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
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
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
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
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.