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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
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.
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
"... Abstract — 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 condi ..."
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Abstract — 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
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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