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Further investigations with the strong probable prime test
 Math. Comp
, 1996
"... Abstract. Recently, Damg˚ard, Landrock and Pomerance described a procedure in which a kbit odd number is chosen at random and subjected to t random strong probable prime tests. If the chosen number passes all t tests, then the procedure will return that number; otherwise, another kbit odd integer ..."
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Abstract. Recently, Damg˚ard, Landrock and Pomerance described a procedure in which a kbit odd number is chosen at random and subjected to t random strong probable prime tests. If the chosen number passes all t tests, then the procedure will return that number; otherwise, another kbit odd integer is selected and then tested. The procedure ends when a number that passes all t tests is found. Let pk,t denote the probability that such a number is composite. The authors above have shown that pk,t ≤ 4 −t when k ≥ 51 and t ≥ 1. In this paper we will show that this is in fact valid for all k ≥ 2 and t ≥ 1. 1.
On using Carmichael numbers for public key encryption systems
, 1997
"... We show that the inadvertent use of a Carmichael number instead of a prime factor in the modulus of an RSA cryptosystem is likely to make the system fatally vulnerable, but that such numbers may be detected. ..."
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We show that the inadvertent use of a Carmichael number instead of a prime factor in the modulus of an RSA cryptosystem is likely to make the system fatally vulnerable, but that such numbers may be detected.
FIPS PUB 1863 FEDERAL INFORMATION PROCESSING STANDARDS PUBLICATION Digital Signature Standard (DSS)
, 2009
"... of Standards and Technology (NIST) is the official series of publications relating to standards and guidelines adopted and promulgated under the provisions of the Federal Information Security Management Act (FISMA) of 2002. Comments concerning FIPS publications are welcomed and should be addressed t ..."
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of Standards and Technology (NIST) is the official series of publications relating to standards and guidelines adopted and promulgated under the provisions of the Federal Information Security Management Act (FISMA) of 2002. Comments concerning FIPS publications are welcomed and should be addressed to the
ACE Encrypt: The Advanced Cryptographic Engine’s Public Key Encryption Scheme ∗
, 2000
"... This document describes the part of the Advanced Cryptographic Engine (ACE) pertaining to public key encryption. It specifies a public key encryption scheme with enough detail to ensure interoperability between different implementations. This scheme is almost as efficient as commercially used scheme ..."
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This document describes the part of the Advanced Cryptographic Engine (ACE) pertaining to public key encryption. It specifies a public key encryption scheme with enough detail to ensure interoperability between different implementations. This scheme is almost as efficient as commercially used schemes, yet unlike such schemes, can be proven secure under reasonable and welldefined intractability assumptions. A concrete security analysis of the scheme is presented. ∗ Change log:
CryptoBytes 3 (1), 1997
, 1997
"... this article we will examine these criteria. The position of RSA Laboratories is that virtually all of these requirements are unnecessary [10,11]. In particular, we will show that the relevance of strong primes to the security of RSA is, at best, doubtful. However, given this position, we will outli ..."
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this article we will examine these criteria. The position of RSA Laboratories is that virtually all of these requirements are unnecessary [10,11]. In particular, we will show that the relevance of strong primes to the security of RSA is, at best, doubtful. However, given this position, we will outline in this article a fast way of generating random strong primes that also satisfy a number of other cryptographic requirements. The method requires no more time to generate strong primes than it takes to generate random primes.
SelfEvaluation ESIGN Signatures
"... This document details security assessment and performance on ESIGN signature scheme. ..."
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This document details security assessment and performance on ESIGN signature scheme.
Algorithmic Number Theory MSRI Publications
"... Quadratic nonresidues 36 Chinese remainder theorem 57 ..."
Algorithmic Number Theory MSRI Publications
"... Quadratic nonresidues 36 Chinese remainder theorem 57 ..."