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Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 520 (1 self)
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ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a
Almost All Primes Can be Quickly Certified
"... This paper presents a new probabilistic primality test. Upon termination the test outputs "composite" or "prime", along with a short proof of correctness, which can be verified in deterministic polynomial time. The test is different from the tests of Miller [M], SolovayStrassen ..."
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Cited by 87 (4 self)
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This paper presents a new probabilistic primality test. Upon termination the test outputs "composite" or "prime", along with a short proof of correctness, which can be verified in deterministic polynomial time. The test is different from the tests of Miller [M], SolovayStrassen
Random Sampling Techniques and Parallel Algorithms Design
, 2003
"... 3.1.1 Randomized Algorithms The technique of randomizing an algorithm to improve its efficiency was first introduced in 1976 independently by Rabin and Solovay & Strassen. Since then, this idea has been used to solve myriads of computational problems ..."
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3.1.1 Randomized Algorithms The technique of randomizing an algorithm to improve its efficiency was first introduced in 1976 independently by Rabin and Solovay & Strassen. Since then, this idea has been used to solve myriads of computational problems
A Note On Monte Carlo Primality Tests And Algorithmic Information Theory
, 1978
"... Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coinflipping and whose conclusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random or patternles ..."
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Cited by 10 (1 self)
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Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coinflipping and whose conclusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random
A Binary Algorithm for the Jacobi Symbol
 ACM SIGSAM Bulletin
, 1993
"... We present a new algorithm to compute the Jacobi symbol, based on Stein's binary algorithm for the greatest common divisor, and we determine the worstcase behavior of this algorithm. Our implementation of the algorithm runs approximately 725% faster than traditional methods on inputs of size ..."
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Cited by 7 (1 self)
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of size 1001000 decimal digits. 1 Introduction Efficient computation of the Jacobi symbol \Gamma a n \Delta is an important component of the Monte Carlo primality test of Solovay and Strassen [9]. Algorithms for computing the Jacobi symbol can also be found on symbolic algebra systems
A Note on Monte Carlo Primality Tests and Algorithmic Information Theory
, 1978
"... Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coinflipping and whose conclusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random or patternles ..."
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Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coinflipping and whose conclusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random
Ecole Polytechnique Fédérale de Lausanne Bachelor semester project: Randomized and Deterministic Primality Testing
"... This project presents some randomized and deterministic algorithms of number primality testing, and, for some of them, their implementation in C++. The algorithms studied here are the naive algorithm (deterministic), the MillerRabin algorithm (randomized), the Fermat algorithm (randomized), the Sol ..."
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), the SolovayStrassen algorithm (randomized) and the AKS algorithm (deterministic). These algorithms are presented with the number theory they need to be understood and with some proofs of the theorems they use.
Primality Testing with Fewer Random Bits
 Computational Complexity
, 1993
"... In the usual formulations of the MillerRabin and SolovayStrassen primality testing algorithms for a number n, the algorithm chooses "candidates" x 1 , x 2 , ..., x k uniformly and independently at random from Z n , and tests if any is a "witness" to the compositeness of n. For ..."
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Cited by 2 (0 self)
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In the usual formulations of the MillerRabin and SolovayStrassen primality testing algorithms for a number n, the algorithm chooses "candidates" x 1 , x 2 , ..., x k uniformly and independently at random from Z n , and tests if any is a "witness" to the compositeness of n
Towards a deterministic polynomialtime Primality Test
, 2002
"... We examine a primality testing algorithm presented in [Man99] and the related conjecture in [Bha01]. We show that this test is stronger than most of the popular tests today: the Fermat test, the Solovay Strassen test and a strong form of the Fibonacci test. From this, we show the correctness of the ..."
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Cited by 7 (2 self)
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We examine a primality testing algorithm presented in [Man99] and the related conjecture in [Bha01]. We show that this test is stronger than most of the popular tests today: the Fermat test, the Solovay Strassen test and a strong form of the Fibonacci test. From this, we show the correctness
Results 1  10
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