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Journal articles on the topic 'Fermat's test'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 January 2023

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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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11

Romashko, Vasyl Mykolayovych, and Olena Vasylivna Romashko-Maistruk. "MAIN PARAMETERS OF THE UNIVERSAL CONCRETE STATE DIAGRAM IN THE REINFORCED CONCRETE ELEMENTS AND STRUCTURES." Collected scientific works of Ukrainian State University of Railway Transport, no. 199 (June 10, 2022): 44–54. http://dx.doi.org/10.18664/1994-7852.199.2022.258672.

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This article presents the research results on the search and methodologicaljustification of the main parametric points of the universal dependence of the concrete deformationdiagram c c in reinforced concrete elements and structures. It is shown that, unlike others, thisdependence is not empirical, but obtained analytically using the hypothesis of "stiffness nonlinearity".The using expediency this hypothesis to describe the concrete stress-strain state in reinforcedconcrete elements and structures is substantiated by the results of experimental studies by otherauthors.The most important dif

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12

Grau, José María, Antonio M. Oller-Marcén, Manuel Rodríguez, and Daniel Sadornil. "Fermat test with Gaussian base and Gaussian pseudoprimes." Czechoslovak Mathematical Journal 65, no. 4 (2015): 969–82. http://dx.doi.org/10.1007/s10587-015-0221-2.

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13

Prikhodko, A. A. "THE RELATIONSHIP OF FERMAT’S SIMPLICITY TEST AND WILSON’S THEOREM IN DETERMINING PRIME NUMBERS." International Journal of Applied and Fundamental Research (Международный журнал прикладных и фундаментальных исследований), no. 4 2022 (2022): 39–44. http://dx.doi.org/10.17513/mjpfi.13376.

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14

Lichtman, Jared Duker, and Carl Pomerance. "Improved error bounds for the Fermat primality test on random inputs." Mathematics of Computation 87, no. 314 (2018): 2871–90. http://dx.doi.org/10.1090/mcom/3314.

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15

EKSTROM, AARON, CARL POMERANCE, and DINESH S. THAKUR. "INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS." Journal of the Australian Mathematical Society 92, no. 1 (2012): 45–60. http://dx.doi.org/10.1017/s1446788712000080.

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AbstractIn 1987, Gordon gave an integer primality condition similar to the familiar test based on Fermat’s little theorem, but based instead on the arithmetic of elliptic curves with complex multiplication. We prove the existence of infinitely many composite numbers simultaneously passing all elliptic curve primality tests assuming a weak form of a standard conjecture on the bound on the least prime in (special) arithmetic progressions. Our results are somewhat more general than both the 1999 dissertation of the first author (written under the direction of the third author) and a 2010 paper on

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16

Ding, Weiyi, and Xiaoxian Tang. "Projections of Tropical Fermat-Weber Points." Mathematics 9, no. 23 (2021): 3102. http://dx.doi.org/10.3390/math9233102.

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This paper is motivated by the difference between the classical principal component analysis (PCA) in a Euclidean space and the tropical PCA in a tropical projective torus as follows. In Euclidean space, the projection of the mean point of a given data set on the principle component is the mean point of the projection of the data set. However, in tropical projective torus, it is not guaranteed that the projection of a Fermat-Weber point of a given data set on a tropical polytope is a Fermat-Weber point of the projection of the data set. This is caused by the difference between the Euclidean me

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17

Candra, Ade, Mohammad Andri Budiman, and Dian Rachmawati. "On Factoring The RSA Modulus Using Tabu Search." Data Science: Journal of Computing and Applied Informatics 1, no. 1 (2017): 30–37. http://dx.doi.org/10.32734/jocai.v1.i1-65.

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It is intuitively clear that the security of RSA cryptosystem depends on the hardness of factoring a very large integer into its two prime factors. Numerous studies about integer factorization in the field of number theory have been carried out, and as a result, lots of exact factorization algorithms, such as Fermat’s factorization algorithm, quadratic sieve method, and Pollard’s rho algorithm have been found. The factorization problem is in the class of NP (non-deterministic polynomial time). Tabu search is a metaheuristic in the field of artificial intelligence which is often used to solve N

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18

Budi, Senthod Setia. "ANALYSIS OF VIOLIN PLAYING TECHNIQUES œCONCERTO IN G MINOR 3RD MOVEMENT BY ANTONIO VIVALDI." Repertoar Journal 1, no. 2 (2021): 292–301. http://dx.doi.org/10.26740/rj.v1n2.p292-301.

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This study aims to describe the playing techniques and violin runners in Antonio Vivaldi's Concerto in g Minor 3rd Movement. This study used qualitative research methods. Data obtained in research through observation, interviews and documentation. The data analysis technique used was data reduction, data presentation and data conclusion. And there is a data validity test using triangulation techniques. The results showed that the playing techniques of Antonio Vivaldi's Concerto in g Minor 3rd Movement consisted of legato, ligatura, staccato, detache and accent. The ornaments contained in it, n

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19

Aminudin, Aminudin, Gadhing Putra Aditya, and Sofyan Arifianto. "RSA algorithm using key generator ESRKGS to encrypt chat messages with TCP/IP protocol." Jurnal Teknologi dan Sistem Komputer 8, no. 2 (2020): 113–20. http://dx.doi.org/10.14710/jtsiskom.8.2.2020.113-120.

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This study aims to analyze the performance and security of the RSA algorithm in combination with the key generation method of enhanced and secured RSA key generation scheme (ESRKGS). ESRKGS is an improvement of the RSA improvisation by adding four prime numbers in the property embedded in key generation. This method was applied to instant messaging using TCP sockets. The ESRKGS+RSA algorithm was designed using standard RSA development by modified the private and public key pairs. Thus, the modification was expected to make it more challenging to factorize a large number n into prime numbers. T

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20

Aditya, Gadhing Putra, Aminuddin Aminuddin, and Sofyan Arifianto. "Improvisasi Algoritma RSA Menggunakan Generate Key ESRKGS pada Instant Messaging Berbasis Socket TCP." Jurnal Repositor 2, no. 11 (2020): 1444. http://dx.doi.org/10.22219/repositor.v2i11.731.

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AbstrakSocket TCP adalah abstraksi yang digunakan aplikasi untuk mengirim dan menerima data melalui koneksi antar dua host dalam jaringan komputer. Jaringan yang biasa kita gunakan bersifat publik yang sangat rentan akan penyadapan data. Masalah ini dapat teratasi dengan menggunakan algoritma kriptografi pada socket TCP, salah satunya menggunakan algoritma RSA. Tingkat keamanan algoritma RSA standar memiliki celah keamanan pada kunci publik ataupun privat yang berasal dari inputan 2 bilangan prima saat pembangkitan kunci, begitupun dengan algoritma improvisasi RSA meskipun menggunakan 4 bilang

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21

Lee, Ki Ha, and Ganquan Xie. "A new approach to imaging with low‐frequency electromagnetic fields." GEOPHYSICS 58, no. 6 (1993): 780–96. http://dx.doi.org/10.1190/1.1443464.

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We present a new method for interpreting electromagnetic (EM) data using ray tomography. Direct application of ray tomography to low‐frequency EM data is difficult because of the diffusive nature of the field. Diffusive EM fields can, however, be mathematically transformed to wavefields defined in a time‐like variable. The transform uniquely relates a field satisfying a diffusion equation in time, or in frequency, to an integral of the corresponding wavefield. If the corresponding wavefields can be computed from low‐frequency EM data, one should be able to interpret these data using techniques

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22

Budiman, Mohammad Andri, and Dian Rachmawati. "Using random search and brute force algorithm in factoring the RSA modulus." Data Science: Journal of Computing and Applied Informatics 2, no. 1 (2018): 45–52. http://dx.doi.org/10.32734/jocai.v2.i1-91.

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Abstract. The security of the RSA cryptosystem is directly proportional to the size of its modulus, n. The modulus n is a multiplication of two very large prime numbers, notated as p and q. Since modulus n is public, a cryptanalyst can use factorization algorithms such as Euler’s and Pollard’s algorithms to derive the private keys, p and q. Brute force is an algorithm that searches a solution to a problem by generating all the possible candidate solutions and testing those candidates one by one in order to get the most relevant solution. Random search is a numerical optimization algorithm that

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23

Khairina, Nurul. "The Comparison of Methods for Generating Prime Numbers between The Sieve of Eratosthenes, Atkins, and Sundaram." SinkrOn 3, no. 2 (2019): 293. http://dx.doi.org/10.33395/sinkron.v3i2.10129.

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Prime numbers are unique numbers. Prime numbers are numbers that only have a dividing factor consisting of numbers 1 and the number itself. The prime numbers from 1 to n that are relatively small can be generated manually, but a prime number generator algorithm is needed to generate prime numbers on a large scale. This study compares three prime number generator algorithms, namely: The Sieve of Eratosthenes, The Sieve of Atkins, and The Sieve of Sundaram. These three sieve algorithms have their own differences in generating prime numbers. The Sieve of Eratosthenes uses a simpler method by cros

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24

Guzelian, Christopher P. "Testing Economic Theory." REVISTA PROCESOS DE MERCADO, October 15, 2018, 303–13. http://dx.doi.org/10.52195/pm.v15i2.54.

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Two years ago, Bob Mulligan and I empirically tested whether the Bank of Amsterdam, a prototypical central bank, had caused a boom-bust cycle in the Amsterdam commodities markets in the 1780s owing to the bank’s sudden initiation of low-fractional-re-serve banking (Guzelian & Mulligan 2015).1 Widespread criticism came quickly after we presented our data findings at that year’s Austrian Economic Research Conference. Walter Block representa-tively responded: «as an Austrian, I maintain you cannot «test» apodictic theories, you can only illustrate them».2 Non-Austrian, so-called «empiri

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