Keyword

finite fields

Description: Algebraic structures with finitely many elements in which addition, subtraction, multiplication, and division by nonzero elements are defined.

Primary topic: Coding theory and cryptography (29%)

Wikidata ID: wiki/Q603880

OpenAlex ID: keywords/finite-fields

The Theory of Error-Correcting Codes

1977 · North-Holland mathematical library · 10,812

A public key cryptosystem and a signature scheme based on discrete logarithms

1985 · T. Elgamal · IEEE Transactions on Information Theory · 8,056

Polynomial Codes Over Certain Finite Fields

1960 · I. S. Reed, G. Solomon · Journal of the Society for Industrial and Applied Mathematics · 3,670

Random Number Generation and Quasi-Monte Carlo Methods.

1993 · Bruce Jay Collings, Harald Niederreiter · Journal of the American Statistical Association · 2,883

The design of Rijndael AES - the advanced encryption standard

2002 · Daemen, Joan, Rijmen, Vincent · 2,874

Fundamentals of Error-Correcting Codes

2003 · W. Cary Huffman, Vera Pless · Cambridge University Press eBooks · 2,464

Finite fields

1996 · Rudolf Lide, Harald Niederreiter · 2,149

Introduction to Finite Fields and their Applications

1994 · Rudolf Lidl, Harald Niederreiter · Cambridge University Press eBooks · 2,069

Error Control Systems for Digital Communication and Storage

1995 · Stephen B. Wicker · Medical Entomology and Zoology · 1,769

A Course in Arithmetic

1973 · Jean-Pierre Serre · Graduate texts in mathematics · 1,713

Finite Geometries

1968 · Peter F. Dembowski · 1,665

A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms

2007 · Taher ElGamal · Springer eBooks · 1,605

Projective Geometries over Finite Fields

1998 · J W P Hirschfeld · 1,553

Finite fields

1983 · Rudolf Lidl · 1,376

Multiparty Computation from Somewhat Homomorphic Encryption

2012 · Ivan Damgård, Valerio Pastro, et al. · Lecture notes in computer science · 1,313

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Low-density parity-check codes based on finite geometries: a rediscovery and new results

2001 · Y. Kou, S. Lin, et al. · IEEE Transactions on Information Theory · 1,303

Basic Number Theory

1967 · André Weil · Springer eBooks · 1,223

Handbook of Combinatorial Designs

2006 · Chapman & Hall/CRC eBooks · 1,181

Efficient Algorithms for Pairing-Based Cryptosystems

2002 · Paulo S. L. M. Barreto, Hae Y. Kim, et al. · Lecture notes in computer science · 1,074

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Cryiptography and Network Security : Principles and Practices, 3rd ed

2003 · William Stallings · Medical Entomology and Zoology · 1,026

Reducing elliptic curve logarithms to logarithms in a finite field

1993 · A.J. Menezes, T. Okamoto, et al. · IEEE Transactions on Information Theory · 1,022

Handbook of Elliptic and Hyperelliptic Curve Cryptography

2005 · Lercier, Reynald, Lubicz, David, et al. · Chapman & Hall/CRC eBooks · 1,007

Compute-and-Forward: Harnessing Interference Through Structured Codes

2011 · Bobak Nazer, Michael Gastpar · IEEE Transactions on Information Theory · 990

Finite Geometries

1968 · Peter Dembowski · Springer eBooks · 938

Effective erasure codes for reliable computer communication protocols

1997 · Luigi Rizzo · ACM SIGCOMM Computer Communication Review · 916

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Works count: 34,600

Citation count: 326,900