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Relevant bibliographies by topics / Fermat's test

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Journal articles

Academic literature on the topic 'Fermat's test'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 January 2023

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Journal articles on the topic "Fermat's test"

1

Aminudin, Aminudin, and Eko Budi Cahyono. "A Practical Analysis of the Fermat Factorization and Pollard Rho Method for Factoring Integers." Lontar Komputer : Jurnal Ilmiah Teknologi Informasi 12, no. 1 (2021): 33. http://dx.doi.org/10.24843/lkjiti.2021.v12.i01.p04.

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The development of public-key cryptography generation using the factoring method is very important in practical cryptography applications. In cryptographic applications, the urgency of factoring is very risky because factoring can crack public and private keys, even though the strength in cryptographic algorithms is determined mainly by the key strength generated by the algorithm. However, solving the composite number to find the prime factors is still very rarely done. Therefore, this study will compare the Fermat factorization algorithm and Pollard rho by finding the key generator public key

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2

Donis-Vela, Alvaro, and Juan Carlos Garcia-Escartin. "A quantum primality test with order finding." Quantum Information and Computation 18, no. 13&14 (2018): 1143–51. http://dx.doi.org/10.26421/qic18.13-14-5.

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Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an integer N, the test tries to find an element of the multiplicative group of integers modulo N with order N-1. If one is found, the number is known to be prime. During the test, we can also show most of the times N is composite with certainty (and a witness) or, after \log\log N unsuccessful attempts to find an element of order N-1, declare it composite with high probability. The algorithm requires O((

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3

Jameson, G. J. O. "Finding pseudoprimes." Mathematical Gazette 95, no. 534 (2011): 420–32. http://dx.doi.org/10.1017/s002555720000351x.

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Recall that Fermat's ‘little theorem’ says that if p is prime and a is not a multiple of p, then ap − 1 ≡ 1 mod p.This theorem gives a possible way to detect primes, or more exactly, non-primes: if for a certain a coprime to n, a − 1 is not congruent to 1 mod n, then, by the theorem, n is not prime. A lot of composite numbers can indeed be detected by this test, but there are some that evade it. Let us give ourselves some notation and terminology to discuss them.

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4

Maksymenko, Yevhen. "The way of effective use of incremental with multiple thinning of test values for Fermat's factoring method." Collection "Information technology and security" 4, no. 1 (2016): 91–99. http://dx.doi.org/10.20535/2411-1031.2016.4.1.96080.

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5

Wahyudi, Agus Anwar Eka, I. Made Oka Widyantara, and Komang Oka Saputra. "Verifikasi Telapak Tangan dengan Multimodal Biometrik Fermat’s Spiral." Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) 3, no. 3 (2019): 408–13. http://dx.doi.org/10.29207/resti.v3i3.1173.

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The use of biometrics in various issues of data security, transactions, privacy has been widely used. Regarding security, surely the level of accuracy in one's self-recognition must be accurate. The palmprint is one of biometrics which has various unique characteristics. These characteristics include geometrical features such as length, width, and area of the palmprint, characteristics of main lines such as heart lines, headlines, and lifelines, tangled or weak lines, delta dot characteristics, and minus characteristics. Main lines and tangled lines, which are often referred to as line feature

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6

Ega Gradini. "FERMAT TEST AND THE EXISTENCE OF PSEUDOPRIMES." Visipena Journal 1, no. 1 (2010): 37–44. http://dx.doi.org/10.46244/visipena.v1i1.21.

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In this paper the author present Fermat test as one of primality tests. In order to perform the ability of the test, the algorithm of the test coded in Mathematica (6.0 version). The application of Fermat’s Little Theorem as well as Euler’s Theorem on the tests are also discussed and this leads to the concept of pseudoprime.

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7

Ega Gradini. "FERMAT TEST AND THE EXISTENCE OF PSEUDOPRIMES." Visipena Journal 2, no. 1 (2011): 13–20. http://dx.doi.org/10.46244/visipena.v2i1.35.

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In this paper the author present Fermat test as one of primality tests. In order to perform the ability of the test, the algorithm of the test coded in Mathematica (6.0 version). The application of Fermat’s Little Theorem as well as Euler’s Theorem on the tests are also discussed and this leads to the concept of pseudoprime.

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8

Jameson, G. J. O. "Finding Carmichael numbers." Mathematical Gazette 95, no. 533 (2011): 244–55. http://dx.doi.org/10.1017/s0025557200002965.

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Recall that Fermat's ‘little theorem’ says that if p is prime and a is not a multiple of p, then ap − 1 ≡ 1 mod p.This theorem gives a possible way to detect primes, or more exactly, non-primes: if for some positive a ≤ n − 1, an − 1 is not congruent to 1 mod n, then, by the theorem, n is not prime. A lot of composite numbers can indeed be detected by this test, but there are some that evade it. In other words, there are numbers n that are composite but still satisfy an − 1 ≡ 1 mod n for all a coprime to n. Such numbers might be called ‘false primes’, but in fact they are called Carmichael num

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9

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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10

Baziw, Erick J. "Derivation of seismic cone interval velocities utilizing forward modeling and the downhill simplex method." Canadian Geotechnical Journal 39, no. 5 (2002): 1181–92. http://dx.doi.org/10.1139/t02-061.

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The seismic cone penetration test (SCPT) has proven to be a very valuable geotechnical tool in facilitating the determination of low strain (<104%) in situ compression (P) and shear (S) wave velocities. The P- and S-wave velocities are directly related to the soil elastic constants of Poisson's ratio, shear modulus, bulk modulus, and Young's modulus. The accurate determination of P- and S-wave velocities from the recorded seismic cone time series is of paramount importance to the evaluation of reliable elastic constants. Furthermore, since the shear and compression wave velocities are squa

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