'uncountable' members would be countable. There are no "uncountable" numbers -- uncountability is a property of the set, not an individual member of the set. The set of reals cannot be placed in one-to-one correspondence with the integers (strictly, positive integers, but it amounts to the same thing). > Dedekind Cuts are a simple abstraction, often used to construct > the Reals from the Rationals in undergraduate calculus courses. > Conceptually, one makes a single "cut" in the set of Rationals, > dividing it into two parts, all of the members of one part being > greater than all of the members of the other. The number of ways > of doing this correspond to the Reals. The number of cuts are 1-to-1 with the Reals, they are not the Reals. There is no way I can make a cut which is 3.1527, only 1-to-1 with the number(s). Important distinction. Cut the rational numbers into two sets, A containing all the negative rationals and all those that have squares less than 2, and B containing all the positive rationals that have squares greater than 2. There you have a cut which is 1.41421... (i.e., sqrt(2)). So you can define irrational numbers from the rationals (an irrational number is a cut such that the first set (A) has no largest member and the second set (B) has no smallest member). -- Paul Foley <mycroft(a)actrix.gen.nz> --- PGPmail preferred PGP key ID 0x1CA3386D available from keyservers fingerprint = 4A 76 83 D8 99 BC ED 33 C5 02 81 C9 BF 7A 91 E8 ---------------------------------------------------------------------- Sometimes a feeling is all we humans have to go on. -- Kirk, "A Taste of Armageddon", stardate 3193.9

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Re: [Math Noise] (fwd)
by ichudov＠algebra.com 17 Dec '03

17 Dec '03

Jim Choate wrote: > Forwarded message: > > > Only countably many real numbers, or members of any uncountable > > set, are denumerable. It is the property of being uncountable, > > rather than of being real or complex, which is important here. > > In short you are saying there are Reals which can not be expressed in the > format: > > AmEm + Am-1Em-1 + ... + A0E0 . B0E-1 + B1E-2 + ... + BnE-n+1 All reals are equivalent to sequences of digits, but there are reals such that there is no algorithm to generate their digits. It happens because there are "more" real numbers than algorithms. > > In general, only countably many members of any uncountable set > > can be precisely specified within any formal system, given names > > comprised of strings of symbols, or other similar things. > > And I contend that ANY number which is Real can be expressed by the decimal > expansion above. Which clearly qualifies as a formal system. I suggest the following mental exercise. FORGET FOR A MOMENT ABOUT REAL NUMBERS. Let's deal with mummies: DEFINITION: I define a mummy as possibly infinite sequence of characters, separated by one dot, such that only characters abcdefghij are allowed. Also, mummies that are represented by finite sequences of characters are by this definition equivalent to mummies that end with an infinite sequence of letters "a". END DEFINITION. Examples: dce.abdefhaabdaaa ae.cacacacacacaca... and so on. Obviously, some of the mummies, such as c.cccccc... (with an ininite sequence of "c") CAN be generated by algorithms. The interesting fact, that i will prove below, is that some of them cannot be generated by any algorithm. THEOREM: The set of mummies is more than countable PROOF: if it is countable, we can construct a mummy that is not counted. it is easy. THEOREM: there are mummies such that there is no algorithm that can print them. PROOF: the set of mummies is more than countable, the set of algorithms is countable, therefore there is no way to construct a one-to-one correspondence between mummies and algorithms. Do you agree? Now let's back to the original problem of real numbers: the only difference between mummies and real numbers is that digits 0123456789 are replaced by characters abcdefghij. Not a whole lot of difference, so everything that applies to mummies applies to real numbers. - Igor.

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Re: GSM technology
by Adam Back 17 Dec '03

17 Dec '03

Steve Shear <azur(a)netcom.com> writes: > [very useful explanation of GSM TDMA, and the new HSCSD] 64 kbit/s tied to ISDN is very nice technology. > ENCRYPTED GSM LINKS > If the GSM phone includes a data port, as some already do, just connect > your laptop, dial your ISP and 'push' the encrypted traffic over that link > (e.g., using TCP/IP and PGPfone). This would obviously be possible, but to my mind reduces the appeal of the system. Not every one has a laptop. Even if the potential user does have a laptop, booting windows95, and starting up PGPfone is an onerous task compared to just dialing a number on a mobile phone. It's a user friendliness issue, and a question of ergonomics. A mobile phone is more portable than a GSM phone with a laptop plugged into the data port. You can't fit the laptop and GSM phone combination into your shirt pocket. What are you going to use for a handset? Radio operators headphone (with mike attached to the headset) plugged into the laptop? That's more dangling wires, and makes the system less portable, and even more onerous to setup (take laptop from carry bag, plug in headphones, plug in phone data port, wait for laptop to boot, etc). Even for crypto enthousiasts, I would submit that many would neglect to go through the hassle of going through PGPfone for most conversations, and would instead just use the mobile phone in the clear (or with A5 encryption). This for similar reasons to the situation with PGP itself, many people rarely use PGP, even though there is abundant software available to use it seamlessly with most mail readers. (I can vouch for mailcrypt.el the emacs interface to PGP, and use it for to anyone who has a PGP key, and does not express displeasure at receiving encrypted email). Also, the cell phone tarriffs may be higher if you need higher bandwidth to get the software only voice codec implementations in PGPfone to produce equivalent full-duplex voice quality to that expected from a digital mobile phone. Not knocking the mobile phone and laptop combination for the purpose of having mobile TCP/IP access from a laptop, I know several people who have this combination, though only at 9.6kbits, and even at that speed it is very neat. Adam -- print pack"C*",split/\D+/,`echo "16iII*o\U@{$/=$z;[(pop,pop,unpack"H*",<> )]}\EsMsKsN0[lN*1lK[d2%Sa2/d0<X+d*lMLa^*lN%0]dsXx++lMlN/dsM0<J]dsJxp"|dc`

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Re: [Math Noise] (fwd)
by Mike Duvos 17 Dec '03

17 Dec '03

Jim Choate <ravage(a)EINSTEIN.ssz.com> writes: > An arbitrary Real can be constructed from the Rationals. If > we accept the proposition, as posed apparently by you and > others, of uncountable Reals then your 'assumption' fails, > otherwise the 'uncountable' members would be countable. We can construct the Reals from the Rationals without having to speak of each specific Real while doing so. A formal system, having only a countable number of strings of symbols from its alphabet, can speak of "The Real Numbers" even though it cannot speak of "The Real Number X" for every single X in the Reals. > A 'limit point' is not the same as 'equal to'. Arbitrarily > close is not equivalent, inherent in the definition of a > limit point is the concept of 'little o' and 'big o', or > worded differently our axiomatic definition of infinity. In standard analysis, the limit of a sequence A[n] is a value x such that given any positive epsilon, no matter how small, we can find a point in the sequence such that all its members after that point are within epsilon of x. Such a limit, if it exists, is unique and exactly defined. "Little o" and "big o" are concepts from complexity theory and I am not precisely sure why you feel they need to be mentioned. > I can, but there is no fundamental rule in mathematics > that requires me to ignore the small but distinct > difference between the element in the original set and the > sequences used to approximate it. In the general case, the limit point will not be a member of the sequence which approximates it. Although every member of the sequence is a finite distance away from the limit, the limit itself is, as I previously mentioned, exactly known without any ambiguity. > It is something that must be agreed upon by accepting a > particular axiomatic definition of infinity. An "infinity" is simply the property of being able to be put in 1-1 correspondence with a proper subset of oneself. > The number of cuts are 1-to-1 with the Reals, they are not > the Reals. There is no way I can make a cut which is > 3.1527, only 1-to-1 with the number(s). Important > distinction. Mathematical objects are sets with structure. We generally consider two mathematical objects equivalent if there exists a 1-1 correspondence between the respective sets which is structure preserving. What the actual members of the set are, and how they were constructed, is usually unimportant. For all practical purposes we may refer to any mathematical object isomorphic to the Reals as "The Reals", without any confusion. -- Mike Duvos $ PGP 2.6 Public Key available $ mpd(a)netcom.com $ via Finger. $

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