2017, Student mathematical library, ISBN 9781470435820, Volume 83., xii, 250 pages

Book

2006, ISBN 9781584885184, xxxiv, 808

Book

Selecta mathematica (Basel, Switzerland), ISSN 1420-9020, 2013, Volume 20, Issue 2, pp. 491 - 584

...–Teichmüller (GT) group. The analogue of the Galois action on the profinite braid groups is an action of the arithmetic fundamental group of a moduli space of elliptic curves on the profinite braid groups in genus one...

Braid groups in genus one | 11M32 | Grothendieck–Teichmüller theory | Mathematics, general | 17B35 (16S30) | Mathematics | Moduli spaces of elliptic curves | 20F36 | Elliptic associators | 32G34 | Grothendieck-Teichmüller theory | MATHEMATICS | MATHEMATICS, APPLIED | MARKED CURVES | GALOIS REPRESENTATIONS | Grothendieck-Teichmuller theory | MODULAR-FORMS | Algebra

Braid groups in genus one | 11M32 | Grothendieck–Teichmüller theory | Mathematics, general | 17B35 (16S30) | Mathematics | Moduli spaces of elliptic curves | 20F36 | Elliptic associators | 32G34 | Grothendieck-Teichmüller theory | MATHEMATICS | MATHEMATICS, APPLIED | MARKED CURVES | GALOIS REPRESENTATIONS | Grothendieck-Teichmuller theory | MODULAR-FORMS | Algebra

Journal Article

Lecture notes in computer science, ISSN 0302-9743, 2006, Volume 3897, pp. 319 - 331

...; the best published results achieve ¿ = log(p)/log(r) ~ 5/4. In this paper we make the first step towards surpassing these limitations by describing a method to construct elliptic curves of prime order and embedding degree k = 12...

Information Systems Applications (incl.Internet) | Data Encryption | Computer Science | Management of Computing and Information Systems | Algorithm Analysis and Problem Complexity | Computer Communication Networks | Operating Systems | Pairing-based cryptosystems | Elliptic curves | elliptic curves | COMPUTER SCIENCE, THEORY & METHODS | pairing-based cryptosystems

Information Systems Applications (incl.Internet) | Data Encryption | Computer Science | Management of Computing and Information Systems | Algorithm Analysis and Problem Complexity | Computer Communication Networks | Operating Systems | Pairing-based cryptosystems | Elliptic curves | elliptic curves | COMPUTER SCIENCE, THEORY & METHODS | pairing-based cryptosystems

Journal Article

Journal of cryptology, ISSN 1432-1378, 2009, Volume 23, Issue 2, pp. 224 - 280

Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairing-based cryptographic systems. Such “pairing-friendly...

Computational Mathematics and Numerical Analysis | Elliptic curves | Efficient implementation | Computer Science | Communications Engineering, Networks | Probability Theory and Stochastic Processes | Coding and Information Theory | Embedding degree | Combinatorics | Pairing-based cryptosystems | MATHEMATICS, APPLIED | ISOMORPHISM | LOGARITHMS | FINITE-FIELDS | ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | CRYPTOSYSTEMS | ORDINARY ABELIAN-VARIETIES | CRYPTOGRAPHIC SIGNIFICANCE | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | DIFFIE-HELLMAN

Computational Mathematics and Numerical Analysis | Elliptic curves | Efficient implementation | Computer Science | Communications Engineering, Networks | Probability Theory and Stochastic Processes | Coding and Information Theory | Embedding degree | Combinatorics | Pairing-based cryptosystems | MATHEMATICS, APPLIED | ISOMORPHISM | LOGARITHMS | FINITE-FIELDS | ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | CRYPTOSYSTEMS | ORDINARY ABELIAN-VARIETIES | CRYPTOGRAPHIC SIGNIFICANCE | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | DIFFIE-HELLMAN

Journal Article

1978, ISBN 9780387084893, Volume 231., xi, 261

Book

IEEE Transactions on Computers, ISSN 0018-9340, 11/2008, Volume 57, Issue 11, pp. 1514 - 1527

.... In this paper, we present an architecture of a state-of-the-art processor for RFID tags with an elliptic curve (EC) processor over GF(2 163...

Processor Architectures | Protocols | Compu | Random access memory | Registers | Special-purpose | Security | Micro-architecture implementation considerations | Elliptic curves | Computer architecture | General | Low-power design | Support for security | Radiofrequency identification | Elliptic curve cryptography | Public-key cryptosystems | Scalable hardware | Arithmetic and logic units | RFID systems | Security processor | public-key cryptosystems | security processor | arithmetic and logic units | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | scalable hardware | elliptic curve cryptography | ENGINEERING, ELECTRICAL & ELECTRONIC | Radio frequency identification (RFID) | Ellipse | Microprocessors | Central processing units | Research | Cryptography | Curves, Elliptic | Methods | Radio frequency identification | Architecture | Modular | Computer information security | Tags | Gates | Arithmetic

Processor Architectures | Protocols | Compu | Random access memory | Registers | Special-purpose | Security | Micro-architecture implementation considerations | Elliptic curves | Computer architecture | General | Low-power design | Support for security | Radiofrequency identification | Elliptic curve cryptography | Public-key cryptosystems | Scalable hardware | Arithmetic and logic units | RFID systems | Security processor | public-key cryptosystems | security processor | arithmetic and logic units | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | scalable hardware | elliptic curve cryptography | ENGINEERING, ELECTRICAL & ELECTRONIC | Radio frequency identification (RFID) | Ellipse | Microprocessors | Central processing units | Research | Cryptography | Curves, Elliptic | Methods | Radio frequency identification | Architecture | Modular | Computer information security | Tags | Gates | Arithmetic

Journal Article

2008, 2nd ed., Discrete mathematics and its applications, ISBN 9781420071467, xviii, 513

Book

1973, London Mathematical Society lecture note series, ISBN 0521200369, Volume 9, v, 248

A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves...

Curves, Elliptic | Elliptic functions

Curves, Elliptic | Elliptic functions

Book

2012, ISBN 9780691151199, xvii, 253

Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture...

Curves, Elliptic | Number theory | Elliptic functions | Mathematics | History & Philosophy | Abstract | PDZ | PBX | Calculus | PBKA | Geometry | Algebra | PBF | Algebraic | PBH | PBMW | Number Theory

Curves, Elliptic | Number theory | Elliptic functions | Mathematics | History & Philosophy | Abstract | PDZ | PBX | Calculus | PBKA | Geometry | Algebra | PBF | Algebraic | PBH | PBMW | Number Theory

Book

Journal of number theory, ISSN 0022-314X, 2019, Volume 204, pp. 1 - 24

We prove Boyd's conjectures relating Mahler's measures and values of L-functions of elliptic curves in the cases when the corresponding elliptic curve...

Elliptic dilogarithms | Elliptic curves | Mahler measure | L-functions | Boyd identities | MATHEMATICS | REGULATOR | UNITS

Elliptic dilogarithms | Elliptic curves | Mahler measure | L-functions | Boyd identities | MATHEMATICS | REGULATOR | UNITS

Journal Article

2011, Student mathematical library : IAS/Park City mathematical subseries, ISBN 0821852426, Volume 58, xiv, 195

Book

Nagoya mathematical journal, ISSN 0027-7630, 12/2017, Volume 228, pp. 124 - 185

To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface...

Article | Secondary 14J28 11G05 | 2010 Mathematics subject classification Primary 14J27 | MATHEMATICS | RANK | FIBRATIONS | Geometry | Algebra | Algorithms | Lattices | Mathematics | Elliptic functions | Curves (geometry) | Number theory

Article | Secondary 14J28 11G05 | 2010 Mathematics subject classification Primary 14J27 | MATHEMATICS | RANK | FIBRATIONS | Geometry | Algebra | Algorithms | Lattices | Mathematics | Elliptic functions | Curves (geometry) | Number theory

Journal Article

2003, Discrete mathematics and its applications, ISBN 1584883650, 440

Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof...

Cryptography | Curves, Elliptic | Number theory | ECIES | digital signature | Tate-Lichtenbaum pairing | Intelligent Systems | cryptography | elliptic curves | Lawrence C. Washington | Combinatorics | Cryptology | EIGamal | Discrete Mathematics | number theory

Cryptography | Curves, Elliptic | Number theory | ECIES | digital signature | Tate-Lichtenbaum pairing | Intelligent Systems | cryptography | elliptic curves | Lawrence C. Washington | Combinatorics | Cryptology | EIGamal | Discrete Mathematics | number theory

eBook

THEORETICAL AND MATHEMATICAL PHYSICS, ISSN 0040-5779, 11/2019, Volume 201, Issue 2, pp. 1565 - 1580

We propose a relativistic generalization of integrable systems describing M interacting elliptic gl(N) Euler-Arnold tops...

CALOGERO | integrable top | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | PHYSICS, MATHEMATICAL | spin Ruijsenaars-Schneider model | elliptic integrable system

CALOGERO | integrable top | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | PHYSICS, MATHEMATICAL | spin Ruijsenaars-Schneider model | elliptic integrable system

Journal Article

Computer aided geometric design, ISSN 0167-8396, 2018, Volume 61, pp. 9 - 19

In materials science and engineering, auxetic behavior refers to deformations of flexible structures where stretching in some direction involves lateral...

Periodic framework | Elliptic curve | Auxetic deformation | Aronhold invariants | Zeolites | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NEGATIVE-POISSONS-RATIO | Algorithms | elliptic curve | zeolites | auxetic deformation | periodic framework

Periodic framework | Elliptic curve | Auxetic deformation | Aronhold invariants | Zeolites | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NEGATIVE-POISSONS-RATIO | Algorithms | elliptic curve | zeolites | auxetic deformation | periodic framework

Journal Article

The Ramanujan journal, ISSN 1572-9303, 2018, Volume 49, Issue 3, pp. 585 - 623

Following Lang and Trotter, we describe a probabilistic model that predicts the distribution of primes p with given Frobenius traces at p for two fixed elliptic curves over $$\mathbb {Q}$$ Q...

Hurwitz–Kronecker class number | Fourier Analysis | Frobenius distributions | 11M41 | Lang–Trotter conjecture for two elliptic curves | Functions of a Complex Variable | 11G05 | Field Theory and Polynomials | Lang–Trotter constant for two elliptic curves | Mathematics | Number Theory | Combinatorics | MATHEMATICS | Lang-Trotter constant for two elliptic curves | PRODUCTS | VARIETIES | Hurwitz-Kronecker class number | Lang-Trotter conjecture for two elliptic curves | Computer science

Hurwitz–Kronecker class number | Fourier Analysis | Frobenius distributions | 11M41 | Lang–Trotter conjecture for two elliptic curves | Functions of a Complex Variable | 11G05 | Field Theory and Polynomials | Lang–Trotter constant for two elliptic curves | Mathematics | Number Theory | Combinatorics | MATHEMATICS | Lang-Trotter constant for two elliptic curves | PRODUCTS | VARIETIES | Hurwitz-Kronecker class number | Lang-Trotter conjecture for two elliptic curves | Computer science

Journal Article

Sensors (Basel, Switzerland), ISSN 1424-8220, 2014, Volume 14, Issue 6, pp. 10081 - 10106

.... first proposed a user authentication protocol based on elliptic curve cryptography (ECC) for WSNs. However, it turned out that Yeh et al...

Wireless sensor network | Authentication protocol | Elliptic curves cryptography | ELECTROCHEMISTRY | SCHEME | CHEMISTRY, ANALYTICAL | ANONYMITY | INSTRUMENTS & INSTRUMENTATION | wireless sensor network | ATTACK | authentication protocol | elliptic curves cryptography | Remote sensors | Smart cards | Wireless networks | Authentication | Monitors | Sensors | Security | Cryptography

Wireless sensor network | Authentication protocol | Elliptic curves cryptography | ELECTROCHEMISTRY | SCHEME | CHEMISTRY, ANALYTICAL | ANONYMITY | INSTRUMENTS & INSTRUMENTATION | wireless sensor network | ATTACK | authentication protocol | elliptic curves cryptography | Remote sensors | Smart cards | Wireless networks | Authentication | Monitors | Sensors | Security | Cryptography

Journal Article

1987, 2nd ed., Graduate texts in mathematics, ISBN 9780387965086, Volume 112., xi, 326

Book

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