[cryptography] teaching crypto to 7th-12th graders

Alfonso De Gregorio adg at crypto.lo.gy
Wed Nov 10 05:04:43 EST 2010


On 09/11/2010 23:00, travis+ml-rbcryptography at subspacefield.org wrote:
> Originally sent to cryptography at metzdowd but never got approved, le sigh.
>
> Gonna teach a class on classical crypto to 7-12th graders this weekend.
> Need to come up with filler - preferably not lecture style - to pad
> out the talk by 50 minutes.

This is going to be a rewarding experience for both teachers and students!

> Was trying to come up with some cute demos, or ways to explain some
> of the more advanced concepts.
>
> Ex:
>
> Talk about tearing a dollar bill in half for spies to recognize each other
> this is very similar to public key crypto; the public key and private key
> are a pair, but not identical.
> It is not, however, a zero-knowledge proof; by showing your half, an adversary
> learns something (what your half looks like). If he took a quick picture, or
> it was covertly filmed, he could impersonate either you or the other person
> later.
>
> ZKP examples abound:
>
> http://en.wikipedia.org/wiki/Zero-knowledge_proof#Abstract_example
>
> Another ZKP example (kinda) involves having a person prove they can
> distinguish red from green.  Also one can ask whether a video of this
> demonstration constitues proof that the prover is not, in fact,
> red-green color blind.  Two pieces of colored paper are a simple prop
> to acquire. :-)
>
> Also, Stinson's visual crypto seems like a great way to teach secret sharing:
> http://www.cacr.math.uwaterloo.ca/~dstinson/visual.html
> It seems like passing around transparencies with those images would be
> a fun thing to break up the lecture format.
>
> Other suggestions are:
> http://csunplugged.org/
> http://www.wisdom.weizmann.ac.il/~naor/puzzler.html
>
> Any others?

'How to Explain Zero-Knowledge Protocols to Your Children' (or the 
Strange Cave of Ali Baba) by Quisquater's and Guillou's families in 
collaboration with Tom Berson is certainly a classic 
http://sparrow.ece.cmu.edu/group/630-f08/readings/ZK-IntroPaper.pdf

Also a classic the Naor's work with Yael Naor and Omer Reingold: 
'Applied Kid Cryptography or How To Convince Your Children You are Not 
Cheating'http://www.wisdom.weizmann.ac.il/~naor/PAPERS/waldo.ps

Stinson's visual crypto would be a great way indeed, and perhaps the 
Moiré Cryptography by Desmedt (CCS 2000) has the promise to make passing 
around transparencies even more fascinating by letting the shares do not 
look random.

In 1997, Kobliz published an article in Cryptologia titled 'Cryptography 
as a Teaching Tool'. His paper contains examples of 'Kid Krypto' (first 
introduced by him with Fellows and Brickell at Crypto '92) that he 
recommends for mid and primary grades. His examples goes from Caesar and 
Vigenère ciphers, to an information hiding protocol for teachers, to 
(going more advanced) Kid-RSA and a perfect code public key system. **A 
shortened version is available 
athttp://www.math.washington.edu/~koblitz/crlogia.html 
<http://www.math.washington.edu/%7Ekoblitz/crlogia.html>

Furthermore, I believe the illustrative example of the Dining 
Cryptographers Problem 
http://en.wikipedia.org/wiki/Dining_cryptographers_problem provided by 
Chaum in the very first number of JoC 
(http://www.cs.cornell.edu/People/egs/herbivore/dcnets.html) can be 
successfully used with 7th-12th graders to introduce advanced concepts 
like secure multi-party computation.

Students could gather around the table for dinner experiment. The 
teacher would play as the waiter and guide them through the protocol 
steps. The material required would be minimal: a coin to flip (or a dice 
to roll) and knowledge of exclusive disjunction (or the XOR truth 
table). Of course, the dining cryptographer problem can be instrumental 
also for talking about attacks at cryptographic protocols. For example, 
the last table-companion can be challenged to discover what happens if 
she tries to manipulate the final result. Protocol complexity could be 
exemplified by increasing the number of fellow guest and noticing how 
painfully slow they find out if the NSA is paying their dinner.

Possibly also of interest: Quisquater has renewed his initiative during 
the Crypto 2009 rump session announcing the HiDalgocrypt project, 'How 
to explain algorithms and cryptography to your (old) children II' 
http://rump2009.cr.yp.to/b48d0defdbc661178002c009b0a05114.pdf

Happy teaching,

-- 
   Alfonso De Gregorio,   blog http://plaintext.crypto.lo.gy

   "The real voyage of discovery consists not in seeking new landscapes but in having new eyes.",   Marcel Proust




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