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Verification of the MillerRabin Probabilistic Primality Test
, 2003
"... Using the HOL theorem prover, we apply our formalization of probability theory to specify and verify the MillerRabin probabilistic primality test. The version of the test commonly found in algorithm textbooks implicitly accepts probabilistic termination, but our own verified implementation satisfie ..."
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Cited by 18 (3 self)
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Using the HOL theorem prover, we apply our formalization of probability theory to specify and verify the MillerRabin probabilistic primality test. The version of the test commonly found in algorithm textbooks implicitly accepts probabilistic termination, but our own verified implementation
Accelerating the Distributed Multiplication Protocol with Applications to the Distributed MillerRabin Primality Test
"... Summary. In the light of information security it is highly desirable to avoid a “single point of failure ” because this would be an attractive target for attackers. Cryptographic protocols for distributed computations are important techniques in pursuing this goal. An essential module in this conte ..."
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classical interpolation formula. The distributed version of the famous probabilistic primality test of Miller and Rabin is built of several modules, which depend on distributed multiplications. Applications of the new method to these modules is studied and its importance for distributed signatures
The Rabin Miller Probabilistic Primality Test: Some Results on the Number of NonWitnesses to Compositeness
"... This paper introduces the reader to the RabinMiller probabilistic primality test, the concept of nonwitnesses to compositeness, and the problem of determining the number of nonwitnesses to compositeness. Given in this paper are two conjectures: one on determining the number of nonwitnesses to co ..."
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This paper introduces the reader to the RabinMiller probabilistic primality test, the concept of nonwitnesses to compositeness, and the problem of determining the number of nonwitnesses to compositeness. Given in this paper are two conjectures: one on determining the number of non
Fast primality testing for integers that fit . . .
"... For large integers, the most efficient primality tests are probabilistic. However, for integers with a small fixed number of bits the best tests in practice are deterministic. Currently the best known tests of this type involve 3 rounds of the MillerRabin test for 32bit integers and 7 rounds for 6 ..."
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For large integers, the most efficient primality tests are probabilistic. However, for integers with a small fixed number of bits the best tests in practice are deterministic. Currently the best known tests of this type involve 3 rounds of the MillerRabin test for 32bit integers and 7 rounds
Formal Verification of Probabilistic Algorithms
, 2002
"... This thesis shows how probabilistic algorithms can be formally verified using a mechanical theorem prover. We begin with an extensive foundational development of probability, creating a higherorder logic formalization of mathematical measure theory. This allows the definition of the probability spac ..."
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Cited by 53 (3 self)
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probabilistic programs: sampling algorithms for four probability distributions; some optimal procedures for generating dice rolls from coin flips; the symmetric simple random walk. In addition, we verify the MillerRabin primality test, a wellknown and commercially used probabilistic algorithm. Our fundamental
Probabilistic Hoarelike Logics in Comparison
"... Abstract. Probabilistic algorithms are recognized for their simplicity and speed. A canonical example is the MillerRabin primality test algorithm. It is simple and achieves high accuracy with a small amount of computation. In this paper, we present two verification exercises of this algorithm usin ..."
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Abstract. Probabilistic algorithms are recognized for their simplicity and speed. A canonical example is the MillerRabin primality test algorithm. It is simple and achieves high accuracy with a small amount of computation. In this paper, we present two verification exercises of this algorithm
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
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], Solovay
Secure Geographic Routing in Wireless Sensor Networks
, 2013
"... the nonexclusive right to publish the Work electronically and in a noncommercial purpose make it accessible on the Internet. The Author warrants that he/she is the author to the Work, and warrants that the Work does not contain text, pictures or other material that violates copyright law. The Auth ..."
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the nonexclusive right to publish the Work electronically and in a noncommercial purpose make it accessible on the Internet. The Author warrants that he/she is the author to the Work, and warrants that the Work does not contain text, pictures or other material that violates copyright law. The Author shall, when transferring the rights of the Work to a third party (for example a publisher or a company); acknowledge the third party about this agreement. If the Author has signed a copyright agreement with a third party regarding the Work, the Author warrants hereby that he/she has obtained any necessary permission from this third party to let Chalmers University of Technology and University of Gothenburg store the Work electronically and make it accessible on the Internet.