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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 ..."
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Cited by 21 (0 self)
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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...
Computational Alternatives to Random Number Generators
, 1999
"... In this paper, we present a simple method for generating randombased signatures when random number generators are either unavailable or of suspected quality (malicious or accidental). ..."
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Cited by 4 (3 self)
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In this paper, we present a simple method for generating randombased signatures when random number generators are either unavailable or of suspected quality (malicious or accidental).
A Survey on IQ Cryptography
 In Proceedings of Public Key Cryptography and Computational Number Theory
, 2001
"... This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying p ..."
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Cited by 3 (1 self)
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This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying problems. We give advice on the selection of the cryptographic parameters and show the impact of this advice on the eciency of some IQ cryptosystems.