applied cryptography - protocols, algorithms, and source code in c

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Unformatted text preview: re complicated, based on the same sorts of hard problems as public-key cryptography. And like public-key algorithms, they tend to be slow and cumbersome. Shamir’s Pseudo-Random-Number Generator Adi Shamir used the RSA algorithm as a pseudo-random-number generator [1417]. While Shamir showed that predicting the output of the pseudo-random-number generator is equivalent to breaking RSA, potential biases in the output were demonstrated in [1401,200]. Blum-Micali Generator This generator gets its security from the difficulty of computing discrete logarithms [200]. Let g be a prime and p be an odd prime. A key x0, starts off the process: xi+1 = gxi mod p The output of the generator is 1 if xi < (p - 1)/2, and 0 otherwise. If p is large enough so that computing discrete logarithms mod p is infeasible, then this generator is secure. Additional theoretical results can be found in [1627,986,985,1237,896,799]. RSA This RSA generator [35,36] is a modification of [200]. The initial parameters are a modulus N which is the product of two large primes p and q, an integer e which is relatively prime to (p - 1) (q - 1), and a random seed x0, where x0 is less than N. xi+1 = xei mod N The output of the generator is the least significant bit of xi. The security of this generator is based on the difficulty of breaking RSA. If N is large enough, then the generator is secure. Additional theory can be found in [1569,1570,1571,30,354]. Blum, Blum, and Shub The simplest and most efficient complexity-theoretic generator is called the Blum, Blum, and Shub generator, after its inventors. Mercifully, we shall abbreviate it to BBS, although it is sometimes called the quadratic residue generator [193]. 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 EarthWe...
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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.

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