Results 1 
2 of
2
Fast Generation of Prime Numbers and Secure PublicKey Cryptographic Parameters
, 1995
"... A very efficient recursive algorithm for generating nearly random provable primes is presented. The expected time for generating a prime is only slightly greater than the expected time required for generating a pseudoprime of the same size that passes the MillerRabin test for only one base. The ..."
Abstract

Cited by 26 (0 self)
 Add to MetaCart
(Show Context)
A very efficient recursive algorithm for generating nearly random provable primes is presented. The expected time for generating a prime is only slightly greater than the expected time required for generating a pseudoprime of the same size that passes the MillerRabin test for only one base. Therefore our algorithm is even faster than presentlyused algorithms for generating only pseudoprimes because several MillerRabin tests with independent bases must be applied for achieving a sufficient confidence level. Heuristic arguments suggest that the generated primes are close to uniformly distributed over the set of primes in the specified interval. Security constraints on the prime parameters of certain cryptographic systems are discussed, and in particular a detailed analysis of the iterated encryption attack on the RSA publickey cryptosystem is presented. The prime generation algorithm can easily be modified to generate nearly random primes or RSAmoduli that satisfy t...
The Algorithmic Column
"... In this column I would like to present and provide an historical perspective for the new breakthrough result due to Manindra Agrawal, Neeraj Kayal and Nitin Saxena: PRIMES 2 P (without assumptions) The paper has not been published yet, and the report can be found at http://www.cse.iitk.ac.in/users/m ..."
Abstract
 Add to MetaCart
(Show Context)
In this column I would like to present and provide an historical perspective for the new breakthrough result due to Manindra Agrawal, Neeraj Kayal and Nitin Saxena: PRIMES 2 P (without assumptions) The paper has not been published yet, and the report can be found at http://www.cse.iitk.ac.in/users/manindra/index.html. The result even deserved a column in the New York Times of August 8th, 2002. Notice that placing the PRIMES and COMPOSITE problems in the class P does not imply that an efficient way to factorize a composite integer has been found, and thus the AKSalgorithm 1 should not affect the security of RSA or PGP.