[Edu-sig] RSA pre college?

kirby urner kirby.urner at gmail.com
Fri Sep 29 20:34:46 CEST 2006

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

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.


More information about the Edu-sig mailing list