Articles tagged story at null program

Flip Foolflim the Dragon Traitor

2011-01-10T00:00:00Z

So I’ve been playing a bit of tabletop role-playing games lately, so here’s another game story like my previous Fire Gem tale. I didn’t think it was that interesting, but I found out that some of my friends were sharing it with each other when I wasn’t around.

A recent character was named Flip Foolflim, a chaotic evil halfling rogue. I had selected his secondary language by the roll of the dice, Draconic, and by coincidence we happened to be fighting a lot of dragonborn. Flip could always understand them when they spoke to each other. I was asked why my halfling would know Draconic, so here’s his story.

Flip had made friends with a dragon — not a typical friendship, obviously. During their initial encounter this dragon realized a use for the little halfling. Flip would regularly head out from the dragon’s lair to one of the local towns where he would round up a group of naïve adventurers who volunteered slay a “treacherous dragon.” Once at the lair, he would turn on them and join his dragon friend in killing the adventurers and keeping the spoils. It was an arrangement both of them enjoyed.

This little scheme went well for some years until Flip, blinded by his greed, greatly underestimated one particular group. Fortunately for Flip, he discovered his mistake before attempting to backstab the adventurers, and instead joined them in slaying his dragon friend.

Without his home in the dragon lair, he wandered for some time before joining a party of adventurers (the PCs of the recent adventure). He worked with them for some time, though not making any close friends. None of his companions appreciated his thumb collection, cut from the right hands of everyone his party struck down — for those who had hands.

One particular fight wasn’t going so well for his side, a situation that he had experienced before back in the dragon lair. In the middle of the fight Flip kneeled before the opponent, swearing his allegiance, and attacked his own party members (other PCs, including my wife’s character). Neither side liked this change, so he found himself with no friends, meeting his end in that battle.

However, when my friends were discussing this I think it wasn’t so much about the story being interesting but something like, “Hey, did you hear Chris had his character attack the other PCs last week?!”

No hard feelings, guys!

A Fractran Short Story

2010-03-09T00:00:00Z

Fractran is a Turing-complete esoteric programming language. A Fractran program is just an ordered list of positive, irreducible fractions. The program's output for an input n is the output of the program run on n multiplied by the first fraction in the list that results in an integer. If no such multiplication results in an integer, the output is the input n. Variables are encoded in the exponents of the prime factorization of the input and output.

Some time ago I thought up an idea for a short story involving Fractran. A mathematician accidentally creates a Fractran program that can trivially factor large composites. Think something like O(log n). It's just the right magical string of, say, 31 fractions.

The story would be a first-person narrative of the mathematician's thoughts during a short time after the discovery, considering many of the consequences of the program. For example, it would render much of cryptography, which plays an essential role in the modern world, useless. He would also wonder if mankind should deserve such a discovery, considering how accidental it was.

This whole idea vanished once I realized that this Fractran program is actually completely trivial. It even runs in O(1) time. It's so trivial as to be worthless. Remember that Fractran stores its data in the number's prime factorization? The Fractran program that can factor any number in constant time is the identity function. To decode the output, which matches the input, all you need to do is factor it!

Interestingly, it doesn't seem to actually be possible to implement the identity function in Fractran (But somehow it's Turing-complete? Hmmm... more investigation needed.), unless you can define your program in terms of its input. For example, the program 1/(n+1) is the identity function for input n.

The Fire Gem

2008-12-22T00:00:00Z

If you are at all familiar with Dungeons and Dragons, you may have already heard of the stories of The Tale of Eric and the Dread Gazebo by Richard Aronson and The Head of Vecna. These are real classics. Read them now, if you haven't already, before you go on. If you are unfamiliar with tabletop role-playing games you should go learn a little about them first.

I would like to share one of my Dungeons and Dragons stories. It won't be anywhere as interesting as the two stories I mentioned, but I have gotten some laughs out of people I tell it to.

Back in my college days, a friend was running a 3.5 campaign and asked me to join in. The other players had rolled up their characters and done a couple practice sessions before I joined, so I was jumping into a group that had already had their start.

It was an evil campaign. Everyone in the group was either evil or neutral. We were serving some kind of evil sorcerer. I felt that being evil allowed much more variety of play and usually gave us more freedom in the game world than being good. If things started to get dry, someone would do something stupid like burn down the nearest town inn. The lawful evil characters weren't so happy about this, though.

I rolled up a chaotic evil half-orc barbarian named Gnohkk. I was lucky on my rolls and had some wonderful stats, so he was very big and strong. Gnohkk started with a two-handed axe that contained a magic fire gem in its head. After some training he was able to cause a fiery explosion at will centered at the location of the fire gem. If an untrained character wielded the axe, upon striking anything he would have to make a saving throw to prevent an explosion.

Because Gnohkk would also suffer from the explosion, this wasn't terribly useful at first, except against targets particularly vulnerable to fire, like trolls and magic trees. The training was mainly to make the axe usable.

At some point during the campaign the party got a hold of a ring of fire resistance, which was then used by Gnohkk. With this ring he was invulnerable to his own explosions, making the axe very powerful. The ring also provided a handful of simple fire spells that made combat more interesting.

Sadly, not long after the ring was found the fire gem axe chipped broke. Before discarding the broken axe, Gnohkk carefully removed the fire gem for safe keeping.

After an intense battle against some type of monsters with big horns, Gnohkk found himself a nice metal helmet. He also managed to scrounge up 10 horns from the monster corpses, which gave him a great idea. When the party got to the next town, Gnohkk visited the blacksmith, and requested to have him affix the 10 horns around the outside of the helmet. In the front of the helmet he wanted to have a socket created and the fire gem embedded inside it. The blacksmith said it would take a couple of days.

I was hoping this giant helmet would make Gnohkk more intimidating. So far in the campaign, every time he had attempted to intimidate an NPC he failed his rolls and came off looking stupid instead.

So, this was pretty cool: a giant horned helmet with a gem in the front. With the helmet on, Gnohkk could explode into a ball of flames at will and without warning. What a wonderful toy for a chaotic evil!

When Gnohkk returned to the blacksmith a couple days later he found the shop was destroyed. Some of the walls remained, the roof was gone, and weapons and tools were thrown all over the area. The blacksmith's charred body had been dead for some time. However, the helmet was completed and basically intact. Gnohkk shrugged, grabbed the helmet and left, all without having to pay a single copper to the now dead blacksmith.

We figured out later what happened (the GM probably just told us). Gnohkk failed to tell the blacksmith about the properties of the gem. When the blacksmith tapped the gem into the socket, the fire gem activated and exploded, killing him and destroying his shop.

Controlling a Minefield

2008-12-16T00:00:00Z

Some time ago I was watching through the entire series of Deep Space 9. It was a Star Trek television show about a space station that rests next a wormhole that connects to the other side of the galaxy (The Delta quadrant).

The Delta quadrant is ruled by a group called the Dominion, and they are looking to conquer the Federation side of the galaxy (the Alpha quadrant). At one point during the series, the Federation needs to temporarily disable the wormhole to prevent Dominion ships from crossing through. They do this by mining the wormhole with identical, cloaked, self-replicating mines.

If a mine is destroyed, the neighboring mines will replicate a replacement. The minefield repairs itself. This makes removing the minefield within a reasonable amount of time difficult to impossible. If even a single mine is left behind, it can replicate the entire minefield again.

The most interesting question here is this:

When the Federation returns and wants to remove the minefield, how would they do it? What would stop the Dominion from doing the same thing?

The first thing that comes to mind is having a kill signal, but what would this signal be? It could simply be a plain "kill" command, but the Dominion could also broadcast such a signal to disable the minefield. Consider that the Dominion could capture a single mine and study everything about its workings. The minefield itself could therefore hold no secrets whatsoever. This leaves out any possibility of a secret kill command stored in the mines.

Here's what I would do, assuming that humans or aliens have not yet discovered some giant breakthrough in factoring in the Star Trek universe. I would randomly generate two very large prime numbers. Today, two 1024-bit primes should be more than enough, but in 350 years even larger numbers would probably be necessary. Then, I multiply these two number together and store this number in the mine software. To disable the minefield, I simply broadcast these two numbers into the minefield. The mines would be programmed to take the product of any pairs of numbers it receives. If the product matches the internal number, the mine shuts down.

Voila! A method for shutting down the minefield. The enemy can know everything about every single mine's construction, including the software and data stored on every mine, but will be unable to disable the minefield without factoring a very large composite number, which would presumably be difficult or impossible (within a reasonable amount of time).

Another possibility would be using a hash. Come up with a strong passphrase, then use a hashing algorithm like SHA-1 or MD5, or whatever is available and appropriate in 350 years, to hash the passphrase. Store the hash in the mines. When you want to disable the minefield, broadcast the passphrase. These mines will hash the broadcast and compare it to the stored hash. It's really the same solution as before: a one-way function. This is also similar to how passwords are stored inside a computer today.

If we wanted more commands, like "don't blow up any ships for awhile" or "increase minefield density", we could generate more composites corresponding to each command. However, once a command is issued, the secret — the two prime numbers — is out, and it cannot be used again. In this case, I would go into the realm of public key cryptography.

I would issue a command, along with a timestamp, and maybe even a nonce that could double as a global identifier for the command, and sign the whole deal using my private key. On each mine I would store the public key. When a command is received, the mines would check the signature before executing the command. I could then issue repeat commands, as the timestamps would change each time. An adversary learns nothing when a command is issued, because the time stamps would make any replay attacks useless.

Minefields just like this exist today all over the Internet, as botnets. Thousands of computers all around the world become infected with malware and come under the control of a single individual or group. Individual machines in the botnet could be taken out, but removing the entire botnet is difficult as it grows and repairs itself. Any security researcher could disassemble the botnet malware and learn anything about it, so the malware can store no secrets. How does a malicious person control the botnet, then, without someone else taking control? Public key cryptography, just as described above.