Log in

Relevant bibliographies by topics / Fermat's factorization / Journal articles

To see the other types of publications on this topic, follow the link: Fermat's factorization.

Journal articles on the topic 'Fermat's factorization'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 43 journal articles for your research on the topic 'Fermat's factorization.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

2

James, Joseph. "UNIQUE FACTORIZATION FERMAT'S LAST THEOREM BEAL'S CONJECTURE." Journal of Progressive Research in Mathematics 10, no. 1 (2016): 1434–39. https://doi.org/10.5281/zenodo.3976651.

Full text

Abstract:

In this paper the following statememt of Fermat\rq{}s Last Theorem is proved.  If  $x, y, z$ are positive integers$\pi$ is an odd prime and  $z^\pi=x^\pi+y^\pi, x, y, z$ are all even. Also, in this paper, is proved (Beal\rq{}s conjecture): The equation $z^\xi=x^\mu+y^\nu$ has no solution in relatively prime positive integers $x, y, z, $ with $\xi, \mu, \nu$ primes at least $3.

APA, Harvard, Vancouver, ISO, and other styles

3

Kritsanapong, Somsuk. "The new integer factorization algorithm based on fermat's factorization algorithm and euler's theorem." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 2 (2020): 1469–76. https://doi.org/10.11591/ijece.v10i2.pp1469-1476.

Full text

Abstract:

Although, Integer Factorization is one of the hard problems to break RSA, many factoring techniques are still developed. Fermat’s Factorization Algorithm (FFA) which has very high performance when prime factors are close to each other is a type of integer factorization algorithms. In fact, there are two ways to implement FFA. The first is called FFA-1, it is a process to find the integer from square root computing. Because this operation takes high computation cost, it consumes high computation time to find the result. The other method is called FFA-2 which is the different technique to

APA, Harvard, Vancouver, ISO, and other styles

4

Oduor, Maurice, Olege Fanuel, Aywa Shem, and Okaka A. Colleta. "CHARACTERIZATION OF CODES OF IDEALS OF THE POLYNOMIAL RING F30 2 [x] mod ô€€€ x30 ô€€€ 1 FOR ERROR CONTROL IN COMPUTER APPLICATONS." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 5 (2016): 6238–47. http://dx.doi.org/10.24297/jam.v12i5.260.

Full text

Abstract:

The study of ideals in algebraic number system has contributed immensely in preserving the notion of unique factorization in rings of algebraic integers and in proving Fermat's last Theorem. Recent research has revealed that ideals in Noethe-rian rings are closed in polynomial addition and multiplication.This property has been used to characterize the polynomial ring Fn 2 [x] mod (xn 1) for error control. In this research we generate ideals of the polynomial ring using GAP software and characterize the polycodewords using Shannon's Code region and Manin's bound.

APA, Harvard, Vancouver, ISO, and other styles

5

Malik, M. Aslam, and M. Khalid Mahmood. "On Simple Graphs Arising from Exponential Congruences." Journal of Applied Mathematics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/292895.

Full text

Abstract:

We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integersaandb, letG(n)denote the graph for whichV={0,1,…,n−1}is the set of vertices and there is an edge betweenaandbif the congruenceax≡b (mod n)is solvable. Letn=p1k1p2k2⋯prkrbe the prime power factorization of an integern, wherep1<p2<⋯<prare distinct primes. The number of nontrivial self-loops of the graphG(n)has been determined and shown to be equal to∏i=1r(ϕ(piki)+1). It is shown that the graphG(n)has2rcomponents. Further, it is proved that the componentΓpof the simp

APA, Harvard, Vancouver, ISO, and other styles

6

Babindamana, Regis Freguin, Gilda Rech Bansimba, and Basile Guy Richard Bossoto. "Lattice Points on the Fermat Factorization Method." Journal of Mathematics 2022 (January 28, 2022): 1–18. http://dx.doi.org/10.1155/2022/6360264.

Full text

Abstract:

In this paper, we study algebraic properties of lattice points of the arc on the conics x 2 − d y 2 = N especially for d = 1 , which is the Fermat factorization equation that is the main idea of many important factorization methods like the quadratic field sieve, using arithmetical results of a particular hyperbola parametrization. As a result, we present a generalization of the forms, the cardinal, and the distribution of its lattice points over the integers. In particular, we prove that if N − 6 ≡ 0 mod 4 , Fermat’s method fails. Otherwise, in terms of cardinality, it has, respectively, 4, 8

APA, Harvard, Vancouver, ISO, and other styles

7

Overmars, Anthony, and Sitalakshmi Venkatraman. "New Semi-Prime Factorization and Application in Large RSA Key Attacks." Journal of Cybersecurity and Privacy 1, no. 4 (2021): 660–74. http://dx.doi.org/10.3390/jcp1040033.

Full text

Abstract:

Semi-prime factorization is an increasingly important number theoretic problem, since it is computationally intractable. Further, this property has been applied in public-key cryptography, such as the Rivest–Shamir–Adleman (RSA) encryption systems for secure digital communications. Hence, alternate approaches to solve the semi-prime factorization problem are proposed. Recently, Pythagorean tuples to factor semi-primes have been explored to consider Fermat’s Christmas theorem, with the two squares having opposite parity. This paper is motivated by the property that the integer separating these

APA, Harvard, Vancouver, ISO, and other styles

8

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

9

Raghunandan, K. R., Aithal Ganesh, Shetty Surendra, and K. Bhavya. "Key Generation Using Generalized Pell’s Equation in Public Key Cryptography Based on the Prime Fake Modulus Principle to Image Encryption and Its Security Analysis." Cybernetics and Information Technologies 20, no. 3 (2020): 86–101. http://dx.doi.org/10.2478/cait-2020-0030.

Full text

Abstract:

AbstractRSA is one among the most popular public key cryptographic algorithm for security systems. It is explored in the results that RSA is prone to factorization problem, since it is sharing common modulus and public key exponent. In this paper the concept of fake modulus and generalized Pell’s equation is used for enhancing the security of RSA. Using generalized Pell’s equation it is explored that public key exponent depends on several parameters, hence obtaining private key parameter itself is a big challenge. Fake modulus concept eliminates the distribution of common modulus, by replacing

APA, Harvard, Vancouver, ISO, and other styles

10

Omollo, Richard, and Arnold Okoth. "Large Semi Primes Factorization with Its Implications to RSA Cryptosystems." BOHR International Journal of Smart Computing and Information Technology 3, no. 1 (2020): 1–8. http://dx.doi.org/10.54646/bijscit.011.

Full text

Abstract:

RSA’s strong cryptosystem works on the principle that there are no trivial solutions to integer factorization. Furthermore, factorization of very large semi primes cannot be done in polynomial time when it comes to the processing power of classical computers. In this paper, we present the analysis of Fermat’s Last Theorem and Arnold’s Theorem. Also highlighted include new techniques such as Arnold’s Digitized Summation Technique (A.D.S.T.) and a top-to-bottom, bottom-to-top approach search for the prime factors. These drastically reduce the time taken to factorize large semi primes as for the

APA, Harvard, Vancouver, ISO, and other styles

11

Somsuk, Kritsanapong. "The new integer factorization algorithm based on Fermat’s Factorization Algorithm and Euler’s theorem." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 2 (2020): 1469. http://dx.doi.org/10.11591/ijece.v10i2.pp1469-1476.

Full text

Abstract:

Although, Integer Factorization is one of the hard problems to break RSA, many factoring techniques are still developed. Fermat’s Factorization Algorithm (FFA) which has very high performance when prime factors are close to each other is a type of integer factorization algorithms. In fact, there are two ways to implement FFA. The first is called FFA-1, it is a process to find the integer from square root computing. Because this operation takes high computation cost, it consumes high computation time to find the result. The other method is called FFA-2 which is the different technique to find p

APA, Harvard, Vancouver, ISO, and other styles

12

Somsuk, Kritsanapong, and Sumonta Kasemvilas. "MFFV3: An Improved Integer Factorization Algorithm to Increase Computation Speed." Advanced Materials Research 931-932 (May 2014): 1432–36. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.1432.

Full text

Abstract:

RSA, a public key cryptosystem, was proposed to protect the information in the insecure channel. The security of RSA relies on the difficulty of factoring the modulus which is the product of two large primes. We proposed Modified Fermat Factorization Version 2 (MFFV2) modified from Modified Fermat Factorization (MFF) to break RSA. The key of MFFV2 is to decrease the number of times of MFF for computing an integers square root. However, MFFV2 is still time-consuming to some extent due to computation time of the subtraction of two integers for all iterations. Thus, this paper aims to propose Mod

APA, Harvard, Vancouver, ISO, and other styles

13

Balasubramanian, Kannan, and Mohana Priya Pitchai. "A survey of fermat factorization algorithms for factoring RSA composite numbers." Multidisciplinary Science Journal 6 (December 15, 2023): 2024ss0101. http://dx.doi.org/10.31893/multiscience.2024ss0101.

Full text

Abstract:

In this research, we delve into the challenges associated with factorization in the context of the RSA cryptosystem. The RSA cryptosystem's security relies on the computational complexity of breaking down its modulus, which is essentially a product of two prime numbers denoted as 'p' and 'q.' Notably, the RSA modulus differs from the typical factorization problem, as it involves exceptionally large prime numbers, each roughly half the size of the modulus itself. If one manages to determine the factors of this modulus, it compromises the security of the entire RSA cryptosystem, as these factors

APA, Harvard, Vancouver, ISO, and other styles

14

A. Longhas, Paul Ryan, Alsafat M. Abdul, and Aurea Z. Rosal. "Factors of Composite 4n2+1 using Fermat’s Factorization Method." International Journal of Mathematics Trends and Technology 68, no. 1 (2022): 53–60. http://dx.doi.org/10.14445/22315373/ijmtt-v68i1p506.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Brent, Richard P. "Factorization of the tenth Fermat number." Mathematics of Computation 68, no. 225 (1999): 429–52. http://dx.doi.org/10.1090/s0025-5718-99-00992-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Ziobro, Rafał. "Fermat’s Little Theorem via Divisibility of Newton’s Binomial." Formalized Mathematics 23, no. 3 (2015): 215–29. http://dx.doi.org/10.1515/forma-2015-0018.

Full text

Abstract:

Abstract Solving equations in integers is an important part of the number theory [29]. In many cases it can be conducted by the factorization of equation’s elements, such as the Newton’s binomial. The article introduces several simple formulas, which may facilitate this process. Some of them are taken from relevant books [28], [14]. In the second section of the article, Fermat’s Little Theorem is proved in a classical way, on the basis of divisibility of Newton’s binomial. Although slightly redundant in its content (another proof of the theorem has earlier been included in [12]), the article p

APA, Harvard, Vancouver, ISO, and other styles

17

Lenstra, A. K., H. W. Lenstra, M. S. Manasse, and J. M. Pollard. "The factorization of the ninth Fermat number." Mathematics of Computation 61, no. 203 (1993): 319. http://dx.doi.org/10.1090/s0025-5718-1993-1182953-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Bahig, Hatem M. "Speeding Up Fermat’s Factoring Method using Precomputation." Annals of Emerging Technologies in Computing 6, no. 2 (2022): 50–60. http://dx.doi.org/10.33166/aetic.2022.02.004.

Full text

Abstract:

The security of many public-key cryptosystems and protocols relies on the difficulty of factoring a large positive integer n into prime factors. The Fermat factoring method is a core of some modern and important factorization methods, such as the quadratic sieve and number field sieve methods. It factors a composite integer n=pq in polynomial time if the difference between the prime factors is equal to ∆=p-q≤n^(0.25) , where p>q. The execution time of the Fermat factoring method increases rapidly as ∆ increases. One of the improvements to the Fermat factoring method is based on studying the

APA, Harvard, Vancouver, ISO, and other styles

19

Pieprzyk, Josef. "Integer Factorization – Cryptology Meets Number Theory." Scientific Journal of Gdynia Maritime University, no. 109 (March 30, 2019): 7–20. http://dx.doi.org/10.26408/109.01.

Full text

Abstract:

Integer factorization is one of the oldest mathematical problems. Initially, the interest in factorization was motivated by curiosity about behaviour of prime numbers, which are the basic building blocks of all other integers. Early factorization algorithms were not very efficient. However, this dramatically has changed after the invention of the well-known RSA public-key cryptosystem. The reason for this was simple. Finding an efficient factoring algorithm is equivalent to breaking RSA. The work overviews development of integer factoring algorithms. It starts from the classical sieve of Era

APA, Harvard, Vancouver, ISO, and other styles

20

Oumar, FALL, and Bachir DEME Chérif. "Polynomial Factorization and Primality Criterion for Fermat Numbers." Polynomial Factorization and Primality Criterion for Fermat Numbers 10, no. 02 (2022): 2579–80. https://doi.org/10.5281/zenodo.6086625.

Full text

Abstract:

Let <em>p </em>be a prime integer and let <em>k </em>∈N<em>. </em>We purpose a factorization of <em>X</em><sup>2<em>k </em></sup>+1 (mod <em>p</em>) allowing ti give a primality criterion for Fermat numbers. Mathematics Subject Classification 2010 11A07 11 A 51

APA, Harvard, Vancouver, ISO, and other styles

21

Lenstra, A. K., H. W. Lenstra, M. S. Manasse, and J. M. Pollard. "Addendum: The Factorization of the Ninth Fermat Number." Mathematics of Computation 64, no. 211 (1995): 1357. http://dx.doi.org/10.2307/2153511.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Vynnychuk, Stepan, and Yevhen Maksymenko. "The modified algorithm of fermat’s factorization method with base foundation of module." Collection "Information technology and security" 6, no. 2 (2018): 79–93. http://dx.doi.org/10.20535/2411-1031.2018.6.2.153492.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Shatnawi, Ahmed S., Mahmoud M. Almazari, Zakarea AlShara, Eyad Taqieddin, and Dheya Mustafa. "RSA cryptanalysis — Fermat factorization exact bound and the role of integer sequences in factorization problem." Journal of Information Security and Applications 78 (November 2023): 103614. http://dx.doi.org/10.1016/j.jisa.2023.103614.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Thakur, Dinesh S. "Fermat–Wilson Supercongruences, Arithmetic Derivatives and Strange Factorizations." Journal de théorie des nombres de Bordeaux 36, no. 2 (2024): 481–91. http://dx.doi.org/10.5802/jtnb.1285.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Somsuk, Kritsanapong. "The improvement of initial value closer to the target for Fermat’s factorization algorithm." Journal of Discrete Mathematical Sciences and Cryptography 21, no. 7-8 (2018): 1573–80. http://dx.doi.org/10.1080/09720529.2018.1502737.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Fragnito, Nicola. "The Last Theorem of Fermat for n=3." Bulletin of Mathematical Sciences and Applications 2 (November 2012): 68–79. http://dx.doi.org/10.18052/www.scipress.com/bmsa.2.68.

Full text

Abstract:

In this paper on FLT, one solves the case n=3 in elementary way, extensible to n odd. The author works only through the sole factorization in factors and with the proceeding for absurd, that is if x, y, z are prime among them, under the hypothesis that (x, y, z) are a solution, one obtains that the first and the second term of an equivalent relation are odd (the first) and even (the second).

APA, Harvard, Vancouver, ISO, and other styles

27

Křížek, Michal, and Jan Chleboun. "A note on factorization of the Fermat numbers and their factors of the form $3h2\sp n+1$." Mathematica Bohemica 119, no. 4 (1994): 437–45. http://dx.doi.org/10.21136/mb.1994.126115.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

29

Wu, Mu-En, Raylin Tso, and Hung-Min Sun. "On the improvement of Fermat factorization using a continued fraction technique." Future Generation Computer Systems 30 (January 2014): 162–68. http://dx.doi.org/10.1016/j.future.2013.06.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Vynnychuk, Stepan, and Yevhen Maksymenko. "Formation of non-uniformity increment for the basic module base in the problem of Fermat’s factorization method." Collection "Information technology and security" 4, no. 2 (2016): 244–54. http://dx.doi.org/10.20535/2411-1031.2016.4.2.110001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Budiman, M. A., D. Rachmawati, and R. Utami. "The cryptanalysis of the Rabin public key algorithm using the Fermat factorization method." Journal of Physics: Conference Series 1235 (June 2019): 012084. http://dx.doi.org/10.1088/1742-6596/1235/1/012084.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

33

Gras, Georges. "Les θ-régulateurs locaux d'un nombre algébrique : Conjectures p-adiques". Canadian Journal of Mathematics 68, № 3 (2016): 571–624. http://dx.doi.org/10.4153/cjm-2015-026-3.

Full text

Abstract:

AbstractLet K/ℚ be Galois and let η K ×be such that Reg∞(η)=0 .We define the local θ–regulator for the ℚp–irreducible characters θ of G = Gal(Kℚ). Let Vθ be the θ-irreducible representation. A linear representation is associated with whose nullity is equivalent to δ≥1. Each yields Regθp modulo p in the factorization of (normalized p–adic regulator). From Prob f ≥ 1 is a residue degree) and the Borel–Cantelli heuristic, we conjecture that for p large enough, RegGp(η) is a p–adic unit (a single with f = δ=1); this obstruction may be led assuming the existence of a binomial probability law confir

APA, Harvard, Vancouver, ISO, and other styles

34

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

35

Arifianto, Sofyan, Aminudin Aminudin, and Muhammad Furqon Sidiq. "Analisa Improvisasi Algoritma RSA Menggunakan RNG LCG pada Instant Messaging Berbasis Socket TCP." JIPETIK:Jurnal Ilmiah Penelitian Teknologi Informasi & Komputer 1, no. 1 (2020): 28–34. http://dx.doi.org/10.26877/jipetik.v1i1.6244.

Full text

Abstract:

Socket 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 public ataupun privat yang berasal dari inputan 2 bilangan prima saat pembangkitan kunci. Beberapa penelitian telah dilakukan untuk mengembangkan algoritma RSA, namun ha

APA, Harvard, Vancouver, ISO, and other styles

36

Lenstra, A. K., H. W. Lenstra, M. S. Manasse, and J. M. Pollard. "Addendum: ‘‘The factorization of the ninth Fermat number” [Math.\ Comp.\ {\bf 61} (1993), no.\ 203, 319–349; MR1182953 (93k:11116)]." Mathematics of Computation 64, no. 211 (1995): 1357. http://dx.doi.org/10.1090/s0025-5718-1995-1303085-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Місько, Віталій Миколайович. "Acceleration of Fermat's factorization method by decimation method with use of several bases." Ukrainian Scientific Journal of Information Security 21, no. 1 (2015). http://dx.doi.org/10.18372/2225-5036.21.8310.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

FALL, Oumar. "Polynomial Factorization and Primality Criterion for Fermat Numbers." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 10, no. 02 (2022). http://dx.doi.org/10.47191/ijmcr/v10i2.05.

Full text

Abstract:

Abstract Let p be a prime integer and let k ∈N. We purpose a factorization of X2k +1 (mod p) allowing ti give a primality criterion for Fermat numbers. Mathematics Subject Classification 2010 11A07 11 A 51

APA, Harvard, Vancouver, ISO, and other styles

39

Bahig, Hazem M., Mohammed A., Khaled A., Amer AlGhadhban, and Hatem M. "Performance Analysis of Fermat Factorization Algorithms." International Journal of Advanced Computer Science and Applications 11, no. 12 (2020). http://dx.doi.org/10.14569/ijacsa.2020.0111242.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Omollo, Richard, and Arnold Okoth. "Large semi primes factorization with its implications to RSAcryptosystems." BOHR International Journal of Smart Computing and Information Technology, 2021, 1–8. http://dx.doi.org/10.54646/bijscit.2021.11.

Full text

Abstract:

RSA’s strong cryptosystem works on the principle that there are no trivial solutions to integer factorization.Furthermore, factorization of very large semi primes cannot be done in polynomial time when it comes to theprocessing power of classical computers. In this paper, we present the analysis of Fermat’s Last Theorem andArnold’s Theorem. Also highlighted include new techniques such as Arnold’s Digitized Summation Technique(A.D.S.T.) and a top-to-bottom, bottom-to-top approach search for the prime factors. These drastically reducethe time taken to factorize large semi primes as for the case

APA, Harvard, Vancouver, ISO, and other styles

41

Bahig, Hazem M., Hatem M., and Yasser Kotb. "Fermat Factorization using a Multi-Core System." International Journal of Advanced Computer Science and Applications 11, no. 4 (2020). http://dx.doi.org/10.14569/ijacsa.2020.0110444.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Dang, Guoqiang. "On the equation f ⁿ + (f″)^m ≡ 1." Demonstratio Mathematica 56, no. 1 (2023). http://dx.doi.org/10.1515/dema-2023-0103.

Full text

Abstract:

Abstract Let n n and m m be two positive integers, and the second-order Fermat-type functional equation f n + ( f ″ ) m ≡ 1 {f}^{n}+{({f}^{^{\prime\prime} })}^{m}\equiv 1 does not have a nonconstant meromorphic solution in the complex plane, except ( n , m ) ∈ { ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 2 , 1 ) , ( 3 , 1 ) } \left(n,m)\in \left\{\left(1,1),\left(1,2),\left(1,3),\left(2,1),\left(3,1)\right\} . The research gives a ready-to-use scheme to study certain Fermat-type functional differential equations in the complex plane by using the Nevanlinna theory, the complex method, and the Weiers

APA, Harvard, Vancouver, ISO, and other styles

43

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 (2024). http://dx.doi.org/10.22219/repositor.v2i11.30959.

Full text

Abstract:

Socket 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 bilangan prim

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!