Calc Crypto and the GPC
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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?
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Re: Article: "Calc Crypto and the GPC"
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ffolkes
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Matt Reed-
I have see similar things done about notes. One time my teacher saw some girls in my class passing notes. He stopped them, took the note, read it to the class, recorded it on a tape reocrder, gave the note back to the girls, called the principal in, and played the tape to him. Just to embarass the girls. It took the whole class time for this. I have seen other things done. Many teachers use embarassment as a means of punishment....and many will go to EXTREAMES to embarass the "note passers."
(Did I spell extreams right?)
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4 September 1998, 08:53 GMT
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Re: Article: "Calc Crypto and the GPC"
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Master Nick
(Web Page)
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I think both the encryption and the compressor would be very useful. As for using it for note passing, this would be really cool! I don't pass notes myself, but I would start just to use the encryption. What I do to pass notes electronically on the calc is save the message on the E2 and give it to someone to give to my friend recieving it. Since everyone in my school has 85s, this is a big problem for intercepting messages. I pretty much solved my problem with my encryption program(uses the most advanced algorithm I have seen for the calc). As of yet, no one has been able to crack it. This was written in basic so just imagine the potential of an ASM version! I also think the compressor is very useful too. I also wrote one of the above types(convert to string) but it didn't work out(my calc crashed and I didn't feel like redoing it). I think it would be easy to do. Just port some compressor for the Z80 from the '80s to Usgard or something. I'm shure by now that source code should be available.
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4 September 1998, 12:57 GMT
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Re: Re: Re: Re: Article: "Calc Crypto and the GPC"
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S.T.L.
(Web Page)
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You see, I frequent the USENET newsgroup sci.crypt, and I've learned a few things. First of all, cryptology is a very mathematical business, and also very difficult. Second of all, there is a LONG history of average joe's algorithms being used in commercial products, and then cracked wide open. The only algorithms that withstand the test of time are those made by experienced cryptanalysts, and even then, most of them get cracked. I'd like to see if any average joe's algorithm could resist linear or differential cryptanalysis, known-plaintext attacks, etc. There are SURPRISINGLY few encryption algorithms that are still good today. I, for the life of me, cannot think of even ONE of them that was designed by an average joe.
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6 September 1998, 23:05 GMT
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Re: Article: "Calc Crypto and the GPC"
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Ben Fuhrman
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This could potentially be the best damned thing to happen to a calc. The possibility of increasing your mem from 1.5x to 2x is astounding and should be implemented ASAP. But what would be even better would be a password program that uses 384 bit encryption. Imagine a program that if the wrong password is entered, would encrypt every damned thing on your calc, so that the only thing you could do is turn it off, and then back on again, to get the password prompt. This would be extremely usefull for those of us who are sick of not being able to use a Ti-92 in school because of the mob of idiots who want to play games, and will grab the calc out of your backpack to do so. Also, compression would be extremely useful for those of us who like to read in class, yet hate to carry huge books (like The Wheel of Time), imagine reading a full sized book on your calc in math when your (idiot?) teacher thinks your doing a math problem. Aside from these few thoughts I have to offer, the possibilities are endless...
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4 September 1998, 16:32 GMT
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Re: Re: Article: "Calc Crypto and the GPC"
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S.T.L.
(Web Page)
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I completely agree with you. Though my school is a tad more sane than yours, apparently. I, frankly, have neither the skills nor the time to make a GPC. Though it is a damned good idea. I do have the skills and time to make calculator encryption. With a new modification I realized while reading these boards, anything could potentially be encrypted with an 8-character password. Thus no one without your secret key on your calc would have access to the encrypted stuff, and even with the calc, they must brute-force the 8-character password.
The book "FlatLand" has no copyright on it any more, it is over 100 years old. I have a copy of it on my computer. When I get the time, I will break it into 40K chunks and make them into TI-92 Text Editor files, probably 5 or 6 in total. This way, a normal TI-92er could read 1 part a day (load a new one from your computer the next day) and a TI-92+er coould read the whole darn thing. :-D
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5 September 1998, 01:07 GMT
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Re: Article: "Calc Crypto and the GPC"
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Justin Marrese
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About encyrption: If the teacher doesn't even know the encryption technique, it doesn't matter how simple it is...
About compression: I have a ti83. If the compression proggie will give me 2x, this will add 27k or so... The problem is that it probably will only add 1.5x (14k) and the compress/decompress programs will have to be on my calc...
If the compress program is more than 10k, Its not worth it. (dont' forget to leave space to run the uncompressed program!)
-- Justin
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4 September 1998, 17:37 GMT
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Re: Re: Re: Article: "Calc Crypto and the GPC"
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S.T.L.
(Web Page)
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Yes, I agree. Other calculators than the TI-83 exist. The 83 isn't that good, anyway. Follows are my opinions on the TI calculators. Please note two things:
1) These are MY opinions. They are just here so you can know what I think.
2) Please do not respond to this post. I do not desire nor want a TI calcuator argument to spring up.
TI-73: Middle school, *gag*. I hope assembly shells are never made for it. Geez, I went through Algebra I with a TI-30, anyone else can too. Assembly shells would mean games, and considering the sorry state of middle schools, that means the decline of math and the rise of games.
TI-80: This calculator is simply too weak. It is not desirable for any higher math.
TI-82 and TI-83: Undesirable. They are too weak, and too close in price to the 85. They are used by high school students taking Algebra. *sigh* Algebra should be taught in middle school.
TI-85: Finally, a calculator that deserves respect. It can be used for Calculus classes, and is very powerful. There is a disturbing amount of games for it, though.
TI-86: A calculator, that, while more powerful than the TI-85, deserves less respect in my opinion. Too many people play games on it, I have seen.
TI-89: A stripped-down TI-92+ with a smaller screen and no geometry. This is less desirable than the TI-92+. Besides, no one needs this thing on the SAT. I got a 1600 with a TI-85 with 1K of free memory.
TI-92: A VERY good calculator, and large screen also. Not to mention that it has very few games for it.
TI-92+: This is the best. A TI-92+ deserves respect. And few to no games. :-D
As you can tell, I don't like games that much. The only - ONLY - game I retain on my TI-85 is the Insane Game. I discovered it a while back, while it was in an early version, and I believe it's worthwhile to keep on my calc.
As I said before, these are my opinions. Disagree or agree with them as you may. But let's not start a "Which TI is better" feud.
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5 September 1998, 01:19 GMT
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Re: Re: Re: Re: Article: "Calc Crypto and the GPC"
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David Yenoki
(Web Page)
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>TI-82 and TI-83: Undesirable. They are too weak, and too close in price to the 85. They are used by high school students taking Algebra. *sigh* Algebra should be taught in middle school.
The TI-82 is weak, however, the TI-83 is quite adequate for all your computing needs. I know many people including myself who took Algebra in middle school, and take more advanced course (PreCalculus onwards) with their beloved TI-83.
>TI-85: Finally, a calculator that deserves respect. It can be used for Calculus classes, and is very powerful. There is a disturbing amount of games for it, though.
The TI-85 is an impotent waste of silicon... When compared to more recent developments. Trying to port programs from the 83 to the 85 is impossible, due to a lack of a function that will (quickly) search a string for a subset, starting from a character. This problem also plagues the 86.
This is in the rudimentary programming language inherent within the system, of course.
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7 September 1998, 20:59 GMT
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Re: Re: Re: Re: Re: Article: "Calc Crypto and the GPC"
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Rich D.
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There are already programs (at least for the 86) which will put a password on the calc, and refuse to start up if you don't type it in correctly. ASE, an assembley shell, does this. Also, I use matrix encryption with a program I wrote, but it's so simple to crack (of course, i wrote it, so it wasn't too hard to figure out a way to bypass it). (It is a one-way encryption, but if you fill the result matrix, and the encryption matrix (filled with random #s when the program is installed) with zeros, it thinks that any password you type is the correct one.
Like the original author of the message said, even if you think your encryption scheme is great, it can be cracked, if you're not a professional. And it's probably simpler to do than you think.
However, no average high-schooler or teacher will know a thing about how the encryption program works, and they won't want to bother trying to crack it either. So it really doesn't matter how weak the encryption scheme is, as long as it's fast. The method I'm using now (the second one i made) gets the password you type from a getkey loop (in basic) and then just one-way encrypts that, and compares it to the encrypted real password (which is why if you set the encrypted password matrix to all zeros and the translation matrix to all zeros, the encryption is useless. It uses matrix multiplication, so anything you type turns into a matrix of zeros.)
Sorry if I rambled. The point is, even crackable encryption methods are fine, if nobody is going to bother to take the time to try to crack them.
Rich D.
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8 July 1999, 18:41 GMT
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