Cryptography Reference
In-Depth Information
Mark:
Notbad.Itsmoreflexible.Butwhatifjustoneofusis
there?
Harry:
What's the difference?
Mark:
That one person really wouldn't be a group. He would be
acting as a vigilante. He could do anything he wanted that
evening. Maybe even something that was less than just.
Harry:
So you want a quorum?
Mark:
Yes. I say two out of three of us should be there before
someone can start invoking the name of the Three Mus-
keteers.
Bob:
What about costumes? What do we wear if we're alone?
Mark:
Doesn't matter. The most important thing is what we
shout as we vanquish the foes. Are we together on this?
Together :
Two out of Three for One and One for Two out of Three!
4.2 Splitting Up Secrets
There are many occasions when you need to split a key or a secret
into numerous puzzle parts so that the secret can only be recovered
if all of the parts are available. This is a good way to force people to
work together. Many nuclear weapons systems, for instance, require
two people to turn two different keys simultaneously. Bank safe de-
posit boxes have two locks and one key is held by the owner while the
other is held by the bank.
1
Splitting information into a number of parts is a good way to
make information disappear. Each part may look like noise, but to-
gether they create the message. These different parts can take differ-
ent paths adding further confusion to the entire process.
There are many neat ways to mathematically split a secret into
parts. This secret might be the key to an encrypted file or it might be
the important factoid itself. The goal is to create
different files or
numbers that must all be present to reconstruct the original number.
There are also threshold schemes that let you recover the secret if you
have some smaller subset of the original parts. If a corporation has
five directors, for instance, youmight require that three be present to
unlock the corporation's secret key used to sign documents.
The mathematics of these schemes is really quite simple and in-
tuitive. Chapter 3 showed how error-correcting codes can be used as
primitive secret-sharing devices. That is, you can split up a secret by
encoding it with a error-correcting code that can correct wrong bits.
n
1
It is not clear to me why the bank needs to have its own key on the box. The
combination to the vault serves the same purpose.
