polynomials over finite fields
Several Classes of Permutation Polynomials over Finite Fields
... of finite prime fields and by Dickson [4] for arbitrary finite ...Permutation polynomials have been studied extensively and have important applications in coding theory, cryp- tography, ...
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Some Problems Concerning Polynomials over Finite Fields, or Algebraic Divertissements
... functions over finite ...their finite difference in every nonzero direction is a permutation polynomial of the ...of polynomials satisfying these properties: in [RS89], [Joh87], [Hir89] and ...
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Galois Groups of Polynomials and the Construction of Finite Fields
... of polynomials of small degree was explored in [1], their general solutions were found which allow for the application of Galois ideas to analyse their splitting ...these polynomials (of degree less than or ...
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On some permutation polynomials over finite fields
... Permutation binomials and the sequence {an } The main tool in the proof of Theorem 1.1 is the following well-known theorem of Hermite [3, Theorem 7.4].. Theorem 3.1 Hermite’s criterion.[r] ...
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A new public key system based on Polynomials over finite fields GF(2)
... This brief analysis shows that encryption operation for both modes for this system has the same complexity as for the EIGamal type encryption. RSA encryption operation in “on-line” mode is faster, but for “off-line” mode ...
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On permutation polynomials over finite fields
... SCHMIDT, W.M., Equations Over Finite Fields, An Elementary Approach, Springer Lecture Notes, 536 1976..[r] ...
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Efficient Indexing of Necklaces and Irreducible Polynomials over Finite Fields
... n over alphabet Σ. A read-once branching program of length n over alphabet Σ is an acyclic directed graph with vertex layers numbered from 0 to n, where (1) layer 0 has a single start node, (2) there is a ...
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Finding irreducible polynomials over finite fields
... fouiid in polvnomiil linic b^ niivc snrdi Ί(ιρ (ΐ\ is n«w ( tsil) si cn to bi rompiitiblc in.. pol>iH)iiuil tmR llif[r] ...
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Fast Evaluation of Polynomials over Binary Finite Fields and Application to Side-channel Countermeasures
... S-boxes. Their method requires 7 non-linear multiplications. The method in [RV13] is based on the Divide-and-Conquer strategy, which is an adaptation of a polynomial evaluation technique by Paterson and Stockmeyer ...
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Extension fields and Galois Theory
... Finite fields are used in application of coding theory, many codes are Constructed as subspaces of vector spaces over finite fields ...Equations over finite fields ...
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Cubic surfaces over finite fields
... defined over a field K are isomorphic over K involves testing for equivalence of cubic polynomials in four variables defined over K under an action of K ∗ × GL(4, K); K ∗ acts by scaling and ...
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A Preliminary Investigation into the Mediating Role of Positive Affect in the Development of Posttraumatic Stress Disorder among African American Female Sexual Assault Survivors
... permutation polynomials started with Hermite who considered the case of finite prime ...Permutation polynomials of arbitrary finite fields were first studied by Dickson ...Permutation ...
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On Polynomials of the Form xrf(x(q−1)/l)
... The main result of this paper was presented by Qiang Wang in BIRS Workshop on Poly- nomials over Finite Fields and Applications in November 2006. The second author wants to thank BIRS for the ...
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Normal high order elements in finite field extensions based on the cyclotomic polynomials
... Normal basis is also an important notion in the theory of finite fields, see [1, 5, 6, 9] for the definition, basic properties and references. One of the most interesting constructions of normal bases come ...
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A new approach in building parallel finite field multipliers
... polynomial arithmetic and irreducible polynomials, extension fields exist for finite fields.. as well.[r] ...
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P R O FI L E S OFLARGE COM BINATORIAL STRUCTURES
... of polynomials in finite fields, connected components of certain forests, prime factor- izations of integers, and a variety of other combinatorial objects have a number of components which is ...
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Properties of sparse random matrices over finite fields
... of Λ). Analytical solutions cannot be obtained in general and we must rely on numerical methods to obtain them. However, there exists two straightforward analytical solutions, the paramagnetic and ferromagnetic states. ...
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Regular proper *-semigroup embeddings and involutionstitle
... all a i = 0. If D is the identity matrix we say that F is n−formally complex and if this true for all n we say that F is formally-complex. On the other hand, if α is the identity then we say that F is D(α )− real and if ...
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A Versatile Multi-Input Multiplier over Finite Fields
... elements over finite fields is used extensively in multivariate public key cryptography and solving system of linear equations over finite ...elements over finite ...
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A Study on Construction of the Advanced Sequential Circuit over Finite Fields
... Unlike the combinational logic circuit implementation, the conventional sequential logic circuit must be considered current and next state. To this end, the next state function had to be derived. To implement this in a ...
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