April 2015 - mathfun@mailman.xmission.com

Re: [math-fun] How to protect computer versus malware
by Henry Baker 14 Apr '15

14 Apr '15

This scheme is not a lot different from a lot of other signing schemes. The attacks are similar. For example, you program an interpreter (e.g., Java) which satisfies all of your security features, except that Java _doesn't_ check the code that it interprets. Game over. MITM. Who signs the code, and why should you trust them? (Untrusted turtles all the way down; more succinctly, turds all the way down, making for a big POS.) Then there are the "weird machines". https://en.wikipedia.org/wiki/Weird_machine It turns out that the paging apparatus of modern Intel processors is so complicated that it is Turing complete. You can execute an arbitrary Turing Machine _without ever (fully) executing a complete instruction_ !! http://www.cs.dartmouth.edu/~sws/pubs/bbss13.pdf "We show that powerful computation on x86 processors is possible without executing any CPU instructions. We demonstrate a Turing-complete execution environment driven solely by the IA32 architectures interrupt han- dling and memory translation tables, in which the pro- cessor is trapped in a series of page faults and double faults, without ever successfully dispatching any instruc- tions. The hard-wired logic of handling these faults is used to perform arithmetic and logic primitives, as well as memory reads and writes. This mechanism can also perform branches and loops if the memory is set up and mapped just right. We discuss the lessons of this execu- tion model for future trustworthy architectures." Return-oriented programming; fashion a machine language out of existing code subsequence "gadgets": https://en.wikipedia.org/wiki/Return-oriented_programming Jacob Torrey's HARES scheme for spoofing the page for reading while executing from another page entirely. The page that is seen by any program scanning memory is completely innocuous, while the pages actually being executed are malware. https://www.wired.com/2015/02/crypto-trick-makes-software-nearly-impossible… https://www.syscan.org/index.php/download/get/8a49fa76c16592ef790bffad08d1a… http://blog.jacobtorrey.com/hares-faq At 04:06 PM 4/13/2015, Warren D Smith wrote: >Here's an idea. >Let's say some program is a stream of bytes. >Every 64th byte is not an "instruction," it is a "security code." >Specifically, the codes are such that the whole ball of wax -- >program+security -- >gets public-key-encoded to something nice, like it has a bunch of 0s. >Your computer has built in hardware for public key crypto. >It terminates execution if program fails to satisfy security demands. > >Point is, it is not possible for anybody to produce malware with valid security >codebytes, unless they already know your computer's secret key. >E.g they either had your cooperation, or they already had access to >your computer's code. > >-- >Warren D. Smith >http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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Re: [math-fun] How to protect computer versus malware
by Warren D Smith 14 Apr '15

14 Apr '15

The scheme I proposed (rather vaguely) is based on the idea of, sort of, an "immune system" for computers, based on "friend vs foe recognition" of code. Essentially, hardware is made available to perform such recognition, and then only "friendly" code is runnable. Thanks to the wonders of PKC, it is infeasible for anybody who does not know your secret key, to create code you will consider friendly. Of course, yes, if somebody can con you into declaring some code is friendly, then you lose. Or, if they can get to you reveal your secret keys. Or, if your computer was already penetrated on day 1 due to hardware or software hacks pre-inserted during manufacturing. One could also imagine multilevel protection where there are multiple levels of friendliness, the higher levels being allowed to access more features of the computer. Is this worth doing? I do not know. Should we declare it all to be a lost battle?

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[math-fun] Sum of squared factorials (question by Asimov/Wolfram)
by Warren D Smith 14 Apr '15

14 Apr '15

> From: Dan Asimov <asimov(a)msri.org> > Also, Wolfram ( http://mathworld.wolfram.com/FactorialSums.html ) states > that > the sequence > > fsq_n := f_n := Sum_{1<=k<=n} (k!)^2 > > contains only a finite set of primes among its terms. Amazing! > > Is there some easy way to see this? --1, 1+4=5, 1+4+36=41, 617, 15017, 533417, ... At first I thought this was going to be trivial, but the initial values of fsq_n often contain giant prime factors, sometimes also with no small primes involved. Such as fsq_31 whose smallest prime factor is 1751935243. I would presume that some n exists such that fsq_n is divisible by a prime P<=n+1, and if so, then fsq_m will be divisible by P for all m>n. So I would suggest, for each prime P>31 in succession, computing fsq_(P-1) mod P; until you get zero; then declare victory. Heuristically (since the sum over primes p of 1/p diverges) this attack ought to succeed, but it might take a while. I haven't done the computation; the odds seem about even that the first such P will be below 10000, but it seems to me entirely possible that the first such P is unreachably large, such as 10^30. The underlying problem here is the divergence I mentioned is very slow, doubly-logarithmic. To make it even worse: I hereby proclaim that I am "heuristically certain" that fsq_n is, for all except a finite number of n, divisible both by an upper, and by a lower, TWIN prime. (If p and p+2 both are prime, than p is the lower and p+2 is the upper twin.) The same sort of proof must exist, but now finding that proof is likely to be so hard that nobody will ever do it!

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[math-fun] Silicon-28 proof of work & quantum computing
by Henry Baker 14 Apr '15

14 Apr '15

FYI -- Forget about uranium; fire up those centrifuges to enrich silicon! http://www.theregister.co.uk/2015/04/14/quantum_computers_could_be_one_step… Incomprehensible boffins bring quantum computers a step closer All we needed was some isotopically enriched silicon. Well, duh! 14 Apr 2015 at 08:59, Kat Hall The long-awaited arrival of quantum computers could be one step closer, as boffins from Oz have for the first time encoded quantum information in silicon. Unlike conventional computers, which store data on transistors and hard drives, quantum computers encode data in states of microscopic objects called qubits. The arrival of this sort of computing would enable the factoring of large numbers Â leading to all sorts of cryptographic advances. But the ability to build quantum computers has eluded computer scientists for decades. However, Australian boffins may have brought that process one step closer, after researchers at New South Wales University placed the qubits inside a thin layer of specially purified silicon, containing only the silicon-28 isotope. In his best attempt at explaining the process to the average schmo, study lead Dr Arne Laucht said: ÂWe demonstrated that a highly coherent qubit, like the spin of a single phosphorus atom in isotopically enriched silicon, can be controlled using electric fields, instead of using pulses of oscillating magnetic field." Associate Professor Morello said the method works by distorting the shape of the electron cloud attached to the atom, using a localised electric field. ÂThis distortion at the atomic level has the effect of modifying the frequency at which the electron responds. ÂTherefore, we can selectively choose which qubit to operate. ItÂs a bit like selecting which radio station we tune to, by turning a simple knob. Here, the ÂknobÂ is the voltage applied to a small electrode placed above the atom.Â The researchers claim this specific type of quantum bit can be manufactured using a similar production technology to that of everyday computers, drastically reducing the time and cost of development. The findings were published in the open-access journal Science Advances. http://advances.sciencemag.org/content/advances/1/3/e1500022.full.pdf

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[math-fun] How to protect computer versus malware
by Warren D Smith 13 Apr '15

13 Apr '15

Here's an idea. Let's say some program is a stream of bytes. Every 64th byte is not an "instruction," it is a "security code." Specifically, the codes are such that the whole ball of wax -- program+security -- gets public-key-encoded to something nice, like it has a bunch of 0s. Your computer has built in hardware for public key crypto. It terminates execution if program fails to satisfy security demands. Point is, it is not possible for anybody to produce malware with valid security codebytes, unless they already know your computer's secret key. E.g they either had your cooperation, or they already had access to your computer's code. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Fwd: [BPARK] 'That equation is a real Enigma !' Rare handwritten papers by Alan Turing (fwd)
by Whitfield Diffie 12 Apr '15

12 Apr '15

> 56-page book contains Turing's thoughts on tricky 'Leibniz notation > dx/dy' Perhaps NSA stands for ``Non-Standard Analysis''. Whit From: Martin Postranecky <mp(a)HEP.UCL.AC.UK> Subject: [BPARK] 'That equation is a real Enigma !' Rare handwritten papers by Alan Turing (fwd) Date: 11 April 2015 13:53:34 BST To: BLETCHLEYPARK(a)LISTSERV.KSU.EDU 11 April 2015 'That equation is a real Enigma !' Rare handwritten papers by Alan Turing set to fetch $1million at auction reveal some maths completely baffled the code-breaking genius - 56-page book contains Turing's thoughts on tricky 'Leibniz notation dx/dy' - It was written at the Bletchley Park code-breaking headquarters in 1942 - Only extensive Turing manuscript thought to exist, the auctioneer said - It will be sold by an anonymous seller by Bonhams in New York on Monday By Lydia Willgress for MailOnline and Daily Mail Reporter A handwritten notebook in which Britain's Enigma machine genius Alan Turing admits he is baffled by an equation could fetch up to $1million ( £690,000 ). The 56-page book bought in Cambridge contains Turing's thoughts on the clearly tricky 'Leibniz notation dx/dy'. 'I find [it] extremely difficult to understand in spite of it having been the one I understood the best once !' he wrote...../snip/ Read more : http://www.dailymail.co.uk/news/article-3034334/Alan-Turing-s-notebook-set-… http://www.bonhams.com/press_release/18431/

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[math-fun] Power series for Riemann's xi function (Landau's capital-xi function)
by Bill Gosper 12 Apr '15

12 Apr '15

On 2015-04-12 13:57, Dan Asimov wrote: > What's now called Riemann's xi function is (up to a constant factor): > > xi(s) := s(s-1) zeta(s) gamma(s/2) pi^(-s/2), > > which is an entire function of s, and its zeroes (the values of s for > which xi(s) = 0) are exactly the mysterious "nontrivial" zeroes of > zeta(s). > > Another function (that Riemann called "xi(t)") is now usually called > Landau's capital-xi(t) function: Ξ(t). > > But since Ξ may not appear correctly in your e-mail, I'll call it X(t): > > X(t) := xi(1/2 + i t). > > It's easy to check that X(t) is real on the real axis and satisfies > > X(t) == X(-t), > > which is equivalent to the "functional equation of zeta". > > I would like to know the power series coefficients of X(t) about 0. > > Mathematica's attempt to do this results in unbelievably complicated > expressions, and I've had very little luck simplifying them. > > Wikipedia gives an expression for this power series — but each > coefficient is expressed as an infinite series in terms of the > mysterious nontrivial zeroes of the zeta function. > > QUESTION (mostly to you-know-who): Is there a more or less > straightforward expression for the power series coefficients of X(t) > ??? > > (Of course, since X(t) == X(-t), only the even powers of t have > nonzero coefficients.) > > --Dan For the first two terms, I get Ξ[t]== -((Gamma[1/4]*Zeta[1/2]*(1 + (1/2)*t^2* (8 - (1/4)*PolyGamma[1, 1/4] + (Derivative[1][Zeta][1/2]^2 - Zeta[1/2]* Derivative[2][Zeta][1/2])/Zeta[1/2]^2)))/ (4*Pi^(1/4))) == (1/(128 \[Pi]^(1/4))) Gamma[1/4] (-(32 + t^2 (128 - 32 Catalan + 4 EulerGamma^2 - 3 \[Pi]^2 + 4 \[Pi] Log[8 \[Pi]] + 4 Log[8 \[Pi]]^2 + 4 EulerGamma (\[Pi] + Log[64 \[Pi]^2]))) Zeta[1/2] + 16 t^2 Zeta''[1/2]) with no help from http://isc.carma.newcastle.edu.au/standard and the promise of worse to come. Let's hope you-know-who has better luck. --rwg

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[math-fun] Oops. Universe not what they said.
by Warren D Smith 12 Apr '15

12 Apr '15

http://arxiv.org/abs/1408.1706 http://iopscience.iop.org/0004-637X/803/1/20/ Peter A. Milne, Ryan J. Foley, Peter J. Brown, and Gautham Narayan: The Changing Fractions of Type Ia Supernova NUV--Optical Subclasses with Redshift, The Astrophysical Journal 803,1 (2015) 20- The "type IA supernova standard candles" that were used to win Nobel pries, prove the universe is accelerating expansion, due to (apparently) Einstein cosmical constant "Lambda," etc, etc... ...aren't. That is, UV observations now show there really are two classes of these candles, which erroneously were lumped into one basket -- and more seriously, one class predominates nearer to us, the other, further. Hence, all that work is now called into question and presumably needs to be entirely redone, and the probable conclusion will be that there is a lot less Lambda than they thought. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Oops. Universe not what they said.
by Warren D Smith 12 Apr '15

12 Apr '15

> From: Mike Stay <metaweta(a)gmail.com> > "What we?ve learned from this is that the amount of dark energy and > the typeof dark energy we infer from supernovae may change slightly > and in a subtle manner, and this may actually be good for bringing the > three methods???supernovae, the CMB and BAO???into better alignment. > This is one of those great moments in science where one incorrect > assumption doesn?t cause us to throw all our results and conclusions > out, but rather where it helps us more accurately understand a > phenomenon that?s puzzled us since we first discovered it." --The key word in all that jive was "may."

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[math-fun] "optimum" keyboard layouts found by simulated annealing
by Warren D Smith 12 Apr '15

12 Apr '15

http://sangaline.com/blog/optimizing_for_swype/

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