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Unformatted text preview: ret is divided up among 50 people so that any 10 can get together and reconstruct the secret. That’s easy. But, can we implement the same secret-sharing scheme with the added constraint that 20 people can get together and prevent the others from reconstructing the secret, no matter how many of them there are? As it turns out, we can . The math is complicated, but the basic idea is that everyone gets two shares: a “yes” share and a “no” share. When it comes time to reconstruct the secret, people submit one of their shares. The actual share they submit depends on whether they wish the secret reconstructed. If there are m or more “yes” shares and fewer than n “no” shares, the secret can be reconstructed. Otherwise, it cannot. Of course, nothing prevents a sufficient number of “yes” people from going off in a corner without the “no” people (assuming they know who they are) and reconstructing the secret. But in a situation where everyone submits their shares into a central computer, this scheme will work. Secret Sharing with Disenrollment
You’ve set up your secret-sharing system and now you want to fire one of your shareholders. You could set up a new scheme without that person, but that’s time-consuming. There are methods for coping with this system. They allow a new sharing scheme to be activated instantly once one of the participants becomes untrustworthy . 3.8 Cryptographic Protection of Databases
The membership database of an organization is a valuable commodity. On the one hand, you want to distribute the database to all members. You want them to communicate with one another, exchange ideas, and invite each other over for cucumber sandwiches. On the other hand, if you distribute the membership database to everyone, copies are bound to fall into the hands of insurance salesmen and other annoying purveyors of junk mail. Cryptography can ameliorate this problem. We can encrypt the database so that it is easy to extract the address of a single person but ha...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
- Fall '10