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Relevant bibliographies by topics / General number field sieve (GNFS)

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Academic literature on the topic 'General number field sieve (GNFS)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "General number field sieve (GNFS)"

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Yang, Yang, Guang Zeng, Zheng Wang, and Wen Bao Han. "Calculation Components Analysis of the Lattice Sieve." Advanced Materials Research 466-467 (February 2012): 298–302. http://dx.doi.org/10.4028/www.scientific.net/amr.466-467.298.

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Currently, the best known algorithm for factoring RSA modulus is the General Number Field Sieve. Through the software optimized implementation of GNFS with RSA-768, we extracted nine main calculation components from the lattice sieve. Detail descriptions and comprehensive analysis of the properties about calculation, memory and communication to the nine components were given in this paper, which makes it possible to use of a variety of computing platforms, such as CPU, FPGA, CELL, and GPU etc, to accelerate the realization of GNFS.

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Gaudry, Pierrick, Laurent Grémy, and Marion Videau. "Collecting relations for the number field sieve in." LMS Journal of Computation and Mathematics 19, A (2016): 332–50. http://dx.doi.org/10.1112/s1461157016000164.

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In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in$\mathbb{F}_{p^{6}}$with the number field sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-$\mathfrak{q}$strategy. We also take into account the Galois action to increase the relation productivity of the sieving phase. To validate our results, we ran several experiments and real computa

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Zhou, Gang. "On General Number Field Sieve and its Polynomial Selection." Applied Mechanics and Materials 519-520 (February 2014): 250–56. http://dx.doi.org/10.4028/www.scientific.net/amm.519-520.250.

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This paper analyzes the algorithm of general number field sieve and suggesting some ofits solving in the problem of larger integers factorization. And a design of its implementation via thelibrary GMP for polynomial selection is discussed. Our work has the advantages of easy extensionsto various applications such as RSA, Discrete logarithm problems, Primality testing and so on.

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Kleinjung, Thorsten. "On polynomial selection for the general number field sieve." Mathematics of Computation 75, no. 256 (2006): 2037–47. http://dx.doi.org/10.1090/s0025-5718-06-01870-9.

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Zhu, Yuqing, Jiejing Wen, Jincheng Zhuang, Chang Lv, and Dongdai Lin. "Refined analysis to the extended tower number field sieve." Theoretical Computer Science 814 (April 2020): 49–68. http://dx.doi.org/10.1016/j.tcs.2020.01.010.

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Schumer, P. D. "On the large sieve inequality in an algebraic number field." Mathematika 33, no. 1 (1986): 31–54. http://dx.doi.org/10.1112/s0025579300013851.

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Gordon, Daniel M. "Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve." SIAM Journal on Discrete Mathematics 6, no. 1 (1993): 124–38. http://dx.doi.org/10.1137/0406010.

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Wang, Qi, Xiubin Fan, Hongyan Zang, and Yu Wang. "The Space Complexity Analysis in the General Number Field Sieve Integer Factorization." Theoretical Computer Science 630 (May 2016): 76–94. http://dx.doi.org/10.1016/j.tcs.2016.03.028.

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Cho, Gook Hwa, Namhun Koo, and Soonhak Kwon. "ON NONLINEAR POLYNOMIAL SELECTION AND GEOMETRIC PROGRESSION (MOD N) FOR NUMBER FIELD SIEVE." Bulletin of the Korean Mathematical Society 53, no. 1 (2016): 1–20. http://dx.doi.org/10.4134/bkms.2016.53.1.001.

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Cojocaru, Alina Carmen, Etienne Fouvry, and M. Ram Murty. "The Square Sieve and the Lang–Trotter Conjecture." Canadian Journal of Mathematics 57, no. 6 (2005): 1155–77. http://dx.doi.org/10.4153/cjm-2005-045-7.

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AbstractLet E be an elliptic curve defined over ℚ and without complex multiplication. Let K be a fixed imaginary quadratic field. We find nontrivial upper bounds for the number of ordinary primes p ≤ x for which ℚ(πp) = K, where πp denotes the Frobenius endomorphism of E at p. More precisely, under a generalized Riemann hypothesis we show that this number is OE(x17/18 log x), and unconditionally we show that this number is We also prove that the number of imaginary quadratic fields K, with −disc K ≤ x and of the form K = ℚ(πp), is ≫E log log log x for x ≥ x0(E). These results represent progres

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Dissertations / Theses on the topic "General number field sieve (GNFS)"

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Stöffler, Christian. "Faktorisieren mit dem General Number Field Sieve." [Ludwigshafen] C. Stöffler, 2007. http://d-nb.info/991129601/34.

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Briggs, Matthew Edward. "An Introduction to the General Number Field Sieve." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36618.

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With the proliferation of computers into homes and businesses and the explosive growth rate of the Internet, the ability to conduct secure electronic communications and transactions has become an issue of vital concern. One of the most prominent systems for securing electronic information, known as RSA, relies upon the fact that it is computationally difficult to factor a "large" integer into its component prime integers. If an efficient algorithm is developed that can factor any arbitrarily large integer in a "reasonable" amount of time, the security value of the RSA system would be nullified

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Podhorský, Jiří. "Integer Factorization on the GPU." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-412908.

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This work deals with factorization, a decomposition of composite numbers on prime numbers and possibilities of its parallelization. It summarizes also the best known algorithms for factoring and most popular platforms for the implementation of these algorithms on the graphics card. The main part of the thesis deals with the design and implementation of hardware acceleration current fastest algorithm on the graphics card by using the OpenCL framework. Subsequently, the work provides a comparison of speeds accelerated algorithm implemented in this work with other versions of the best known algor

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Καραπάνος, Νικόλαος. "Η μέθοδος παραγοντοποίησης ακεραίων αριθμών number field sieve : θεωρία και υλοποίηση". Thesis, 2010. http://nemertes.lis.upatras.gr/jspui/handle/10889/3735.

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Πολλά κρυπτογραφικά σχήματα δημόσιου κλειδιού βασίζονται στο γεγονός ότι είναι υπολογιστικά δύσκολο να παραγοντοποιήσουμε μεγάλους ακέραιους αριθμούς. Ο ταχύτερος, και ταυτόχρονα πολυπλοκότερος, κλασσικός αλγόριθμος που είναι γνωστός μέχρι σήμερα για την παραγοντοποίηση ακεραίων μήκους άνω των 110 δεκαδικών ψηφίων είναι ο General Number Field Sieve (GNFS). Ο αλγόριθμος αυτός είναι ο καρπός πολλών ετών έρευνας, κατά τη διάρκεια της οποίας παράγονταν ολοένα και ταχύτεροι αλγόριθμοι για να καταλήξουμε μέχρι στιγμής στον αλγόριθμο GNFS. Πρωταρχικός σκοπός της παρούσης μεταπτυχιακής εργασίας είναι

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Chin, Chia-Hao, and 金家豪. "A study of parameter tuning for General Number Field Sieve." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/48838233767226645004.

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碩士<br>國立中央大學<br>資訊工程學系碩士在職專班<br>92<br>With the explosive growth rate of the Internet, there are more and more data transferred by Internet. Therefore, the ability to conduct electronic communications and transactions securely has become an issue of vital concern. The public key cryptosystem arises because the conventional secret-key cryptosystem can not meet the needs of distribution application. RSA is a very popular public key cryptosystem and its security relies on the difficulty of factoring a large number. Because of the popularity of this algorithm, much research has gone into this probl

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Skoková, Adéla. "Podpůrné algoritmy číselného síta." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321408.

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Title: Supporting algorithms of number field sieve Author: Adéla Skoková Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: In this work we study the first part of the algorithm of number field sieve, generating of polynomials. At first we describe all the algorithm of the sieve for understanding of the role of polynomials and their impact on the entire algorithm. Then we present their characteristics and evaluation. The last part is about the most effective know algorithms of generating polynomials, invented by Thorsen Klinjung. Keywords: GNFS, Number

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Skoková, Adéla. "Podpůrné algoritmy číselného síta." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-331755.

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Title: Supporting algorithms of number field sieve Author: Adéla Skoková Department: Department of Algebra Supervisor: prof. RNDr. Aleš Drápal, CSc., DSc. Abstract: In this work we study the first part of the algorithm of number field sieve, generating of polynomials. At first we describe all the algorithm of the sieve for understanding of the role of polynomials and their impact on the entire algorithm. Then we present their characteristics and evaluation. The last part is about the most effective know algorithms of generating polynomials, invented by Thorsen Klinjung. The second Kleinjung al

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Μπακογιάννης, Χρήστος. "Υλοποίηση της μεθόδου παραγοντοποίησης ακεραίων αριθμών number field sieve σε παράλληλο υπολογιστικό περιβάλλον". Thesis, 2010. http://nemertes.lis.upatras.gr/jspui/handle/10889/3734.

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Η διείσδυση των υπολογιστών, τόσο στα σπίτια μας, όσο και κυρίως στις επιχειρήσεις, κατά τα τελευταία χρόνια, καθώς επίσης και ο συνεχώς αυξανόμενος ρυθμός χρήσης του διαδικτύου, έχουν καταστήσει την ανάγκη για ασφαλείς ηλεκτρονικές επικοινωνίες και συναλλαγές κάτι παραπάνω από επιτακτική. Ένα από τα κυρίαρχα, σήμερα, συστήματα ασφαλούς ανταλλαγής δεδομένων είναι ο αλγόριθμος RSA, η ασφάλεια του οποίου βασίζεται στο γεγονός ότι είναι πολύ δύσκολο να παραγοντοποιήσουμε έναν «μεγάλο» αριθμό στους πρώτους παράγοντές του. Ο RSA αλγόριθμος θεωρείται αρκετά ασφαλής, αν βέβαια χρησιμοποιούμε κατάλληλ

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Book chapters on the topic "General number field sieve (GNFS)"

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Bernstein, Daniel J., and A. K. Lenstra. "A general number field sieve implementation." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0091541.

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Elkenbracht-Huizing, Marije. "A multiple polynomial general number field sieve." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61581-4_45.

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Weber, Damian. "Computing discrete logarithms with the general number field sieve." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61581-4_70.

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Weber, Damian. "An Implementation of the General Number Field Sieve to Compute Discrete Logarithms mod p." In Advances in Cryptology — EUROCRYPT ’95. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-49264-x_8.

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Sarkar, Palash, and Shashank Singh. "A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm." In Advances in Cryptology – ASIACRYPT 2016. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-53887-6_2.

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Balasubramanian, Kannan, and M. Rajakani. "The Quadratic Sieve Algorithm for Integer Factoring." In Algorithmic Strategies for Solving Complex Problems in Cryptography. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-2915-6.ch018.

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At the time when RSA was invented in 1977, factoring integers with as few as 80 decimal digits was intractable. The first major breakthrough was quadratic sieve, a relatively simple factoring algorithm invented by Carl Pomerance in 1981, which can factor numbers up to 100 digits and more. It's still the best-known method for numbers under 110 digits or so; for larger numbers, the general number field sieve (GNFS) is now used. However, the general number field sieve is extremely complicated, for even the most basic implementation. However, GNFS is based on the same fundamental ideas as quadratic sieve. The fundamentals of the Quadratic Sieve algorithm are discussed in this chapter.

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Balasubramanian, Kannan, and Ahmed Mahmoud Abbas. "Integer Factoring Algorithms." In Algorithmic Strategies for Solving Complex Problems in Cryptography. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-2915-6.ch017.

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Most cryptographic systems are based on an underlying difficult problem. The RSA cryptosystem and many other cryptosystems rely on the fact that factoring a large composite number into two prime numbers is a hard problem. The are many algorithms for factoring integers. This chapter presents some of the basic algorithms for integer factorization like the Trial Division, Fermat's Algorithm. Pollard's Rho Method, Pollard's p-1 method and the Elliptic Curve Method. The Number Field Sieve algorithm along with Special Number field Sieve and the General Number Field Sieve are also used in factoring large numbers. Other factoring algorithms discussed in this chapter are the Continued Fractions Algorithms and the Quadratic Sieve Algorithm.

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Conference papers on the topic "General number field sieve (GNFS)"

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Hamdi, Shah Muhammad, Syed Tauhid Zuhori, Firoz Mahmud, and Biprodip Pal. "A Compare between Shor's quantum factoring algorithm and General Number Field Sieve." In 2014 International Conference on Electrical Engineering and Information Communication Technology (ICEEICT). IEEE, 2014. http://dx.doi.org/10.1109/iceeict.2014.6919115.

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Pallab, Pritam, and Abhijit Das. "AVX-512-based Parallelization of Block Sieving and Bucket Sieving for the General Number Field Sieve Method." In 18th International Conference on Security and Cryptography. SCITEPRESS - Science and Technology Publications, 2021. http://dx.doi.org/10.5220/0010515206530658.

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