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Cryptology Research for High School Student?
John3 asks: "My daughter is enrolled in an Advanced Science Research (ASR) course, at the local high school. The students join the program in 10th grade, choose a research topic, and then locate a mentor to work with them on their topic until high school graduation. My daughter took a cryptology course this past summer, and now she has chosen cryptology for her ASR topic. Most HS students pick mainstream research fields (medicine, genetics), so her science teacher is a bit unsure of where my daughter might locate a cryptology research project appropriate for advanced high school students (especially one that doesn't require security clearance). I'm hoping my fellow Slashdot readers might know of current cryptology/cryptography research projects that offered opportunities for a high school student to participate."
Not exactly on topic of finding a mentor, but this request reminded me of my early Computer Science studies when my friends and I took turns coming up with encrypted strings, posted them on a newsgroup we frequented, and made it into a competition as to who could decrypt it first.
We started with simple stuff like letter substitution, ROT13, etcetera. And then moved on to masking and all sorts of fun/complicated algorithms. This was very educational, in the sense of learning about cryptography. We learned interesting concepts, and rapidly developed tools/scripts/methods for attempt to decrypt arbitrary strings.
Much fun.
- shazow
Why not have them replicate some existing work? That's usually a good way for folks to get a feel for what's going on. Since the MD5 collision source code got published recently, why not have them try to replicate that?
2 cents,
Queen B
HDGary secures my bank
It is extremely hard to suggest anything here unfortunately. Most mathematical research in this area requires a very strong background, and students generally just don't have the experience. The best thing you can do is point her at relatively new areas. Along those lines, I suggest quantum computing. Very few people "get" quantum computing right now, and its relatively easy to get started. From the description of the other course I gather she can program in some sort of language. Get her to simulate quantum computations on a regular computer - use a high level programming language. Then you can start investigating quantum algorithms. Start with simple algorithms like searching and sorting, and build up to quantum algorithms like Shor's algorithm for factoring integers. For the research component, have her try to devise a quantum algorithm for some sort of problem. Relatively few people have looked at this, so the field is wide open.
In Soviet America the banks rob you!
There are plenty of jobs our there that deal with encryption that don't require a security clearence, or much math. Heck, Adobe was using ROT13 for parts of their drm in 2002...
.gov and .edu institutions that have hundreds of man-years of math research to build from.
The point is, lots of companies now use encryption in their products, and there is lots of interesting research to be examined about how products are using encryption (lots of products do it pretty bad, but a few do it really well). Go find a drm product, or vpn product, or any wifi developer and they will be doing something with crypto. Look at the work by the girl who optimized DES (? irrc, might have been aes) as her high school project.
That being said, if you think you've got a new encryption algorithm at that age, you will probably see it as an example problem in your crypto classes later on in life. Leave new algorithm to the
Sera
Slashdot, where armchair scientists get shouted down and armchair theologians get modded up.
CPRM might be a bit advanced for high school, but a practical break is an undergraduate homework assignment. (Hint: Assume you have known plaintest for the encrypted media key. How many trial encryptions do you have to do before finding a player key?)
Note that this is a PROTOCOL, not a CIPHER. You can build a flimsy building out of indestructible bricks, and people do it all the time.
In general, the best possible exercise is breaking something, even if it's a bit of a straw man. Implement a discrete log solution (given g, p, and y = g^x mod p, find x) for composite p with known factors less that some convenient limit like 2^32. Or show how to recover a DSA secret key given two different signatures with the same k (and thus r).
Cryptography in its modern form certainly has areas an exceptional high school student could explore, but I suspect most students would be daunted or bored by most work in it.
However there's lots of exciting forms of information leakage exploits that a high school student with a modicum of math & computer background could explore, especially if they spent a little while studying an introductory machine learning or information theory textbook. For example:
1. crack passwords by listening to keyboard sounds
2. determine what a computer user is doing by watching their mouse
hand, the light shining on the back wall of their office,
their keyboard motion, or their facial expressions
3. write a password search routine that is informed by all unencrypted
information on their computer drive, public information about them
found on the internet, etc
4. predict whether a corporation is going to announce a major transaction
by looking at public information about their executives travel behavior
5. use videos of poker player's faces to predict the strength of their hand
These kinds of projects have almost infinite freedom and room for a clever or creative student to do something truly new. The techniques used are different than the basic methods of mainstream cryptographic, but certainly related.