Relevant bibliographies by topics / Cryptography Algebraic fields

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Cryptography Algebraic fields'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Cryptography Algebraic fields"

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Huque, Md Sirajul, Sk Bhadar Saheb, and Jayaram Boga. "An Approach to Secure Data Aggregation in Wireless Sensor Networks (WSN) using Asymmetric Homomorphic Encryption (Elliptic Curve Cryptography) Scheme." International Journal of Advanced Research in Computer Science and Software Engineering 7, no. 7 (2017): 263. http://dx.doi.org/10.23956/ijarcsse/v7i7/0162.

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Wireless sensor networks (WSN) are a collection of autonomous collection of motes. Sensor motes are usually Low computational and low powered. In WSN Sensor motes are used to collect environmental data collection and pass that data to the base station. Data aggregation is a common technique widely used in wireless sensor networks. [2] Data aggregation is the process of collecting the data from multiple sensor nodes by avoiding the redundant data transmission and that collected data has been sent to the base station (BS) in single route. Secured data aggregation deals with Securing aggregated d
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Liu, Qian, and Yujuan Sun. "Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3." Journal of Algebra and Its Applications 18, no. 04 (2019): 1950069. http://dx.doi.org/10.1142/s0219498819500695.

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Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are
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Ping, Yuan, Baocang Wang, Yuehua Yang, and Shengli Tian. "Building Secure Public Key Encryption Scheme from Hidden Field Equations." Security and Communication Networks 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/9289410.

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Multivariate public key cryptography is a set of cryptographic schemes built from the NP-hardness of solving quadratic equations over finite fields, amongst which the hidden field equations (HFE) family of schemes remain the most famous. However, the original HFE scheme was insecure, and the follow-up modifications were shown to be still vulnerable to attacks. In this paper, we propose a new variant of the HFE scheme by considering the special equation x2=x defined over the finite field F3 when x=0,1. We observe that the equation can be used to further destroy the special structure of the unde
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Sokolov, A. V., and O. N. Zhdanov. "THE CLASS OF PERFECT TERNARY ARRAYS." «System analysis and applied information science», no. 2 (August 7, 2018): 47–54. http://dx.doi.org/10.21122/2309-4923-2018-2-47-54.

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In recent decades, perfect algebraic constructions are successfully being use to signal systems synthesis, to construct block and stream cryptographic algorithms, to create pseudo-random sequence generators as well as in many other fields of science and technology. Among perfect algebraic constructions a significant place is occupied by bent-sequences and the class of perfect binary arrays associated with them. Bent-sequences are used for development of modern cryptographic primitives, as well as for constructing constant amplitude codes (C-codes) used in code division multiple access technolo
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Buchmann, Johannes, Markus Maurer, and Bodo Möller. "Cryptography based on number fields with large regulator." Journal de Théorie des Nombres de Bordeaux 12, no. 2 (2000): 293–307. http://dx.doi.org/10.5802/jtnb.281.

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Abduldaim, Areej M. "Algebraic Verification Algorithm." International Journal of System Modeling and Simulation 3, no. 1 (2018): 7. http://dx.doi.org/10.24178/ijsms.2018.3.1.07.

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Authentication over insecure public networks or with untrusted servers raises more concerns in privacy and security.Modern algebra is one of the significantfields of mathematics. It is a combination of techniques used for a variety of applications including the process of the manipulation of the mathematical categories. In addition,modern algebra deals in depth with the study of abstractions such as groups, rings and fields,the main objective of this article is to provide a novel algebraic verification protocol using ring theory. The protocol is blind, meaning that it detects only the identity
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Awasthi, Ambrish, and Rajendra K. Sharma. "Primitive transformation shift registers over finite fields." Journal of Algebra and Its Applications 18, no. 09 (2019): 1950171. http://dx.doi.org/10.1142/s0219498819501718.

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Linear feedback shift registers (LFSRs) are widely used cryptographic primitives for generating pseudorandom sequences. Here, we consider systems which are efficient generalizations of LFSRs and produce pseudorandom vector sequences. We study problems related to the cardinality, existence and construction of these systems and give certain results in this direction.
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Yi, Hai-Bo, Zhe Nie, and Bin Li. "Efficient implementations of Gaussian elimination in finite fields on ASICs for MQ cryptographic systems." Journal of Discrete Mathematical Sciences and Cryptography 21, no. 3 (2018): 797–802. http://dx.doi.org/10.1080/09720529.2018.1449354.

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CARANAY, PERLAS C., and RENATE SCHEIDLER. "AN EFFICIENT SEVENTH POWER RESIDUE SYMBOL ALGORITHM." International Journal of Number Theory 06, no. 08 (2010): 1831–53. http://dx.doi.org/10.1142/s1793042110003770.

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Power residue symbols and their reciprocity laws have applications not only in number theory, but also in other fields like cryptography. A crucial ingredient in certain public key cryptosystems is a fast algorithm for computing power residue symbols. Such algorithms have only been devised for the Jacobi symbol as well as for cubic and quintic power residue symbols, but for no higher powers. In this paper, we provide an efficient procedure for computing 7th power residue symbols. The method employs arithmetic in the field ℚ(ζ), with ζ a primitive 7th root of unity, and its ring of integers ℤ[ζ
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A. A., Ibrahim. "GCD of Aunu Binary Polynomials of Cardinality Seven Using Extended Euclidean Algorithm." International Journal of Mathematics and Computer Research 09, no. 09 (2021). http://dx.doi.org/10.47191/ijmcr/v9i9.02.

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Finite fields is considered to be the most widely used algebraic structures today due to its applications in cryptography, coding theory, error correcting codes among others. This paper reports the use of extended Euclidean algorithm in computing the greatest common divisor (gcd) of Aunu binary polynomials of cardinality seven. Each class of the polynomial is permuted into pairs until all the succeeding classes are exhausted. The findings of this research reveals that the gcd of most of the pairs of the permuted classes are relatively prime. This results can be used further in constructing som
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Dissertations / Theses on the topic "Cryptography Algebraic fields"

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Wilcox, Nicholas. "A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography." Oberlin College Honors Theses / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528649455201473.

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Wong, Kenneth Koon-Ho. "Applications of finite field computation to cryptology : extension field arithmetic in public key systems and algebraic attacks on stream ciphers." Queensland University of Technology, 2008. http://eprints.qut.edu.au/17570/.

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In this digital age, cryptography is largely built in computer hardware or software as discrete structures. One of the most useful of these structures is finite fields. In this thesis, we explore a variety of applications of the theory and applications of arithmetic and computation in finite fields in both the areas of cryptography and cryptanalysis. First, multiplication algorithms in finite extensions of prime fields are explored. A new algebraic description of implementing the subquadratic Karatsuba algorithm and its variants for extension field multiplication are presented. The use of cy-
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Ferreira, Jamil 1956. "Sobre corpos de funções algébricas e algumas relações com a criptografia." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306598.

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Orientador: Sueli Irene Rodrigues Costa<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-23T07:10:07Z (GMT). No. of bitstreams: 1 Ferreira_Jamil_D.pdf: 1528200 bytes, checksum: a1ca349425c4bcf544a36d17d3157b3c (MD5) Previous issue date: 2013<br>Resumo: O número de classes de divisores de grau zero, h, de corpos de funções algébricas elípticos e hiperelípticos desempenha papel importante nos esquemas criptográficos baseados em curvas elípticas e hiperelípticas. Nesse contexto, h é um nú
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Alexander, Nicholas Charles. "Algebraic Tori in Cryptography." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1154.

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Communicating bits over a network is expensive. Therefore, cryptosystems that transmit as little data as possible are valuable. This thesis studies several cryptosystems that require significantly less bandwidth than conventional analogues. The systems we study, called torus-based cryptosystems, were analyzed by Karl Rubin and Alice Silverberg in 2003 [RS03]. They interpreted the XTR [LV00] and LUC [SL93] cryptosystems in terms of quotients of algebraic tori and birational parameterizations, and they also presented CEILIDH, a new torus-based cryptosystem. This thesis introduces
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Caullery, Florian. "Polynomes sur les corps finis pour la cryptographie." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4013/document.

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Les fonctions de F_q dans lui-même sont des objets étudiés dans de divers domaines tels que la cryptographie, la théorie des codes correcteurs d'erreurs, la géométrie finie ainsi que la géométrie algébrique. Il est bien connu que ces fonctions sont en correspondance exacte avec les polynômes en une variable à coefficients dans F_q. Nous étudierons trois classes de polynômes particulières: les polynômes Presque Parfaitement Non linéaires (Almost Perfect Nonlinear (APN)), les polynômes planaires ou parfaitement non linéaire (PN) et les o-polynômes.Les fonctions APN sont principalement étudiées p
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Baktir, Selcuk. "Efficient algorithms for finite fields, with applications in elliptic curve cryptography." Link to electronic thesis, 2003. http://www.wpi.edu/Pubs/ETD/Available/etd-0501103-132249.

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Thesis (M.S.)--Worcester Polytechnic Institute.<br>Keywords: multiplication; OTF; optimal extension fields; finite fields; optimal tower fields; cryptography; OEF; inversion; finite field arithmetic; elliptic curve cryptography. Includes bibliographical references (p. 50-52).
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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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Akleylek, Sedat. "On The Representation Of Finite Fields." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612727/index.pdf.

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The representation of field elements has a great impact on the performance of the finite field arithmetic. In this thesis, we give modified version of redundant representation which works for any finite fields of arbitrary characteristics to design arithmetic circuits with small complexity. Using our modified redundant representation, we improve many of the complexity values. We then propose new representations as an alternative way to represent finite fields of characteristic two by using Charlier and Hermite polynomials. We show that multiplication in these representations can be achieved wi
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Angulo, Rigo Julian Osorio. "Criptografia de curvas elípticas." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/6976.

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Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-03-20T17:15:17Z No. of bitstreams: 2 Dissertação - Rigo Julian Osorio Angulo - 2017.pdf: 1795543 bytes, checksum: 4342f624ff7c02485e9e888135bcbc18 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-03-21T12:06:48Z (GMT) No. of bitstreams: 2 Dissertação - Rigo Julian Osorio Angulo - 2017.pdf: 1795543 bytes, checksum: 4342f624ff7c02485e9e888135bcbc18 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD
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Fujdiak, Radek. "Analýza a optimalizace datové komunikace pro telemetrické systémy v energetice." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-358408.

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Telemetry system, Optimisation, Sensoric networks, Smart Grid, Internet of Things, Sensors, Information security, Cryptography, Cryptography algorithms, Cryptosystem, Confidentiality, Integrity, Authentication, Data freshness, Non-Repudiation.
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Books on the topic "Cryptography Algebraic fields"

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Algebraic curves and cryptography. American Mathematical Society, 2010.

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Winterhof, Arne, Harald Niederreiter, Alina Ostafe, and Daniel Panario. Algebraic curves and finite fields: Cryptography and other applications. De Gruyter, 2014.

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1965-, Aubry Yves, Ritzenthaler Christophe 1976-, Zykin Alexey 1984-, and Geocrypt Conference (2011 : Bastia, France), eds. Arithmetic, geometry, cryptography and coding theory: 13th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, March 14-18, 2011, CIRM, Marseille, France : Geocrypt 2011, June 19-24, 2011, Bastia, France. American Mathematical Society, 2012.

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International Conference Arithmetic, Geometry, Cryptography and Coding Theory (14th 2013 Marseille, France). Algorithmic arithmetic, geometry, and coding theory: 14th International Conference, Arithmetic, Geometry, Cryptography, and Coding Theory, June 3-7 2013, CIRM, Marseille, France. Edited by Ballet Stéphane 1971 editor, Perret, M. (Marc), 1963- editor, and Zaytsev, Alexey (Alexey I.), 1976- editor. American Mathematical Society, 2015.

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Lahyane, Mustapha. Algbra for secure and reliable communication modeling: CIMPA Research School and Conference Algebra for Secure and Reliable Communication Modeling, October 1-13, 2012, Morelia, State of Michoaczn, Mexico. Edited by Martínez-Moro Edgar editor. American Mathematical Society, 2015.

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Myasnikov, Alexei G. Non-commutative cryptography and complexity of group-theoretic problems. American Mathematical Society, 2011.

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Shparlinski, Igor E. Finite fields: Theory and computation : the meeting point of number theory, computer science, coding theory, and cryptography. Kluwer Academic Publishers, 1999.

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L, Mullen Gary, Panario Daniel, and Shparlinski Igor E, eds. Finite fields and applications: Eighth International Conference on Finite Fields and Applications, July 9-13, 2007, Melbourne, Australia. American Mathematical Society, 2008.

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L, Mullen Gary, Stichtenoth H. 1944-, and Tapia-Recillas Horacio 1945-, eds. Finite fields with applications to coding theory, cryptography, and related areas: Proceedings of the Sixth International Conference on Finite Fields and Applications, held at Oaxaca, México, May 21-25, 2001. Springer, 2002.

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Alta.) WIN (Conference) (2nd 2011 Banff. Women in Numbers 2: Research directions in number theory : BIRS Workshop, WIN2 - Women in Numbers 2, November 6-11, 2011, Banff International Research Station, Banff, Alberta, Canada. Edited by David Chantal 1964-, Lalín Matilde 1977-, and Manes Michelle 1970-. American Mathematical Society, 2013.

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Book chapters on the topic "Cryptography Algebraic fields"

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Petit, Christophe, Michiel Kosters, and Ange Messeng. "Algebraic Approaches for the Elliptic Curve Discrete Logarithm Problem over Prime Fields." In Public-Key Cryptography – PKC 2016. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49387-8_1.

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Avanzi, Roberto Maria, and Preda Mihăilescu. "Generic Efficient Arithmetic Algorithms for PAFFs (Processor Adequate Finite Fields) and Related Algebraic Structures." In Selected Areas in Cryptography. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24654-1_23.

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Lasjaunias, Alain. "Continued Fractions for Certain Algebraic Power Series over a Finite Field." In Finite Fields with Applications to Coding Theory, Cryptography and Related Areas. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-59435-9_17.

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Lloris Ruiz, Antonio, Encarnación Castillo Morales, Luis Parrilla Roure, Antonio García Ríos, and María José Lloris Meseguer. "Two Galois Fields Cryptographic Applications." In Arithmetic and Algebraic Circuits. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67266-9_12.

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Meyer, Andreas, Stefan Neis, and Thomas Pfahler. "First Implementation of Cryptographic Protocols Based on Algebraic Number Fields." In Information Security and Privacy. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-47719-5_9.

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"Finite Fields and Function Fields." In Algebraic Geometry in Coding Theory and Cryptography. Princeton University Press, 2009. http://dx.doi.org/10.2307/j.ctvdtphcs.4.

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"1. Finite Fields and Function Fields." In Algebraic Geometry in Coding Theory and Cryptography. Princeton University Press, 2010. http://dx.doi.org/10.1515/9781400831302-002.

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Higgins, Peter M. "6. Algebra and the arithmetic of remainders." In Algebra: A Very Short Introduction. Oxford University Press, 2015. http://dx.doi.org/10.1093/actrade/9780198732822.003.0006.

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‘Algebra and the arithmetic of remainders’ considers a new type of algebra, which is both an ancient topic and one that has found major contemporary application in Internet cryptography. It begins with an outline of abstract algebra, including groups, rings, and fields. Semigroups and groups are algebras with a single associative operation, while rings and fields are algebras with two operations linked via the distributive law. Lattices are algebras with an ordered structure, while vector spaces and modules are algebras where the members can be multiplied by scalar quantities from other fields or rings. The rules of modular arithmetic (or clock arithmetic) and solving linear congruences are also described.
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Bolfing, Andreas. "Preliminaries." In Cryptographic Primitives in Blockchain Technology. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198862840.003.0002.

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Blockchains are heavily based on mathematical concepts, in particular on algebraic structures. This chapter starts with an introduction to the main aspects in number theory, such as the divisibility of integers, prime numbers and Euler’s totient function. Based on these basics, it follows a very detailed introduction to modern algebra, including group theory, ring theory and field theory. The algebraic main results are then applied to describe the structure of cyclic groups and finite fields, which are needed to construct cryptographic primitives. The chapter closes with an introduction to complexity theory, examining the efficiency of algorithms.
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"Algebraic Number Field." In Encyclopedia of Cryptography and Security. Springer US, 2011. http://dx.doi.org/10.1007/978-1-4419-5906-5_1135.

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