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An improved Las Vegas primality test

1989
*
Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89
*

We present a modification of the Goldwasser-Kilian-Atkin

doi:10.1145/74540.74545
dblp:conf/issac/KaltofenVY89
fatcat:qguddgzxu5g6ldrcxqtwc32lhm
*primality**test*, which, when given*an*input n, outputs either prime or composite, along with a certificate of correctness which may be verified in ... This is a substantial*improvement*, in that the Watson equations have much smaller coefficients than do the Hilbert equations. ... assertion of*primality*. ...##
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Taxonomy and Practical Evaluation of Primality Testing Algorithms
[article]

2020
*
arXiv
*
pre-print

In this paper,

arXiv:2006.08444v1
fatcat:ndiycg36arh3rk6fau72nck5iu
*an*intensive survey is thoroughly conducted among the several*primality**testing*algorithms showing the pros and cons, the time complexity, and a brief summary of each algorithm. ...*Primality**testing*algorithms are used to determine whether a particular number is prime or composite. ... Experimental Setup for*Las*-*Vegas**Test*Proth, Lucas, and Picklington*tests*are randomized*Las*-*Vegas**primality**tests*which means that they always give the right answer. ...##
###
Page 1191 of Mathematical Reviews Vol. , Issue 87c
[page]

1987
*
Mathematical Reviews
*

Fiirer, Martin (CH-ZRCH) 87c:11123 Deterministic and

*Las**Vegas**primality**testing*algorithms. Automata, languages and programming (Nafplion, 1985), 199-209, Lecture Notes in Comput. ... This paper is*an*excellent up-to-date survey of*primality**test*- ing and factoring methods, including the recent*primality**testing*method due to L. M. Adleman et al. ...##
###
Page 3201 of Mathematical Reviews Vol. , Issue 95f
[page]

1995
*
Mathematical Reviews
*

The new bounds give us

*an**improvement*on previous bounds for the minimum distance of the duals of BCH codes. ... (English summary) Finite fields: theory, applications, and algorithms (*Las**Vegas*, NV, 1993), 213-216, Contemp. Math., 168, Amer. Math. Soc., Providence, RI, 1994. ...##
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Random primes in arithmetic progressions
[article]

2022
*
arXiv
*
pre-print

However, sampling random b-bit integers and

arXiv:2202.05955v2
fatcat:pa4saqzrlzgnjg7nqq6xzofad4
*testing*their*primality*using AKS algorithm results in a*Las**Vegas*randomized algorithm. ... The well-known technique for this is to sample random integers and*test*them for*primality*. In order to get*Las**Vegas*algorithm, we rely on the celebrated AKS algorithm. ...##
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Fast Primality Testing for Integers That Fit into a Machine Word

2015
*
Conference on Current Trends in Theory and Practice of Informatics
*

For large integers, the most efficient

dblp:conf/sofsem/ForisekJ15
fatcat:sgkxx7nx6jaedo3ftkgwa5i5fm
*primality**tests*are probabilistic. However, for integers with a small fixed number of bits the best*tests*in practice are deterministic. ... Up to our knowledge, our implementations are the fastest one-shot deterministic*primality**tests*for 32-bit and 64-bit integers to date. ... We also*tested*about 1000 pairs of bases, each time computing the count of numbers that are strong pseudoprimes with both bases. ...##
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Recent developments in primality proving

1999
*
Mathematics and Computers in Simulation
*

While proving compositeness of a natural number is a computational task that can be easily done in polynomial time, proving

doi:10.1016/s0378-4754(99)00051-8
fatcat:xlksnpewr5bylfxq6tv7dntqhu
*primality*of*an*arbitrary positive i n teger is a harder task. ... Only two main streams of usefull algorithms are known in this direction: elliptic curve*primality*provers (ECPP, Mo1]) and cyclotomy ( BovdH], Mi1]). ... The more common*Las**Vegas*variant uses randomization only for searching several small primitive roots of unity of orders p k j , which can be found with high probability of success. ...##
###
Page 3841 of Mathematical Reviews Vol. , Issue 95g
[page]

1995
*
Mathematical Reviews
*

(English summary) Finite fields: theory, applications, and algorithms (

*Las**Vegas*, NV, 1993), 227-233, Contemp. Math., 168, Amer. Math. Soc., Providence, RI, 1994. ... He also describes the Carmichael numbers with respect to a pri- mality*test*using Rédei functions. The Solovay-Strassen*primality**test*is based on the congruence k'?~!)/? = (<) mod p. ...##
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Spatially Regularized Fusion of Multiresolution Digital Surface Models

2017
*
IEEE Transactions on Geoscience and Remote Sensing
*

*An*efficient solver is presented to solve the optimization in reasonable time, e.g. running in real-time on standard computer vision camera images. ... We further incorporate local planarity assumption as

*an*additional constraint to the optimization problem, thus reducing the noise compared to pixel-wise approaches. ... ACKNOWLEDGMENT The authors would like to thank European Space Imaging (EUSI) for providing the WorldView-2 data of London, and the SkyBox video of

*Las*

*Vegas*. ...

##
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Infinite sets of primes with fast primality tests and quick generation of large primes

1989
*
Mathematics of Computation
*

This answers affirmatively the question of whether there exists

doi:10.1090/s0025-5718-1989-0968154-x
fatcat:thorficedzfydbim7g53nt2ybu
*an*infinite set of primes whose membership can be*tested*in polynomial time, and is a main result of the paper. ... Also, for every n € Q, we show how to randomly produce a proof of the*primality*of n. The expected time is that needed for l| exponentiations mod n. ... We thank the referee, who made many useful comments that helped*improve*the paper. ...##
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Almost all primes can be quickly certified

1986
*
Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86
*

This paper presents a new probabilistie

doi:10.1145/12130.12162
dblp:conf/stoc/GoldwasserK86
fatcat:r33yd4ohibd7vivthksverieya
*primality**test*. ... The*test*is different from the*tests*of Miller [M], Solovay-Strassen [SSI, and Rabin [R] in that its assertions of*primality*are certain, rather than being correct with high probability or dependent on ... • Is there a probabilistic*primality**test*which is alaways correct and probably fast on every prime input, i.e a*Las**Vegas**primality**test*? ...##
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Primality testing using elliptic curves

1999
*
Journal of the ACM
*

Under the conjecture that the gap between consecutive primes is bounded by some polynomial in their size, the

doi:10.1145/320211.320213
fatcat:t6u76trumnamvmbyew5aitjflm
*test*is shown to run in expected polynomial time for all primes, yielding a*Las**Vegas**primality*... We present a*primality*proving algorithm-a probabilistic*primality**test*that produces short certificates of*primality*on prime inputs. ... This algorithm has been further*improved*in Kaltofen et al. [1989] and Atkin and Morain [1993] . Further discussions of elliptic curves and*primality**testing*may be found in Morain [1990] . ...##
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Randomized Algorithms: Methods and Techniques

2011
*
International Journal of Computer Applications
*

Indeed, the problem of

doi:10.5120/3436-4510
fatcat:fnbjh73m3fawte2n4t75dzg5qe
*testing*a given integer for*primality*has no known deterministic polynomial-time algorithm. ... The*Las**Vegas*method is a randomized method which also uses random variable or random processes, but it always produces the correct result (not*an*approximation). ...##
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The NP-completeness column

2005
*
ACM Transactions on Algorithms
*

This means that the

doi:10.1145/1077464.1077476
fatcat:dactzqst4bhqrnqbxy26vyeqyq
*Las**Vegas*algorithm was far from practical, although its mere existence led many to conjecture that*primality**testing*is in P. ... Still more was known about*primality**testing*in 1992. ...##
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Page 3110 of Mathematical Reviews Vol. , Issue 95e
[page]

1995
*
Mathematical Reviews
*

(English summary) Finite fields: theory, applications, and algorithms (

*Las**Vegas*, NV, 1993), 51-61, Contemp. Math., 168, Amer. Math. Soc., Providence, RI, 1994. ... Nonetheless, to*improve*the security of such a coding, it is necessary to*test*the algorithms which find such words in random codes. ...
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