Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters

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Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters (1995)

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by Ueli M. Maurer

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30 - 0 self

BibTeX

@MISC{Maurer95fastgeneration,
    author = {Ueli M. Maurer},
    title = {Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters},
    year = {1995}
}

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Abstract

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 pseudo-prime of the same size that passes the Miller-Rabin test for only one base. Therefore our algorithm is even faster than presently-used algorithms for generating only pseudo-primes because several Miller-Rabin 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 public-key cryptosystem is presented. The prime generation algorithm can easily be modified to generate nearly random primes or RSA-moduli that satisfy t...

Keyphrases

prime number fast generation secure public-key cryptographic parameter expected time specified interval prime parameter prime generation algorithm random prime independent base heuristic argument iterated encryption attack rsa public-key cryptosystem several miller-rabin test efficient recursive algorithm security constraint provable prime detailed analysis miller-rabin test sufficient confidence level certain cryptographic system presently-used algorithm

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