[Edu-sig] RSA pre college?

Kevin Driscoll driscollkevin at gmail.com
Fri Sep 29 21:38:47 CEST 2006

I love teaching modulo!  There are countless ways to create
exploratory learning opportunities in which students discover the need
for modulo.  And once a student starts programming, modulo really
starts to feel like the lost operator.

This is a situation in which programming yields a new perspective on
mathematics.  In the same way that we learn the inadequacy of doubles
for representing non-terminating decimal values, the modulo gives new
depth to the usefulness of division.

Most students in the US remember doing division with a remainder ("R =
").  I've employed their nostalgia and sense of mastery over this
procedure to help them step into modulo.


On 9/29/06, kirby urner <kirby.urner at gmail.com> wrote:
> I've been brainstorming with other math teachers on the relevance of
> the Python modulo operator, a primitive right down there with + * /
> and -, but which doesn't get a lot of focus in traditional K-12
> textbooks these days.  Why not?
> The old answer was:  Modulo Arithmetic belongs to something called
> Number Theory, which although a have for math purists, has precious
> little to do with the real world, and so we should focus on basic
> arithmetic (the "big four" operations) and leave the modulo stuff for
> college (and even then, only if they choose to become math majors).
> The old answer is full of holes of course.  We have Modulo Arithmetic
> devices all over the place in every day life.  Clocks, for example.
> Indeed, the individual columns of our positional notation, are simply
> Modulo Stacks with carry (hit the Modulus, pop the stack, carry 1,
> restore 0).  Furthermore, we now have RSA running in just about every
> web client, ready to frame your secure session with a web server
> authorized to accept your Visa charge (what out for phishing!).
> I think the new answer is closer to the mark:  there's no excuse for
> avoiding Modulo Arithmetic, and if your school does so, that's a sure
> sign of mediocrity and you might want to pass that back to your
> parents ("mom, our math teacher said we we won't study Modulo Anything
> this year, but Bugs Bunny said it's important" (or was it Mighty
> Mouse?)).
> So once your school buys onto this bandwagon, maybe your teacher will
> deign to project a good shell.  Python's is excellent, but not the
> only game in town.  J's is wildly powerful by design (hyperdimensional
> arrays a favorite breakfast food), worth poking around in.
> Then there's GameMaker.
> Nothing wrong with playing in a Game Engine, though I think Gerald's
> Darwin @ Home is more impressive:  he rolls his own, using the most
> minimalist Physics Rules, and starting with the earliest Java AWT,
> then moving to JOGL.  Any EIG VPython killer app has yet to be
> started, let alone offered in beta AFAIK.  Please update me if I'm
> wrong about that.
> For more on Darwin @ Home, watch Gerald's excellent Google Video,
> hosted in the left margin of Myspace.com/4Dstudios.
> In sum, I think RSA *will* be making inroads as a curriculum standard
> in many good schools, right up there with "differentiation by parts"
> as a relevant algorithm to know about.  And one of the benefits is
> cryptography opens History, both fictionally and nonfictionally.  Neal
> Stephenson has trailblazed extensively in this direction.
> One thread:  RSA was stumbled upon in slightly different form by some
> British cryptologists, but classified immediately as "too dangerous"
> for the general public.
> MIT, with the push of needing a business class solution to an emerging
> real world challenge (i.e. the need to encrypt on the fly, based on
> any two parties making random contact through the Internet), had no
> incentive to classify (quite the reverse).
> Plus when the cyberpunks discovered the NSA was offering resistence
> (in part because of the British example -- her dutiful civil servants
> inspire respect in many corners), the lid simply blew off, with PGP
> coming out of New Zealand and paranoid geeks teaching their own
> mothers how to generate public keys (better protection than tin foil).
> Given this turgid history, it's somewhat understandable why high
> schools might choose to stay in the bleechers, leaving RSA to the big
> boyz 'n girlz to kick around.  But that's not an optimum way to leave
> it, especially now that the patent has run out, and rolling one's own
> is not in violation of anyone's legal rights.  At Saturday Academy, I
> like projecting that website where you're promised big Reward Money,
> if you're able to crack some of their Modulo Ns (i.e. public keys)
> into two constituent Probable Primes (an even bigger reward if p
> and/or q turn out Improbably Composite?).
> "Python:  It's Not Just for War Colleges Anymore" -- probably won't
> fly as a bumper sticker, but I do find it funny (it alludes to its
> dark DARPA past).  Put a goofy little snake with rolling eyes in the
> corner, with this funny Revolutionary War hat, a Blunderbuss in its
> coils.  Reminds of Don't Tread on Me.
> Kirby
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