Cryptography Reference
In-Depth Information
appears.
The Publius system
created by Marc
Waldman, Aviel D.
Rubin and Lorrie Faith
Cranor uses basic secret
sharing algorithms to
distribute the key to a
document. [WRC00] For
more, see Section 10.6.
Now imagine that the word gets out that the information is hid-
den in the combination of these four sites. Which one of the four
is responsible? Disney World, the White House, the hackers in Eu-
rope, or you? It is impossible to use the least-significant bits of each
of these images to point the finger at anyone. The hidden informa-
tion is the sum of the four and any one of the four could have been
manipulated to ensure that the final total is the hidden information.
Who did it? If you arrange it so that the hidden information is found
in the total of 100 possible images, no one will ever have the time to
track it down.
Of course, there are still problems with the plan. Imagine that
Disney World used a slick, ray-traced image from one of their films
like
Toy Stor y
. These images often have very smooth surfaces with
constant gradients that usually have very predictable least significant
bits. This would certainly be a defense against accusations that they
This system is just like
the classic topic ciphers
which used a topic as
the one-time pad.
The Chi-Squared Test
and other measures of
randomness can be
found in Don Knuth's
[Knu81].
manipulated the least significant bits to send out a secret message.
The images chosen as the foils should have a very noisy set of least
significant bits.
4.3 Building Secret-Sharing Schemes
Secret-sharing schemes are easy to explain geometrically, but adapt-
ing them to computers can involve some compromises. The most
important problem is that computers really deal only with integers.
Lines from real numbered domains are neither efficient nor often
practical. For instance, five numbers involved in a typical scheme for
hiding a secret as the intersection of two lines. Two numbers describe
the slope and
-intercept of one line, two numbers describe the sec-
ondline,andonenumberdescribesthe
y
x
coordinate of the intersec-
tion point. If
is an integer, then it is not possible to choose lines
at random that have both integers for their slope and
x
y
-intercept. If
they are available, there will be a few of them.
You can use floating-point numbers, but they add their own insta-
bility. First, youmust round off values. This can be a significant prob-
lem because both sides must do all rounding-off the same. Second,
you might encounter big differences in floating-point math. Two dif-
ferent CPUs can come up with different values for
.Theanswers
will be very close, but they might not be the same because the differ-
ent CPUs could be using slightly different representations of values.
Most users of floating-point hardware don't care about these verymi-
nor differences because all of their calculations are approximations.
x/y
