Unformatted text preview: r example, if three shadows are required to reconstruct the message, then it is a point in three-dimensional space. Each shadow is a different plane. With one shadow, you know the point is somewhere on the plane. With two shadows, you know the point is somewhere on the line formed where the two planes intersect. With three shadows, you can determine the point exactly: the intersection of the three planes. Previous Table of Contents Next Products | Contact Us | About Us | Privacy | Ad Info | Home Use of this site is subject to certain Terms & Conditions, Copyright © 1996-2000 EarthWeb Inc. All rights reserved. Reproduction whole or in part in any form or medium without express written permission of EarthWeb is prohibited. Read EarthWeb's privacy statement. To access the contents, click the chapter and section titles. Applied Cryptography, Second Edition: Protocols, Algorthms, and Source Code in C (cloth)
Brief Full Advanced Search Search Tips (Publisher: John Wiley & Sons, Inc.) Author(s): Bruce Schneier ISBN: 0471128457 Publication Date: 01/01/96 Search this book:
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This scheme uses prime numbers . For an (m, n)-threshold scheme, choose a large prime, p, greater than M. Then choose n numbers less than p, d1 , d2 , ..., dn, such that: 1. The d values are in increasing order; di < di+1 2. Each di is relatively prime to every other di 3. d1 * d2 * ... * dm > p * dn-m+2 * dn-m+3 * ... * dn To distribute the shadows, first choose a random value r and compute M' = M + rp The shadows, ki, are ki = M' mod di Any m shadows can get together and reconstruct M using the Chinese remainder theorem, but any m -1 cannot. See  for details. Karnin-Greene-Hellman
This scheme uses matrix multiplication . Choose n +1 m-dimensional vectors, V0 , V1 , ..., Vn, such that any possible m * m matrix formed out of those vectors has rank m. The vector U is a row vector of dimension m +1. M is the matrix product...
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