Unformatted text preview: inary code is NP-complete. A good description of this algorithm can be found in ; see also . Following is just a quick summary. Let dH(x,y) denote the Hamming distance between x and y. The numbers n, k, and t are system parameters. The private key has three parts: G’ is a k * n generator matrix for a Goppa code that can correct t errors. P is an n * n permutation matrix. S is a k * k nonsingular matrix. The public key is a k * n matrix G: G = SG’P. Plaintext messages are strings of k bits, in the form of k-element vectors over GF(2). To encrypt a message, choose a random n-element vector over GF(2), z, with Hamming distance less than or equal to t. c = mG + z To decrypt the ciphertext, first compute c’ = cP-1. Then, using the decoding algorithm for the Goppa code, find m’ such that dH(m’ G, c’) is less than or equal to t. Finally, compute m = m’S-1. In his original paper, McEliece suggested that n = 1024, t = 50, and k = 524. These are the minimum values required for security. Table 19.7 ElGamal Speeds for Different Modulus Lengths with a 160-bit Exponent (on a SPARC II) 512 bits Encrypt Decrypt Sign Verify 0.33 sec 0.24 sec 0.25 sec 1.37 sec 768 bits 0.80 sec 0.58 sec 0.47 sec 5.12 sec 1024 bits 1.09 sec 0.77 sec 0.63 sec 9.30 sec 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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----------- Although the algorithm was one of the first public-key algorithms, and there were n...
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