Unformatted text preview: re complicated, based on the same sorts of hard problems as publickey cryptography. And like publickey algorithms, they tend to be slow and cumbersome. Shamir’s PseudoRandomNumber Generator
Adi Shamir used the RSA algorithm as a pseudorandomnumber generator [1417]. While Shamir showed that predicting the output of the pseudorandomnumber generator is equivalent to breaking RSA, potential biases in the output were demonstrated in [1401,200]. BlumMicali 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 complexitytheoretic 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 © 19962000 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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