HDTenEightyP/NetNews huggingface dataset:
From: aet@mullian.ee.mu.OZ.AU (bert thompson)
Subject: Re: HELP on RSA scheme for Encryption/Decryption
Organization: Computer Science, University of Melbourne, Australia
Distribution: na
Date: Mon, 16 Nov 1992 03:47:09 GMT

jorchard@dciem.dciem.dnd.ca (Jeff Orchard) writes:

>I would like to know the algorithm for encrypting/decrypting codes
>with the RSA scheme.  I took it in first year algebra, but I sold my
>textbook and can't remember for the life of me how it went.

>Could someone out there with better resources (or better memory)
>help me?

--------------------------------------------------------------------------------

RSA in 30 seconds:

choose two big primes p q  such that p /= q
let n = p * q

also choose random e such that e < phi_n and e and phi_n are coprime 
	where
	phi_n = phi n = (p-1)*(q-1) since p and q are prime.

(phi is the euler phi function)


then encode message (a number):

m -> m^e (mod n)

decode message:

c -> c^d (mod n)
	where
	d = inverse e (mod phi_n)
	(i.e. d*e = 1 (mod phi_n))

--------------------------------------------------------------------------------

well that's the idea essentially. but you also have to write the algorithms
for finding inverses, powers, big primes etc.

	bert.

--------------------------------------------------------------------------------
bert thompson	aet@munagin.ee.mu.oz.au.
SITEE		school of information technology and electrical engineering
		university of melbourne
--------------------------------------------------------------------------------
Newsgroups: sci.math,sci.physics
From: abond@rvgs.vak12ed.edu (Andrew H. Bond)
Subject: Re: Hypercube/k-cube
Organization: Virginia's Public Education Network (Roanoke)
Date: Fri, 20 Nov 92 10:39:30 GMT

leife@ii.uib.no  writes:
> Question about Hypercubes/k-cubes.
> ---------------------------------
> 
> Can someone please help me in finding relevant
> litterature which outlines basic properties of
> the hypercube/k-cube.
> 
> (My view of a k-cube is a graph where vertices
> correspond to the binary k-tuples and the edges
> connect those vertices having a Ham. distance
> of 1)
> 
> Thanks,
> 
> 	Erik
> 
> ==========================================
> 
> 

For an entertaining look at dimensions check out _Flatland,_A
Romance_Of_Many_Dimensions_, by Edwin Abbot

BTW, I have found that Dover books (a publisher of the above),
is an excellent, low cost source (Flatland cost $2.25 new),
classic technical works, many of which are out of print and
otherwise unavailable.

	You can write for a free catalog:

	Dept. GI
	Dover Publications, Inc.
	31 East 2nd St.
	Mineola, NY 11501

No, I don't work for Dover, I am just a very satisfied
customer, and I want to see them do well for my own selfish
reasons (I want them to pub. more titles)!

Thanks for the bandwidth--AHB.
-- 
Andrew H. Bond, Roanoke Valley Graduate Center
Newsgroups: sci.math
Subject: Re: exp(pi*sqrt(x))
From: harper@kauri.vuw.ac.nz (John Harper)
Date: Tue, 24 Nov 1992 01:03:59 GMT
Organization: Victoria University of Wellington

In article <1992Nov23.001203.20604@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>In article <1992Nov22.124131.17689@husc15.harvard.edu> blom@husc15.harvard.edu writes:
>>Aitken once remarked that exp(pi*sqrt(163)) differs from an integer by
>>less than 10^-12.  Why and when does exp(pi*sqrt(x)) approximate an integer?
>
>Q(sqrt(-163)) (the field of rationals extended to complex quadratic
>field with sqrt(-163)) is a unique factorization domain ("class number
>1").  The 9 numbers that work here are 1 2 3 7 11 19 43 67 163, the
>larger ones work much better for getting good integer approximations
>this way.

According to Maple, exp(Pi*sqrt(37))=199148647.999978 correct to 15 figures.
This looks close to an integer to me even though 37 isn't in the list above.
Is there a "good" reason why it is so close?

John Harper Mathematics Dept. Victoria University Wellington New Zealand
Newsgroups: sci.math
From: roth@gauss.enet.dec.com (Jim Roth)
Subject: Re: Bounds on Quadratic Forms ?
Organization: Digital Equipment Corporation
Date: 18 NOV 92 18:35:19    


In article <1992Nov5.021547.1@cc.newcastle.edu.au>, eemn@cc.newcastle.edu.au (Brett Ninness) writes...

>I have a quadratic form f(x) = x^T A x where x is a positive 
>semidefinite matrix.  I want to know the maximum value
>that f(x) can attain subject to a norm constraint on x.
>Now I know that if the norm I choose is the 2 norm, then
>I can use the Rayleigh-Ritz theorm to bound via
>the maximum eigenvalue of A.  But I want to use the 
>infinity norm.  I know that if I bound the infinity norm
>then I have a bound on the 2 norm and again I
>can use Rayleigh-Ritz, but I want something tighter than
>this.

You could test all 2^N cases but I don't think that is too efficient :-)

This sounds like it's related to a problem in the geometry of
numbers of finding the shortest vector in a lattice, where it
can be handled by a sequence of unimodular transformations in a pretty
efficient manner.  See, for example, Knuth, Vol II, _The Art of Computer
Programming_, the secton on the spectral test for multiplicative
congruential random number generators.  Another referece is
Zasenhaus & Post _Algorithmic Algebraic Number Theory_ which has a
section on the subject.  I have a few papers at home on efficient
algorithms but don't recall the exact citations off the top of my
head.  I don't think the last word has been spoken on such algorithms,
but the ones out there are not bad.

- Jim
Newsgroups: sci.math
From: edp@math.zk3.dec.com (Eric Postpischil)
Subject: Re: comparison problem
Reply-To: edp@math.zk3.dec.com (Eric Postpischil)
Organization: Digital Equipment Corporation
Distribution: usa
Date: Wed, 18 Nov 1992 19:15:33 GMT

In article <1992Nov18.161028.11906@seas.gwu.edu>, chihy@seas.gwu.edu
(Chih-Hsun Yao) writes:

>Describe an algorithm that finds the largest and second largest integer in a
>set of (2^m) integers using at most m+(2^m)-2 comparisons.
>(Hint: Consider binary tree tournament)

Bigger hint:  Consider recursion.  Let f(k)=k+(2^k)-2 and suppose you
had a procedure that could find the largest and second largest of a set
of 2^k integers, but the procedure only worked for k < m.  Could you
make a new procedure that worked for k=m?


                                -- edp (Eric Postpischil)
                                "Always mount a scratch monkey."
                                edp@rusure.enet.dec.com
From: des@thrain.anu.edu.au (David Stewart 249-4502 room 134)
Newsgroups: sci.math
Subject: Re: Cryptography and P=NP
Date: 15 Nov 1992 22:09:46 GMT
Organization: School of Mathematical Sciences, Australian National University
Distribution: world
NNTP-Posting-Host: 150.203.15.22


If P=NP then **every** public key cryptosystem is in trouble!

(Computing the private key given the public key is in NP -- given the private key
the point is that the public key is easy to compute, but not vice-versa.)

-- 
------------------------------------------------------------------------
David Stewart			Program in Advanced Computation
des@thrain.anu.edu.au		School of Mathematical Sciences
				Australian National University
------------------------------------------------------------------------
David Stewart			Program in Advanced Computation
des@thrain.anu.edu.au		School of Mathematical Sciences
				Australian National University
Newsgroups: sci.math,sci.physics
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: RSA Encryption
Keywords: cryptography, primes
Organization: Department of Mathematics, Smogville, USA
Date: Sun, 22 Nov 92 22:42:08 GMT

In article <1992Nov22.011016.6268@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

>Apropos of which, here is my proof that P=NP.  (I came up with it
>around 1972, if you have an earlier source then it's not mine after
>all.)  Computers double in speed every 18 months or so, whence any
>exponential time problem can be solved in linear time by waiting the
>requisite number of months for the problem to become solvable in one
>month and then starting the computation.  This counts the waiting time,
>and has the additional advantage that you can use your computer on
>something else while waiting.

Very interesting.  Like Lewis Carroll's jokes, there is a real fact
lurking in this one.  *If* the world's future was predictable in
polynomial time from initial data, and *if* P was not equal to NP, one
could use the contrapositive of Pratt's joke to prove that the rate of
speed of computers cannot double each 18 months or so forever.

Of course, this assumes the world's future is deterministically
predictable, which it's not, thanks to quantum mechanics.  (Please
folks, don't mention chaos.  I'm sick of it.)  I leave it as an exercise
for the reader to ponder what corrections need to be made to my previous
paragraph to take quantum mechanics into account.
Organization: Penn State University
Date: Wed, 18 Nov 1992 14:47:23 EST
From: <REA105@psuvm.psu.edu>
Newsgroups: sci.math
Subject:    basic skills

Coming from a public high school in which everyone is required to take at least
 three years of math, I feel qualified to say that the state of math education
is America needs help.  I know people that graduated from high school not havin
g even had a class of geometry.  Granted I do not like the idea of teachers tea
ching to national standards, but something has got to be done and soon.
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math
Subject: Re: Office Hours
Date: 21 Nov 92 22:21:35 GMT
Distribution: sci
Organization: M.I.T. Artificial Intelligence Lab.

Emma Gottesman suggests that I post my notice to the undergraduates also.
Actually, my notice was addressed to "Everyone, regardless of their status,
who is interested in learning new mathematics". In addition to putting
copies in all faculty and grad student mailboxes, I also posted it on 
various bulletin boards in the math department.

One person who apparently is not a student stopped by and said he wanted to
read Goedel's proof, which I agreed to do, but he never came back. Another
one, who is a sophomore, stopped by a few days ago and expressed interest
in mathematical logic, linguistics, languages such as ancient Greek
(and reading math in it) and Sanskrit, and philosophy. That suited me 
fine and I'm looking forward to seeing how it goes. Of course, I am hoping
for people to talk to about the other topics as well.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math
From: steve@hubcap.clemson.edu ("Steve" Stevenson)
Subject: Re: 1+1/2+1/3+1/4+...+1/n
Organization: Clemson University
Date: Thu, 19 Nov 1992 19:23:21 GMT

gay@selkirk.sfu.ca (Ian D. Gay) writes:

>>I've a problem. I have to calculate the sum 1+1/2+1/3+1/4+...+1/n.

>Everybody's computer is too slow!

>1 = 1
>1/2 + 1/3 < 1
>1/4 + 1/5 + 1/6 + 1/7 < 1
>etc.
>You will need to sum at least 100 such lines, and the 100th line
>has 2^99 terms!

Hm. See earlier comments by others on using Maple. Seems that they
got it without waiting forever. :-)







-- 
===============================================================================
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906
Newsgroups: sci.math
From: nissim@mary.fordham.edu (Leonard J. Nissim)
Subject: Re: help me take a derivative of this complex function
Organization: Fordham University
Date: Tue, 17 Nov 1992 18:12:00 GMT
News-Software: VAX/VMS VNEWS 1.41    
Distribution: usa
X-Posted-From: mary.fordham.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

In article <1992Nov17.124151.17533@husc3.harvard.edu>, 
mlevin@husc8.harvard.edu (Michael Levin) writes...
> 
>    I have a set of functions in complex variables that I need to take
>a derivative of, for a fractals project I am going to do. I've looked
>up everything in a book, except one thing. All the other functions
>(comon arithmetic, powers, etc.) are "derived" like real functions,
>but I can't find this one anywhere.  Here it is:
>f(c) for a complex c, is equal to c', where the real part of c' is
>equal to the imaginary part of c, and vice versa. In other words, f()
>simply switches the real and imaginary parts of the variable it's
>applied to. so, what would be f'()? If anyone has any clues, please
>send email to mlevin@husc8.harvard.edu. Thanks in advance.
>BTW, I am a biology, not math, major, so take it easy if this involves
>very complex stuff (or if it is a stupid question...).
> 
>Mike Levin

Since the function f(z) = u(x,y) + iv(x,y)   (where z=x+iy)
does NOT satisfy the second Cauchy-Riemann equation, it is not differentiable 
(as a complex function).  So f'(z) does not exist.  

(First C-R equation:  du/dx = dv/dy (sorry, no partial deriv. on the keyboard) 
 Second C-R equation: du/dy = -(dv/dx)  )
 For f() as described above, we have f(x+iy) = y + ix.  
So, u=y and v=x; the first equation becomes 0=0, but the second becomes 1=-1.
See the definition of f'(z) for complex functions in any complex analysis text.
-------------------------------------------------------------------------------
Leonard J. Nissim  (nissim@mary.fordham.edu)   
Disclaimer:  "I speak only for myself."
-------------------------------------------------------------------------------

Xref: sparky sci.math:15036 sci.physics:18955 sci.astro:12043 sci.bio:4141 sci.chem:4611 misc.education:4333
From: hdev@dutiaj.tudelft.nl (Hans de Vreught)
Newsgroups: sci.math,sci.physics,sci.astro,sci.bio,sci.chem,misc.education
Subject: Re: Is Math Hard?
Date: 16 Nov 92 08:46:13 GMT
Followup-To: sci.math

mccolm@darwin.math.usf.edu. (Gregory McColm) writes:
>One thing not being mentioned:  American teachers have been 
>underpayed for a VERY LONG time.

>Well, women's lib put an end to all that.  Bright women don't 
>have to work for peanuts any more.  But local gov't refuses 
>to adjust to a more European pay scale (and professional 
>standards), and the result is a muddled mixture of desperate 
>idealists, burnouts, incompetents, and survivors.  A perfect 
>system with a perfect curriculum is doomed to fail until 
>we improve the profession.

What are the wages generally encountered at the US education system?
I can give you the Dutch equivalents. Over here a year salary consist of 12
moth salaries + 8% holiday allowance. Furthermore I will assume $1 = f1.75
(which is almost correct +/- one or two cents). I'm not 100% sure about the
salary scales of Nursery and First level education (but I believe they are
right).

Nursery education (below kindergarten)   $24861 - $38576
First level education                    $24861 - $42924
Second level education (high school)     $26150 - $57424
Assistent professor                      $26150 - $57424
Associate professor                      $50944 - $62489
Full professor                           $53588 - $100614

These numbers might look much higher than in the States but over in Europe
social security and income tax are way over what is normal in the States. But
that is of course completely indepemdent of the education profession. Over
here in Europe teaching is also an underpaid profession.
--
Hans de Vreught                          | John von Neumann:
hdev@dutiba.twi.tudelft.nl               | Young man, in mathematics
Delft University of Technology (TWI-ThI) | you don't understand things,
The Netherlands                          | you just get used to them.
From: n9146070@waldorf.cc.wwu.edu (Jacob C Kesinger)
Newsgroups: sci.math
Subject: Square root
Date: 18 Nov 92 03:13:03 GMT
Article-I.D.: waldorf.n9146070.722056383
Organization: Western Washington University

There was a previous post about ways to find the square root of a number...

Here's my contribution:

Find the Taylor series about a (I used a=1, for simplicity)

(x-1)^.5=1+ (x-1)/2- (x-1)^2/4 +3(x-1)^3/8 -......

This is nasty, messy, ugly, and very likely wrong.  However, it IS
a method (*grin*)

Jake Kesinger
n9146070@henson.cc.wwu.edu
Newsgroups: sci.math
From: Jim.Buddenhagen@launchpad.unc.edu (Jim Buddenhagen)
Subject: dodecahedron in S3
Organization: University of North Carolina Extended Bulletin Board Service
Date: Tue, 17 Nov 1992 20:42:58 GMT

Given a (regular pentagonal faced) dodecahedron of edge  e  living in
a 3-sphere of radius  r  , how does one compute the dihedral angle in
terms of s = e/r ?
--
   The opinions expressed are not necessarily those of the University of
     North Carolina at Chapel Hill, the Campus Office for Information
        Technology, or the Experimental Bulletin Board Service.
           internet:  laUNChpad.unc.edu or 152.2.22.80
Newsgroups: sci.math
From: news@massey.ac.nz (USENET News System)
Subject: Re: Arch algorithm
Organization: Massey University
Date: Mon, 16 Nov 92 21:07:19 GMT

In article <1992Nov16.045332.15669@infodev.cam.ac.uk>, gjm11@cus.cam.ac.uk (G.J. McCaughan) writes:
> 
> In article <1992Nov15.023738.29429@osuunx.ucc.okstate.edu>, gcouger@olesun.okstate.edu (Gordon Couger) writes:
> 
> > I doing some design work of hyper parabolic (saddle shaped) structures 
> > it occurred to me that cantary (absolutely unsure of the spelling) arch, .
> > if a chain is hung by its ends it forms the arch I am interested in, would
> > give much better use of the floor space near the walls. 
> > 
I tried e-mail but it bounced.

Others have already said what a catenary is etc. but haven't mentioned the
structural considerations. A catenary has the property that, for an arch of
uniform weight per unit length, the stress will be purely compression. From
a structural point of view, then, this is the appropriate structure for a self
supporting arch. If you want to support a horizontal load, then you need a
different shape (a parabola if the arch is light compared to the supported
load).

Of course, the structure with maximal strength to weight ratio will have
tapering arches and will not be a catenary. My calculus of variations is a
bit rusty so I won't try to solve this :-)

Terry Moore
Newsgroups: sci.math,misc.education
From: sonix@schunix.uucp (Duane Morin)
Newsgroups: sci.math
Subject: Overlapping area under a spiral?
Date: 19 Nov 92 20:05:52 GMT
Organization: SCHUNIX Public Access Unix for Worcester County, Massachusetts, USA

Question:  A current project involves scanning a particular image area with 
a transducer in a spiralled pattern.  We need to cover a known area size with
our scan.  Can someone help us with the math for calculating the area under
a spiral?  

Our problem lies in the overlap.  the transducer face is 3/8" (sorry for 
the english units) radius.  Roughly, the area that we want it's center to
travel is 1/8".  Along the spiral that we draw we will select 9 points 
in a 3x3 grid, meaning that there will be overlap at each reading of some
of the area from the reading at a different point.  What we need to know
is the total area that will be covered by the scan, constrained to a few
variables that we can fiddle with.

What we're working with:

	R = E + p0 <-- best theta I can manage
	  where E is eccentricity (distance from origin at start)
		p is pitch (change in R for every degree 0)

	x = (E+p0)cos0       y = (E+p0)sin0

Where do we go from here?  I'm sorry if this sounds like a real minor-league
question, but sometimes the wisdom of the net is alot quicker than digging
through the old calculus books.  Besides, the chief engineer is working on 
it and I'd love to beat him to the answer. :)

Email responses preferred, to keep the traffic out of this group.  

Thanks for any help you can give,
 Duane Morin
 Software Development Manager
 Walker Sonix, Inc.
 Worcester, MA 01604
Newsgroups: sci.math
From: frisch1@athena.mit.edu (Jonathan Katz)
Subject: closed forms
Organization: Massachusetts Institute of Technology
Date: Sun, 22 Nov 1992 20:15:55 GMT

>Another question that could belong here: How does one proof that there is
>no closed form expression of \int(exp(-x**2))? 
>Peter

Good question...I hope someone will post this.
Otherwise, please send me an email about it, too!
Thnaks

---
Jonathan
Newsgroups: sci.math,sci.physics
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Three-sided coin
Date: Mon, 16 Nov 1992 21:17:35 GMT
Organization: Security APL, Inc.

In article <jim.721702281@st-michael> jim@cs.UAlberta.CA (Jim Easton) writes:
>Given that it is possible to bounce from one state to another it
>is more probable to bounce out of a high energy state to a lower
>energy state than it is the reverse.  I claim that the lowest energy
>state is the most probable and therefore conclude that the three states
>should be equal in energy.
>
>That implies that the thickness is equal to the diameter.

To combine two ideas mentioned in this thread, I would believe that, *if* the
energy states are equal, then (under a reasonable set of assumptions -- "soft
landing" is *not* a reasonable assumption), the probability of a particular
side is proportional to the surface area.

I doubt very much that you can create a coin which lands on either side or
the edge with equal probability regardless of the height it is "dropped"
from, or of its angular momentum.
Newsgroups: sci.math
From: palais@binah.cc.brandeis.edu
Subject:  Re: Covariant & Lie Derivative
Reply-To: palais@binah.cc.brandeis.edu
Organization: Brandeis University
Date: Tue, 17 Nov 1992 18:52:37 GMT

I posted this message a little while ago, in response to message 
15638 from phfrom@nyx.uni-konstanz.de (Hartmut Frommert), but a
transmission problem completely garbled it and I'm trying again. 
-----
> rscott@libws3.ic.sunysb.edu (Robert Scott) writes:

>>ISN'T IT EASY TO SHOW THAT THE LIE ALGEBRA OF SYMMETRIES OF AN
>>AFFINE CONNECTION ON A CONNECTED FINITE-DIMENSIONAL MANIFOLD IS
>>FINITE-DIMENSIONAL?  THUS THE LIE ALGEBRA OF INFINITESIMAL
>>SYMPLECTOMORPHISMS OF A SYMPLECTIC MANIFOLD IS FAR TOO BIG TO
>>PRESERVE AN AFFINE CONNECTION.

>You confuse me a bit :)

>If I understand right, the covariant derivative must only preserve the
>symplectic metric j with components

>  j_{ab} = j_{[ab]} = - j_{ba} ,

>not the set of all symplectic transformations, to obtain a metricity
>condition analogous to the Riemannian: There the Levi-Civita connection 
>only leaves (pseudo)-orthogonal g invariant, not all elements of the
>Lorentz group. The symplectic metricity condition reads explicitely

Newsgroups: sci.math
From: greg@athena.cs.uga.edu (Greg Whitlock)
Subject: faq?
Organization: University of Georgia, Athens
Date: Mon, 16 Nov 1992 22:49:20 GMT

I'm been watching this group for a few weeks and haven't seen a
faq.  Is there one?  If so, can someone forward me the most 
recent edition?

thanks

-greg
From: kinnersley@kuhub.cc.ukans.edu (Bill Kinnersley)
Newsgroups: sci.math
Subject: Counting Families of Subsets
Date: 15 Nov 92 21:29:50 GMT
Article-I.D.: kuhub.1992Nov15.152951.44802
Organization: University of Kansas Academic Computing Services

Take a base set S with N elements.  There are 2^N subsets of S.
I want to consider families of these subsets.  All together there
are 2^{2^N} such families, but I want to impose a condition.

Let F be a family such that all elements of F are distinct subsets,
and no element of F is a subset of another.

How many families like this are there, for given N?

If you call the number K(N), then the first few values are:

N        K

0        1
1        2
2        5
3       19
4      167

Can you tell me even the order of magnitude for K(N)?  It appears to be
much less than 2^{2^N}.

-- 
--Bill Kinnersley
Newsgroups: sci.math
From: dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott)
Subject: Geometrical parking problem.
Organization: Electrical and Electronic Eng., University of Adelaide
Date: Tue, 17 Nov 1992 22:58:21 GMT



A car of length L reverses into a parking space without touching the kerb.

Has anyone calculated the minimum theoretical length of the parking space?