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Unformatted text preview: s the length of the message—nothing more. This is true because R, S, T, U, and M all have the same length; seeing anyone of them gives the length of M. Remember, M isn’t being split in the normal sense of the word; it is being XORed with random values. 3.7 Secret Sharing
You’re setting up a launch program for a nuclear missile. You want to make sure that no single raving lunatic can initiate a launch. You want to make sure that no two raving lunatics can initiate a launch. You want at least three out of five officers to be raving lunatics before you allow a launch. This is easy to solve. Make a mechanical launch controller. Give each of the five officers a key and require that at least three officers stick their keys in the proper slots before you’ll allow them to blow up whomever we’re blowing up this week. (If you’re really worried, make the slots far apart and require the officers to insert the keys simultaneously—you wouldn’t want an officer who steals two keys to be able to vaporize Toledo.) We can get even more complicated. Maybe the general and two colonels are authorized to launch the missile, but if the general is busy playing golf then five colonels are required to initiate a launch. Make the launch controller so that it requires five keys. Give the general three keys and the colonels one each. The general together with any two colonels can launch the missile; so can the five colonels. However, a general and one colonel cannot; neither can four colonels. A more complicated sharing scheme, called a threshold scheme, can do all of this and more—mathematically. At its simplest level, you can take any message (a secret recipe, launch codes, your laundry list, etc.) and divide it into n pieces, called shadows or shares, such that any m of them can be used to reconstruct the message. More precisely, this is called an (m,n)-threshold scheme. With a (3,4)-threshold scheme, Trent can divide his secret sauce recipe among Alice, Bob, Carol, and Dave, such that any three of them can put their shadows together and reconstr...
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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