Posted on 3 September 1998

The following text was written by S.T.L.:

Well, it's late at night (yet again) and I'm in the mood for a good rant. Well, this article explores one particular idea, but it's also about a general issue. And somehow, I get to another particular idea after the middle. Ah well. I initally had a long 2-line name, but I suppose "Calc Crypto" is acceptable for "Calculator Encryption".

Quite a while ago, I started to become fascinated with Number Theory (primes and such) and I had a TI-85. Obviously in class, when I had all my work done, I fiddled around with it. I made primality proving programs and all sorts of stuff. But the TI-85 was pretty limited because much of Number Theory involves really huge numbers.

Anyways, that meant that if I *wanted* to do anything remotely nifty, I had to whittle it down into a smaller version so my TI-85 could run the thing. Thus, after reading one of my books, I had an idea. It basically goes back to something that a lot of my classmates do, but I hardly ever: passing notes.

Now, I'm not one to advocate passing notes. But, I know enough to know some features of them:

• A passed note has to be done in relative secrecy. After all, the teacher certainly can't know what's in the note, eh?
• A passed note has to be done quickly. This is more of a side-effect of writing them on paper, because if it is passed slowly, then anyone can open it up and read it. You *could* give it to Al, "Hey Al, give this to Bob in your next class, cause I don't have him in any of my classes" but then you have to trust Al.
• A passed note doesn't contain that much information, but it can contain a fair amount, up to a written pages' worth.

This got me thinking. What if industrial-strength encryption was provided on TI calculators? Now, I'm not talking about cheesy, "I dreamed this up last night" encryption, because every programmer seems to fancy himself a cryptographer. I'm talking about an encryption algorithm that is used in commercial software, and has no easy way to break it. (Yes, it's related to Number Theory.) This could solve problems of classroom communication. (And yes, it could be used elsewhere.) But first, an interlude.

Words used here:

• Encryption: Scrambling a message so no one can read it, without a Secret Key.
• Decryption: Descrambling said message with the Secret Key.
• Public Key Encryption: Most encryption involves two people sharing one secret key. The stuff I'm thinking of allows one person to give everyone their Public Key, which allows messages to be SENT to them, but only their Secret Key would let them read it.
• Compression: Making a message take up less space.

And we're back.... Now, what would public-key encryption do for note passing? First of all:

• Forget secrecy. You can scrawl the note on the blackboard, and the teacher won't be able to read it, without intercepting your TI. (Solution: decrypt the message in another class, or get a locking program.)
• Forget timeliness. You can (w/o scrawling the note on the blackboard) write it down on a sheet of paper, and get your classmates to give it to someone - but you could let them do it next class. Then you don't have to trust them not to read it.

Of course, all these things would be hard unless the program could compress messages. With the ideas I currently have, public keys would be a string of 64 characters, and messages 64 or 128. This is because I know a way for extremely simple Special Purpose Compression, it would really only work for the Calculator Encryption project.

And, importantly, all someone would have to do is give out their Public Key to everyone who has the encryption program. Their Secret Key remains on their calculator, their Public Key goes everywhere. (Public encrypts messages, Secret decrypts messages.)

Well, I've done this for the TI-85 already. Problem was, it used really, really cheesy 8-bit encryption. I can crack that in my head. But with the TI-92, I could program 384-bit encryption. That's the low end of commercial PC software, and the best part is: while it's not immune to the government, or even to a large corporation, it will defeat most anyone a high schooler fears. (Though a large, well-funded university could be amused for a month trying to break it.) I've already got plans as to how to actually implement this thing, too.

My question to everyone, is this concept of Calculator Encryption USEFUL or WORTHLESS? I've only thought of one application for this, but it probably has more. And there are more questions along with this: exactly what SORT of programs would be useful on a TI calculator? For example:

• I got this idea for Calculator Encryption off of the PC program PGP.
• The TI-92 Text Editor is basically a PC's NOTEPAD.EXE.
• Spreadsheets?
• Games? (Well, I know the answer to this one, but I had to mention it, else everyone would tell me I forgot it.)
• General Purpose Compressors? (Very, VERY hard to implement, I would guess, but possible.)
• Other programs?

Actually, the idea of the General Purpose Compressor is VERY interesting. Probably more interesting than Calculator Encryption. *ahem* I think I want to talk about that for a little while. Well, I've gone from a particular idea, to a general idea, back to a particular idea that will turn out to be pretty general. Hehehe. Anyways...

If one had (let's use an abbreviation) a GPC, what TI calculators could it run on? Of course, the TI-92+, the TI-92, and the TI-89. (After all, if it won't run on them, where WOULD a GPC run?) Most likely I could see a TI-86 or TI-85 assembly program running it. Putting a GPC on a TI-83 or TI-82 is doubtful, but maybe a programmer would find a way. Ironically, the more lower-end the calculator, the nifiter a GPC would be. A General Purpose Compressor would crunch programs/data into a smaller space, thus (in effect) giving you more memory, at the cost of not being able to use the compressed program until uncompression. Sort of like the TI-92+ data archive.

Now, I envision a BRIGHT future for a GPC. Imagine being able to store twice the amount of data your calculator should hold (it would probably be closer to 1.5x, but let's stick with 2x). For a TI-85, that's about 40K (or is it 50? I don't remember). For a TI-92, that would be 120K. For a TI-92+, it could store an absolutely amazing 1MB of data! (Though still, no single uncompressed program/data could be more than 180K. Ah, I'll live with it.)

In fact, games (arrrgh! Ah well, I suppose I have to explore what a GPC means to them too) could have a large compressed bundle of levels included with them. When one level is needed, it could be uncompressed, used, then recompressed to make room for the next level. Thus you could create truly massive games with 2x the amount of levels you'd have without a GPC.

And I bet there's all SORTS of nifty applications for a General Purpose Compressor. Though it's 3 in the morning, and I can barely think coherent thoughts. *ahem* I, for one, would love to craft a GPC, though I don't have the assembly skills to do so. Probably it'd be a project close to making a shell.

Right now, the Special Purpose Compressor I have in mind doesn't really compress at all. All it does is transform integers into strings. What it does it convert an integer into base 2. Then it converts the base 2 to base 64. This of course saves space, and makes a 384-bit integer into a 64-character string. This is because the binary expression "110010011011" can be represented as the hexadecimal (base 16) expression "C9B". I think. I'm rusty on my Bin-Hex translating skills. But a General Purpose Compressor could work on real numbers, strings themselves, lists, matrices, and programs.

What's odd is that a list on the TI-92 seems to take up less space than the identical list on the TI-85. Hmmmm. I do't have time to explore this further. (The reason follows). Perhaps it uses some sort of compression already.

Ah, a quick note: I've been writing articles with a very short amount of time between them, but I'll slow down - I go back to school soon. And it does take me a while to become obsessed enough about something to write a good article. :-D

Well, thank you for sticking with me through this long rant. I have enough of my thoughts, what I'd appreciate are YOUR thoughts! Let's see....

• Would Calculator Encryption be a useful, or worthless idea?
• Where else could Calculator Encryption be used?
• What other programs would be useful or worthless?
• Would the General Purpose Compressor be useful or worthless?
• What could the General Purpose Compressor be used in?
• Anything else?