Relevant bibliographies by topics / Primality test

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Primality test'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Primality test"

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Martino, Gabriele. "Primality Test." American Journal of Computational Mathematics 03, no. 01 (2013): 59–60. http://dx.doi.org/10.4236/ajcm.2013.31009.

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Lee, Sang-Un, and Myeong-Bok Choi. "The Primality Test." Journal of the Korea Society of Computer and Information 16, no. 8 (2011): 103–8. http://dx.doi.org/10.9708/jksci.2011.16.8.103.

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Valluri, Maheswara Rao. "Combinatorial primality test." ACM Communications in Computer Algebra 54, no. 4 (2020): 129–33. http://dx.doi.org/10.1145/3465002.3465004.

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In 1879, Laisant-Beaujeux gave the following result without proof: If n is a prime, then [EQUATION] This paper provides proofs of the result of Laisant-Beaujeux in two cases explicitly: (1) If an integer of the form n = 4k + 1, k > 0 is prime, then ([EQUATION]) and (2) If an integer of the form n = 4k + 3, k ≥ 0 is prime, then [EQUATION]. In addition, the author proposes important conjectures based on the converse of the above theorems which aim to establish primality of n. These conjectures are scrutinized by the given combinatorial primality test algorithm which can also distinguish patte
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Chau, H. F., and H. K. Lo. "Primality Test Via Quantum Factorization." International Journal of Modern Physics C 08, no. 02 (1997): 131–38. http://dx.doi.org/10.1142/s0129183197000138.

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We consider a probabilistic quantum implementation of a variation of the Pocklington–Lehmer N - 1 primality test using Shor's algorithm. O ( log 3 N log log N log log log N) elementary q-bit operations are required to determine the primality of a number N, making it (asymptotically) the fastest known primality test. Thus, the potential power of quantum mechanical computers is once again revealed.
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Zhang, Zhenxiang, Weiping Zhou, and Xianbei Liu. "A generalised Lucasian primality test." Bulletin of the Australian Mathematical Society 74, no. 3 (2006): 419–41. http://dx.doi.org/10.1017/s0004972700040478.

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We present a primality test for numbers of the form Mh, n = h·2n ±1 (in particular with h divisible by 15), which generalises Berrizbeitia and Berry's test for such numbers with h ≢ 0 mod 5. With our generalised test, the primality of such a number Mh, n can be proved by means of a Lucas sequence with a seed determined by h and πq — primary irreducible divisor of a prime q ≡ 1 mod 4. We call the prime q a judge of the number Mh, n. We prescribe a sequence S of 48 primes ≡ 1 mod 4 in the interval [13, 2593] such that, for all odd h = 15t < 108 and for all n < 7.3 1011, each number Mh, n h
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Moshonkin, A. G., and I. M. Khamitov. "A New Probabilistic Primality Test." Journal of Mathematical Sciences 249, no. 1 (2020): 79–84. http://dx.doi.org/10.1007/s10958-020-04920-z.

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Couveignes, Jean-Marc, Tony Ezome, and Reynald Lercier. "A faster pseudo-primality test." Rendiconti del Circolo Matematico di Palermo 61, no. 2 (2012): 261–78. http://dx.doi.org/10.1007/s12215-012-0088-0.

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Ega Gradini. "COMPARISON STUDY OF FERMAT, SOLOVAY-STRASSEN AND MILLER-RABIN PRIMALITY TEST USING MATHEMATICA 6.0." Visipena Journal 3, no. 1 (2012): 1–10. http://dx.doi.org/10.46244/visipena.v3i1.48.

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This paper presents three primality tests; Fermat test, Solovay-Strassen test, and Rabin-Miller test. Mathematica software is used to carry out the primality tests. The application of Fermat’s Litle Theorem as well as Euler’s Theorem on the tests was also discussed and this leads to the concept of pseudoprime. This paper is also discussed some results on pseudoprimes with certain range and do quantitative comparison. Those primality tests need to be evaluated in terms of its ability to compute as well as correctness in determining primality of given numbers. The answer to this is to create a s
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Ishmukhametov, Shamil Talgatovich, Bulat Gazinurovich Mubarakov, and Ramilya Gakilevna Rubtsova. "On the Number of Witnesses in the Miller–Rabin Primality Test." Symmetry 12, no. 6 (2020): 890. http://dx.doi.org/10.3390/sym12060890.

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In this paper, we investigate the popular Miller–Rabin primality test and study its effectiveness. The ability of the test to determine prime integers is based on the difference of the number of primality witnesses for composite and prime integers. Let W ( n ) denote the set of all primality witnesses for odd n. By Rabin’s theorem, if n is prime, then each positive integer a < n is a primality witness for n. For composite n, the power of W ( n ) is less than or equal to φ ( n ) / 4 where φ ( n ) is Euler’s Totient function. We derive new exact formulas for the power of W ( n ) depending on
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Lee, Sang-Un. "A Step-by-Step Primality Test." Journal of the Institute of Webcasting, Internet and Telecommunication 13, no. 3 (2013): 103–9. http://dx.doi.org/10.7236/jiibc.2013.13.3.103.

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Dissertations / Theses on the topic "Primality test"

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Siracusa, Mia. "Primality Testing." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/scripps_theses/1073.

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Hammad, Yousef Bani. "Novel Methods for Primality Testing and Factoring." Queensland University of Technology, 2005. http://eprints.qut.edu.au/16142/.

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From the time of the Greeks, primality testing and factoring have fascinated mathematicians, and for centuries following the Greeks primality testing and factorization were pursued by enthusiasts and professional mathematicians for their intrisic value. There was little practical application. One example application was to determine whether or not the Fermat numbers, that is, numbers of the form F;, = 2'" + 1 were prime. Fermat conjectured that for all n they were prime. For n = 1,2,3,4, the Fermat numbers are prime, but Euler showed that F; was not prime and to date no F,, n 2 5 has be
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Kasarabada, Yasaswy. "A Verilog Description and Efficient Hardware Implementation of the Baillie-PSW Primality Test." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1471347471.

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Giostra, Sara. "Il test di primalità aks." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9033/.

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La tesi presenta l'algoritmo AKS, deterministico e polinomiale, scoperto dai matematici Agrawal, Kayal e Saxena nel 2002. Esso si basa su una generalizzazione del Piccolo Teorema di Fermat all'anello dei polinomi a coefficienti in Zp.
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Wedeniwski, Sebastian. "Primality tests on commutator curves." [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=963295438.

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Arnault, François. "Sur quelques tests probabilistes de primalité." Poitiers, 1993. http://www.theses.fr/1993POIT2317.

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Nous étudions dans cette thèse quelques tests probabilistes de primalité, en particulier ceux qui, vraisemblablement à cause de leur simplicité et de leur rapidité d'éxécution, sont implantés dans les systèmes de calcul formel usuels. Nous commençons par présenter dans le chapitre 1 le test probabiliste de primalité le plus connu : le test de Rabin. Nous rappelons entre autres le théorème de Rabin, qui permet de majorer la probabilité d'échec de ce test. Nous donnons dans les chapitres 3 et 6 deux méthodes permettant de construire des nombres composés déclarés premiers par le test de Rabin des
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Morain, François. "Courbes elliptiques et tests de primalité." Lyon 1, 1990. http://www.theses.fr/1990LYO10170.

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Nous decrivons dans cette these l'application de la theorie des courbes elliptiques definies sur les corps finis a la construction d'algorithmes efficaces de primalite exacte. Nous faisons le lien entre le probleme de la representation des nombres premiers par des formes quadratiques binaires et la theorie du corps de classe. A ce propos, nous donnons un algorithme rapide de construction du corps de classe d'un corps quadratique imaginaire a l'aide des fonctions de weber. Nous en deduisons le calcul des invariants des courbes elliptiques a multiplication complexe dans un corps fini en resolvan
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Breitenbacher, Dominik. "Paralelizace faktorizace celých čísel z pohledu lámání RSA." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2015. http://www.nusl.cz/ntk/nusl-234905.

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This paper follows up the factorization of integers. Factorization is the most popular and used method for RSA cryptoanalysis. The SIQS was chosen as a factorization method that will be used in this paper. Although SIQS is the fastest method (up to 100 digits), it can't be effectively computed at polynomial time, so it's needed to look up for options, how to speed up the method as much as possible. One of the possible ways is paralelization. In this case OpenMP was used. Other possible way is optimalization. The goal of this paper is also to show, how easily is possible to use paralelizion and
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Ezome, Mintsa Tony Mack Robert. "Courbes elliptiques, cyclotomie et primalité." Toulouse 3, 2010. http://thesesups.ups-tlse.fr/825/.

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L'information est très précieuse, c'est pourquoi au moment de la stocker ou de la transmettre, il est nécessaire de la protéger. La factorisation des grands entiers est un problème diffcile, elle constitue ainsi une base de sécurité en cryptographie asymétrique. Il est donc très utile de pouvoir déterminer la primalité de grands entiers afin de construire des entiers difficilement factorisables qui pourront servir en cryptographie asymétrique. Pour ce faire on a recours aux tests de primalité. Le test AKS (inventé par Agrawal, Kayal et Saxena) est un algorithme polynômial déterministe de preuv
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Bronder, Justin S. "The AKS Class of Primality Tests: A Proof of Correctness and Parallel Implementation." Fogler Library, University of Maine, 2006. http://www.library.umaine.edu/theses/pdf/BronderJS2006.pdf.

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Book chapters on the topic "Primality test"

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Stiglic, Anton. "Primality Test." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_469.

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Liskov, Moses. "Fermat Primality Test." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_448.

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Stiglic, Anton. "Probabilistic Primality Test." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_472.

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Kozen, Dexter C. "Miller’s Primality Test." In The Design and Analysis of Algorithms. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4400-4_38.

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Atkin, A. "Intelligent primality test offer." In AMS/IP Studies in Advanced Mathematics. American Mathematical Society, 1997. http://dx.doi.org/10.1090/amsip/007/01.

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Sethi, Gunjan, and Harsh. "Limiting Check Algorithm: Primality Test." In Advances in Intelligent Systems and Computing. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8289-9_67.

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Liskov, Moses. "Miller–Rabin Probabilistic Primality Test." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_461.

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Kozen, Dexter C. "Analysis of Miller’s Primality Test." In The Design and Analysis of Algorithms. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-4400-4_39.

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Bressoud, David M. "Primitive Roots and a Test for Primality." In Factorization and Primality Testing. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-4544-5_9.

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Dietzfelbinger, Martin. "5. The Miller-Rabin Test." In Primality Testing in Polynomial Time. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-25933-6_5.

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Conference papers on the topic "Primality test"

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Kaltofen, E., T. Valente, and N. Yui. "An improved Las Vegas primality test." In the ACM-SIGSAM 1989 international symposium. ACM Press, 1989. http://dx.doi.org/10.1145/74540.74545.

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Asaduzzaman, Abu, Chok M. Yip, and Anindya Maiti. "CUDA-assisted energy-efficient primality test." In SOUTHEASTCON 2014. IEEE, 2014. http://dx.doi.org/10.1109/secon.2014.6950678.

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da Silva, Joao Carlos Leandro. "Carmichael numbers and a new primality test." In Electronics Engineers in Israel (IEEEI 2010). IEEE, 2010. http://dx.doi.org/10.1109/eeei.2010.5662138.

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Daghigh, Hassan, Amir Mehdi Yazdani kashani, and Ruholla Khodakaramian Gilan. "Primality test for mersenne numbers using elliptic curves." In 2014 11th International ISC Conference on Information Security and Cryptology (ISCISC). IEEE, 2014. http://dx.doi.org/10.1109/iscisc.2014.6994029.

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Purdy, Carla, Yasaswy Kasarabada, and George Purdy. "Hardware implementation of the Baillie-PSW primality test." In 2017 IEEE 60th International Midwest Symposium on Circuits and Systems (MWSCAS). IEEE, 2017. http://dx.doi.org/10.1109/mwscas.2017.8053007.

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Galligo, André, and Stephen Watt. "A numerical absolute primality test for bivariate polynomials." In the 1997 international symposium. ACM Press, 1997. http://dx.doi.org/10.1145/258726.258788.

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Le Masle, Adrien, Wayne Luk, and Csaba Andras Moritz. "Parametrized hardware architectures for the Lucas primality test." In 2011 International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation (SAMOS XI). IEEE, 2011. http://dx.doi.org/10.1109/samos.2011.6045453.

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Li, Huiheng, and Rui Wang. "A primality test based on modular hyperbolic curves." In 2020 2nd International Conference on Machine Learning, Big Data and Business Intelligence (MLBDBI). IEEE, 2020. http://dx.doi.org/10.1109/mlbdbi51377.2020.00013.

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Hosung Jo and Heejin Park. "Performance analysis and improvement of JPV primality test for smart IC cards." In 2014 International Conference on Big Data and Smart Computing (BIGCOMP). IEEE, 2014. http://dx.doi.org/10.1109/bigcomp.2014.6741451.

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Dordevic, Goran, and Milan Markovic. "On Optimization of Miller-Rabin Primality Test on TI TMS320C54x Signal Processors." In 2007 14th International Workshop in Systems, Signals and Image Processing and 6th EURASIP Conference focused on Speech and Image Processing, Multimedia Communications and Services - EC-SIPMCS 2007. IEEE, 2007. http://dx.doi.org/10.1109/iwssip.2007.4381195.

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