Using the HOL theorem prover, we apply our formalization of probability theory to specify and verify the Miller-Rabin probabilistic primality test. The version of the test commonly found in algorithm textbooks implicitly accepts probabilistic termination, but our own verified implementation

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

This paper introduces the reader to the Rabin-Miller probabilistic primality test, the concept of non-witnesses to compositeness, and the problem of determining the number of non-witnesses to compositeness. Given in this paper are two conjectures: one on determining the number of non

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 Miller-Rabin test for 32-bit integers and 7 rounds

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 Miller-Rabin primality test, a well-known and commercially used probabilistic algorithm. Our fundamental

Abstract. Probabilistic algorithms are recognized for their simplicity and speed. A canonical example is the Miller-Rabin primality test algorithm. It is simple and achieves high accuracy with a small amount of computation. In this pa-per, we present two verification exercises of this algorithm

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

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

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