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Unformatted text preview: to Alice and S to Bob. To reconstruct the message, Alice and Bob have only one step to do: (4) Alice and Bob XOR their pieces together to reconstruct the message: R•S=M This technique, if done properly, is absolutely secure. Each piece, by itself, is absolutely worthless. Essentially, Trent is encrypting the message with a one-time pad and giving the ciphertext to one person and the pad to the other person. Section 1.5 discusses one-time pads; they have perfect security. No amount of computing power can determine the message from one of the pieces. It is easy to extend this scheme to more people. To split a message among more than two people, XOR more random-bit strings into the mixture. In this example, Trent divides up a message into four pieces: (1) Trent generates three random-bit strings, R, S, and T, the same length as the message, M. (2) Trent XORs M with the three strings to generate U: M•R•S•T=U (3) Trent gives R to Alice, S to Bob, T to Carol, and U to Dave. Alice, Bob, Carol, and Dave, working together, can reconstruct the message: (4) Alice, Bob, Carol, and Dave get together and compute: R•S•T•U=M This is an adjudicated protocol. Trent has absolute power and can do whatever he wants. He can hand out gibberish and claim that it is a valid piece of the secret; no one will know it until they try to reconstruct the secret. He can hand out a piece to Alice, Bob, Carol, and Dave, and later tell everyone that only Alice, Carol, and Dave are needed to reconstruct the secret, and then fire Bob. But since this is Trent’s secret to divide up, this isn’t a problem. However, this protocol has a problem: If any of the pieces gets lost and Trent isn’t around, so does the message. If Carol, who has a piece of the sauce recipe, goes to work for the competition and takes her piece with her, the rest of them are out of luck. She can’t reproduce the recipe, but neither can Alice, Bob, and Dave working together. Her piece is as critical to the message as every other piece combined. All Alice, Bob, or Dave know i...
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- Fall '10