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FINITE FIELDS
"... This handout discusses finite fields: how to construct them, properties of elements in a finite field, and relations between different finite fields (including their Galois groups). We write Z/(p) and Fp interchangeably for the field of size p. Here is an executive summary of the main results. • Eve ..."
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This handout discusses finite fields: how to construct them, properties of elements in a finite field, and relations between different finite fields (including their Galois groups). We write Z/(p) and Fp interchangeably for the field of size p. Here is an executive summary of the main results
Probabilistic Algorithms In Finite Fields
 SIAM J. Comput
, 1979
"... We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theor ..."
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Cited by 98 (1 self)
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We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding
Motives over finite fields
 these Proceedings
, 1993
"... Abstract. The category of motives over the algebraic closure of a finite field is ..."
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Cited by 20 (8 self)
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Abstract. The category of motives over the algebraic closure of a finite field is
Finite fields
, 2010
"... 3. Introduction to error correcting codes. Contents 0.1 Group theory........................... 3 ..."
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3. Introduction to error correcting codes. Contents 0.1 Group theory........................... 3
On functions of finite fields
"... I describe on functions of finite fields, about differentially uniformities and nonlinearlities of functions in this paper, mainly about planar functions over finite fields of characteristic an odd prime p and about almost perfect nonlinear functions and almost bent functions over finite fields of c ..."
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I describe on functions of finite fields, about differentially uniformities and nonlinearlities of functions in this paper, mainly about planar functions over finite fields of characteristic an odd prime p and about almost perfect nonlinear functions and almost bent functions over finite fields
Program correctness on finite fields
"... Key words. Finite fields, pseudofinite fields, program correctness, FloydHoare derivation. ..."
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Key words. Finite fields, pseudofinite fields, program correctness, FloydHoare derivation.
FiniteField Consensus
, 2013
"... This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers {0,..., p − 1}, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions on ..."
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This work studies consensus networks over finite fields, where agents process and communicate values from the set of integers {0,..., p − 1}, for some prime number p, and operations are performed modulo p. For consensus networks over finite fields we provide necessary and sufficient conditions
A public key cryptosystem and a signature scheme based on discrete logarithms
 ADV. IN CRYPTOLOGY, SPRINGERVERLAG
, 1985
"... A new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. ..."
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Cited by 1551 (0 self)
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A new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields.
The number of directions determined by a function over a finite field
 J. Combin. Theory Ser. A
"... finite field ..."
On the Brauer monoid for finite fields
, 2008
"... The definition of the Brauer monoid was given in [3]. In this article it is studied by the notions of modifications [6] and 0cohomology [5]. We investigate the impact of invertible elements of modifications on the structure of the Brauer monoid, especially for finite fields. ..."
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Cited by 1 (1 self)
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The definition of the Brauer monoid was given in [3]. In this article it is studied by the notions of modifications [6] and 0cohomology [5]. We investigate the impact of invertible elements of modifications on the structure of the Brauer monoid, especially for finite fields.
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