## Visual Cryptography

Suppose that 6 thieves have
deposited their loot in a numbered Swiss bank account. Being thieves, they
do not trust each other not to withdraw the money and take the next plane
to Brazil. However, being sentimental, they do not assume a conspiracy
of two or more thieves that will try to take out the money without "authorization"
and they want any two of them to able to withdraw the money. They therefore
want to divide the secret number into shares so that from each share you
cannot learn anything about the secret number, but from any two shares
you can reconstruct the secret number.

This problem is the by now classical secret sharing problem
(see Doug
Stinson's bibliography on secret sharing schemes ). The twist here
is that the thieves's representatives will *not *have a computer with
them when they come to withdraw the money, so they want to be to it visually:
each thief gets a transparency. The transparency should yield *no *information
about the secret number (even implicitly). However, by taking *any *two
transparencies, stacking them together and aligning them, the secret number
should "pop out". The transparencies themselves will be prepared
by a (trusted) computer. How can this be done?

For starters, can you think of a method that will let two thieves split
a secret between them? Solution

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