Algebraic number theory
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Field theory
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Narendra Karmarkar
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Finite ring
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Field (mathematics)
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Field (algebra)
Finite field
In algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains a finite number of elements, called its order (the size of the underlying set). As with any ...
Cantor-Zassenhaus algorithm
Cantor-Zassenhaus algorithm
In computational algebra, the Cantor–Zassenhaus algorithm is a well known method for factorising polynomials over finite fields (also called Galois fields).The algorithm consists mainly of exponentiat...
Field with one element
In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted ...
Linear code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutio...
Rijndael S-box
The Rijndael S-box is a matrix (square array of numbers) used in the Rijndael cipher, which the Advanced Encryption Standard (AES) cryptographic algorithm was based on. The S-box (substitution box) s...
Rijndael S-box - Wikipedia
Hasse–Witt matrix
Generalized minimum-distance decoding
In coding theory, generalized minimum-distance (GMD) decoding provides an efficient algorithm for decoding concatenated codes, which is based on using an errors-and-erasures decoder for the outer code...
Tripling-oriented Doche–Icart–Kohel curve
The tripling-oriented Doche–Icart–Kohel curve is a form of an elliptic curve that has been used lately in cryptography; it is a particular type of Weierstrass curve. At certain conditions some operati...
Tripling-oriented Doche–Icart–Kohel curve - Wikipedia
MQV
MQV (Menezes–Qu–Vanstone) is an authenticated protocol for key agreement based on the Diffie–Hellman scheme. Like other authenticated Diffie-Hellman schemes, MQV provides protection against an active ...
Schoof's algorithm
Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography where it is important to know the numb...
Carlitz exponential
Dowling geometry
In combinatorial mathematics, a Dowling geometry, named after Thomas A. Dowling, is a matroid associated with a group. There is a Dowling geometry of each rank for each group. If the rank is at least ...
Steinberg representation
In mathematics, the Steinberg representation, or Steinberg module or Steinberg character, denoted by St, is a particular linear representation of a reductive algebraic group over a finite field or lo...
XTR
In cryptography, XTR is an algorithm for public-key encryption. XTR stands for ‘ECSTR’, which is an abbreviation for Efficient and Compact Subgroup Trace Representation. It is a method to represent el...
Chien search
In abstract algebra, the Chien search, named after Robert T. Chien, is a fast algorithm for determining roots of polynomials defined over a finite field. The most typical use of the Chien search is in...
Chien search - Wikipedia
Hidden Field Equations
Hidden Fields Equations (HFE) is a public key cryptosystem which was introduced at Eurocrypt in 1996 and proposed by (French) Jacques Patarin following the idea of the Matsumoto and Imai system. HFE i...
Tate pairing
In mathematics, Tate pairing is any of several closely related bilinear pairings involving elliptic curves or abelian varieties, usually over local or finite fields, based on the Tate duality pairin...
Preparata code
In coding theory, the Preparata codes form a class of non-linear double-error-correcting codes. They are named after Franco P. Preparata who first described them in 1968.
Let m be an odd number, ...
Hamming code
In telecommunication, Hamming codes are a family of linear error-correcting codes that generalize the Hamming(7,4)-code invented by Richard Hamming in 1950. Hamming codes can detect up to two-bit erro...
Trigonometry in Galois fields
In mathematics, trigonometry analogies are supported by the theory of quadratic extensions of finite fields, also known as Galois fields. The main motivation to deal with a finite field trigonometry i...
Trigonometry in Galois fields - Wikipedia
Drinfel'd module
In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, ...
GF(2)
GF(2) (also F2, Z/2Z or Z2) is the Galois field of two elements. It is the smallest finite field.
The two elements are nearly always called 0 and 1, being the additive and multiplicative identitie...
Triangular network coding
In coding theory, triangular network coding (TNC) is a network coding based packet coding scheme introduced by Qureshi, Foh & Cai (2012).Previously, packet coding for network coding was done using...
Triangular network coding - Wikipedia
Schoof–Elkies–Atkin algorithm
KCDSA
KCDSA (Korean Certificate-based Digital Signature Algorithm) is a digital signature algorithm created by a team led by the Korea Internet & Security Agency (KISA). It is an ElGamal variant, simil...
Elliptic curve cryptography
Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. One of the main benefits in comparison with non-ECC ...
BCH code
In coding theory, the BCH codes form a class of cyclic error-correcting codes that are constructed using finite fields. BCH codes were invented in 1959 by French mathematician Alexis Hocquenghem, and ...
BCH code - Wikipedia
Computation of cyclic redundancy checks
Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary message string, with a fixed number o...
Computation of cyclic redundancy checks - Wikipedia
Galois geometry
Galois geometry (so named after the 19th century French Mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or G...
Cantor–Zassenhaus algorithm
In computational algebra, the Cantor–Zassenhaus algorithm is a well known method for factorising polynomials over finite fields (also called Galois fields).The algorithm consists mainly of exponentiat...
Galois/Counter Mode
Galois/Counter Mode (GCM) is a mode of operation for symmetric key cryptographic block ciphers that has been widely adopted because of its efficiency and performance. GCM throughput rates for state of...
Galois/Counter Mode - Wikipedia