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An improved Las Vegas primality test

E. Kaltofen, T. Valente, N. Yui
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 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.  ... 
doi:10.1145/74540.74545 dblp:conf/issac/KaltofenVY89 fatcat:qguddgzxu5g6ldrcxqtwc32lhm

Taxonomy and Practical Evaluation of Primality Testing Algorithms [article]

Anas AbuDaqa, Amjad Abu-Hassan, Muhammad Imam
2020 arXiv   pre-print
In this paper, 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.  ... 
arXiv:2006.08444v1 fatcat:ndiycg36arh3rk6fau72nck5iu

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.  ... 

Random primes in arithmetic progressions [article]

Pascal Giorgi, Bruno Grenet, Armelle Perret du Cray, Daniel S. Roche
2022 arXiv   pre-print
However, sampling random b-bit integers and 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.  ... 
arXiv:2202.05955v2 fatcat:pa4saqzrlzgnjg7nqq6xzofad4

Fast Primality Testing for Integers That Fit into a Machine Word

Michal Forisek, Jakub Jancina
2015 Conference on Current Trends in Theory and Practice of Informatics  
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.  ...  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.  ... 
dblp:conf/sofsem/ForisekJ15 fatcat:sgkxx7nx6jaedo3ftkgwa5i5fm

Recent developments in primality proving

Preda Mihăilescu
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 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.  ... 
doi:10.1016/s0378-4754(99)00051-8 fatcat:xlksnpewr5bylfxq6tv7dntqhu

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.  ... 

Spatially Regularized Fusion of Multiresolution Digital Surface Models

Georg Kuschk, Pablo d'Angelo, David Gaudrie, Peter Reinartz, Daniel Cremers
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.  ... 
doi:10.1109/tgrs.2016.2625040 fatcat:abrpiwtptrdmhn3rqpi66a46ne

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

J{ános Pintz, William L. Steiger, Endre Szemer{édi
1989 Mathematics of Computation  
This answers affirmatively the question of whether there exists 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.  ... 
doi:10.1090/s0025-5718-1989-0968154-x fatcat:thorficedzfydbim7g53nt2ybu

Almost all primes can be quickly certified

S Goldwasser, J Kilian
1986 Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86  
This paper presents a new probabilistie 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 ?  ... 
doi:10.1145/12130.12162 dblp:conf/stoc/GoldwasserK86 fatcat:r33yd4ohibd7vivthksverieya

Primality testing using elliptic curves

Shafi Goldwasser, Joe Kilian
1999 Journal of the ACM  
Under the conjecture that the gap between consecutive primes is bounded by some polynomial in their size, the 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] .  ... 
doi:10.1145/320211.320213 fatcat:t6u76trumnamvmbyew5aitjflm

Randomized Algorithms: Methods and Techniques

Kuldeep Sharma, Deepak Garg
2011 International Journal of Computer Applications  
Indeed, the problem of 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).  ... 
doi:10.5120/3436-4510 fatcat:fnbjh73m3fawte2n4t75dzg5qe

The NP-completeness column

David S. Johnson
2005 ACM Transactions on Algorithms  
This means that the 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.  ... 
doi:10.1145/1077464.1077476 fatcat:dactzqst4bhqrnqbxy26vyeqyq

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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