Results 1 - 10 of 11

Fast probabilistic algorithms for verification of polynomial identities

by J. T. Schwartz - J. ACM , 1980
"... ABSTRACT The starthng success of the Rabm-Strassen-Solovay 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 ..."
Abstract - Cited by 520 (1 self) - Add to MetaCart
ABSTRACT The starthng success of the Rabm-Strassen-Solovay 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

Notes on Public Key Cryptography And Primality Testing Part 1: Randomized Algorithms Miller–Rabin and Solovay–Strassen Tests

by Jean Gallier, C Jean Gallier
"... ..."
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Abstract not found

Almost All Primes Can be Quickly Certified

by Shafi Goldwasser, Joe Kilian
"... 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], Solovay-Strassen ..."
Abstract - Cited by 87 (4 self) - Add to MetaCart
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], Solovay-Strassen

Random Sampling Techniques and Parallel Algorithms Design

by Mukund N. Thapa, Sanguthevar Rajasekaran, Sandeep Sen , 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

by Gregory J. Chaitin, Jacob T. Schwartz , 1978
"... Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coin-flipping 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 ..."
Abstract - Cited by 10 (1 self) - Add to MetaCart
Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coin-flipping 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

by Jeffrey Shallit, Jonathan Sorenson - 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 worst-case behavior of this algorithm. Our implementation of the algorithm runs approximately 7--25% faster than traditional methods on inputs of size ..."
Abstract - Cited by 7 (1 self) - Add to MetaCart
of size 100--1000 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

by Carlo Primality, Gregory J. Chaitin, Jacob T. Schwartz , 1978
"... Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coin-flipping 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 coin-flipping 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

by Monica Perrenoud, Professor Mohammad, Amin Shokrollahi
"... 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 Miller-Rabin algorithm (randomized), the Fermat algorithm (randomized), the Sol ..."
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), the Solovay-Strassen 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

by René Peralta, Victor Shoup - Computational Complexity , 1993
"... In the usual formulations of the Miller-Rabin and Solovay-Strassen 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 ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
In the usual formulations of the Miller-Rabin and Solovay-Strassen 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 polynomial-time Primality Test

by Neeraj Kayal, Nitin Saxena, Supervisor Dr. Manindra Agarwal , 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 ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
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 of 11