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pro vyhledávání: '"Lucas primality test"'
Akademický článek
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Akademický článek
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Publikováno v:
Arab Journal of Mathematical Sciences, Vol 24, Iss 1, Pp 9-15 (2018)
We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p ∣ F p − p 5 . We then discuss these results in the context of primality testing.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9daadc71291a632453b2fddf109ebb45
http://www.sciencedirect.com/science/article/pii/S1319516617300646
http://www.sciencedirect.com/science/article/pii/S1319516617300646
Autor:
Gyöngyvér Kiss
Publikováno v:
Acta Universitatis Sapientiae: Informatica, Vol 7, Iss 2, Pp 125-142 (2015)
This paper deals with an implementation of the elliptic curve primality proving (ECPP) algorithm of Atkin and Morain. As the ECPP algorithm is not deterministic, we are developing a strategy to avoid certain situations in which the original implement
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b3b527be39395513a27ddd20438b8db2
https://doaj.org/article/cc5bd56c40ca4302ad5745c6a259d5b4
https://doaj.org/article/cc5bd56c40ca4302ad5745c6a259d5b4
Publikováno v:
Designs, Codes and Cryptography. 77:515-539
In his extensive memoir on the sequences that now bear his name, Lucas provided some primality tests for numbers $$N$$N, where $$N\pm 1$$N±1 is divisible by a large prime power. No proofs were provided for these tests, and they are not correct as st
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a8da78def8bb60a11f6c6f2ae951467d
https://doi.org/10.1007/s10623-015-0088-0
https://doi.org/10.1007/s10623-015-0088-0
Autor:
Shigenori Uchiyama, Kazuki Azami
Publikováno v:
JSIAM Letters. 6:1-4
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6f73f9f7c992a215c701e39623a13347
https://doi.org/10.14495/jsiaml.6.1
https://doi.org/10.14495/jsiaml.6.1
Autor:
Shamil Ishmukhametov, B. Mubarakov
Publikováno v:
Lobachevskii Journal of Mathematics. 34:304-312
The well-known Miller-Rabin Primality Test MRPT is used to check naturals to be prime or composite. We study the dependence between the length of testing numbers and the number of rounds of MRPT sufficient to give the correct answer and give some rec
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::edbe24f1275e53786fc5ccb3e29c6f7f
https://doi.org/10.1134/s1995080213040100
https://doi.org/10.1134/s1995080213040100
Publikováno v:
International Journal of Computer Network and Information Security. 5:51-57
The RSA cryptosystem, invented by Ron Rivest, Adi Shamir and Len Adleman was first publicized in the August 1977 issue of Scientific A merican. The security level of this algorith m very much depends on two large prime nu mbers. To check the primalit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::36785c5a981313ae1c8d757437deb5a1
https://doi.org/10.5815/ijcnis.2013.09.07
https://doi.org/10.5815/ijcnis.2013.09.07
Autor:
Sang-Un Lee
Publikováno v:
The Journal of the Institute of Webcasting, Internet and Telecommunication. 13:103-109
Miller-Rabin method is the most prevalently used primality test. However, this method mistakenly reports a Carmichael number or semi-prime number as prime (strong lier) although they are composite numbers. To eradicate this problem, it selects k numb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9f50b3297366a397759acf6d22761645
https://doi.org/10.7236/jiibc.2013.13.3.103
https://doi.org/10.7236/jiibc.2013.13.3.103
Publikováno v:
2016 International Conference on Accessibility to Digital World (ICADW).
With the increasing popularity and usage of cryptography and network security, prime generation and primality testing has become a significant issue. Various primality tests have been introduced in the past and we compare and contrast some popular pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dcdcea3fce0821a08208968d19f60f16
https://doi.org/10.1109/icadw.2016.7942510
https://doi.org/10.1109/icadw.2016.7942510