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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...
Managing integrity in design information flows
 ComputerAided Design
, 1996
"... This paper addresses integrity rules that are embedded within engineering design applications and that apply between applications. A representation for integrity rules that are embedded in applications is presented and a set of related methods developed for: (a.) maintaining the integrity condition ..."
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Cited by 9 (1 self)
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This paper addresses integrity rules that are embedded within engineering design applications and that apply between applications. A representation for integrity rules that are embedded in applications is presented and a set of related methods developed for: (a.) maintaining the integrity condition of application developed data, (b) managing the precedence order between applications, in the context of (c.) changing the schema and the associated mix of applications and (d.) iterated execution of applications and change propagation. Both integrity rules literally embedded within external applications and others required to be embedded within a database are considered. The techniques are demonstrated with an extensive example.
Editorial Board
"... CONNECTIONS (ISSN 02261776) is published twice annually by the International Network for Social Network Analysis (INSNA), located at the ..."
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CONNECTIONS (ISSN 02261776) is published twice annually by the International Network for Social Network Analysis (INSNA), located at the
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"... inequality in information theory, and where I(l,n) is the mutual The code C is the set of vectors satisfying XH =O. In many information betwen [ and n. Using a slight modification of a applications it is desirable to know, for a given weight w, technique of Lipster [7], we obtain whether C contains ..."
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inequality in information theory, and where I(l,n) is the mutual The code C is the set of vectors satisfying XH =O. In many information betwen [ and n. Using a slight modification of a applications it is desirable to know, for a given weight w, technique of Lipster [7], we obtain whether C contains any words of weight w, i.e., whether there is a vector of weight w satisfying XH = 0. Again, the best general algorithm known for deciding this requires an exponential search, in this case through all 2k codewords, and a faster algorithm would be highly desirable. In this correspondence we will show that it is unlikely that anyone will ever discover substantially faster algorithms for ~;+a $ E,t <+ logeither of these problems, by showing that both of them belong to t+J $ +2aZ a large class of difficult combinatorial problems, the NPcomN plete problems. with,&(.$) = E[A,(X,&$1&$]. Hence from (26) and (27) we have II. NPCOMPLETE PROBLEMS Pt>$$ exp ( j3t). The following discussion will describe in heuristic language a X: set of results that can be made quite precise. We refer the interested reader to [1, Ch. lo], [3], [4], or [5] for details. Therefore (24) actually attains this lower bound and thereby is The class P is defined to be the set of computational problems optimal over all admissible nonlinear codings. which can be solved by an algorithm which is guaranteed to REFERENCES terminate in a number of steps bounded by a polynomial in the
EXTENDING WARING'S CONJECTURE TO 471,600,000
, 1989
"... Abstract. Two computer techniques are described that the authors used to confirm Waring's Conjecture to 471,600,000, thus extending R. M. Stemmler's result of 200,000 computed in 1964. M. C. Wunderlich increased the result to 175,600,000 in August 1988, and in the following October, J. M. Kubina, us ..."
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Abstract. Two computer techniques are described that the authors used to confirm Waring's Conjecture to 471,600,000, thus extending R. M. Stemmler's result of 200,000 computed in 1964. M. C. Wunderlich increased the result to 175,600,000 in August 1988, and in the following October, J. M. Kubina, using a method suggested by JeanMarc Deshouillers, raised it to 471,600,000. In 1770 Edward Waring asserted in his Meditationes Algebraicae that every positive integer can be written as the sum of four squares, as the sum of nine nonnegative cubes, and as the sum of nineteen fourth powers. Later that year Lagrange proved the case for the sums of four squares. The function g(k) is usually defined as the smallest integer n such that every positive integer can be written as the sum of n kth powers of nonnegative integers. In 1772 Euler obtained a lower bound for g(k) by noting that if (1) 3k = q2k + r, with 0 < r < 2k, then the number q2k \ =(q