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Title: Incomplete character sums and polynomial interpolation of the discrete logarithm
Authors: Niederreiter, H. 
Winterhof, A.
Issue Date: 2002
Source: Niederreiter, H., Winterhof, A. (2002). Incomplete character sums and polynomial interpolation of the discrete logarithm. Finite Fields and their Applications 8 (2) : 184-192. ScholarBank@NUS Repository.
Abstract: In the first part of the paper, certain incomplete character sums over a finite field Fp r are considered which in the case of finite prime fields Fp are of the form ∑n=A A+N-1 x(g(n)ψ(f(n)), where A and N are integers with 1 ≤ N < p, g and f are polynomials over Fp, and χ denotes a multiplicative and ψ an additive character of Fp. Excluding trivial cases, it is shown that the above sums are at most of the order of magnitude N1/2pr/4. Recently, Shparlinski showed that a polynomial f over the integers which coincides with the discrete logarithm of the finite prime field Fp for N consecutive elements of Fp must have a degree at least of the order of magnitude Np-1/2. In this paper this result is extended to arbitrary Fp r. The proof is based on the above new bound for incomplete hybrid character sums. © 2002 Elsevier Science (USA).
Source Title: Finite Fields and their Applications
ISSN: 10715797
DOI: 10.1006/ffta.2001.0334
Appears in Collections:Staff Publications

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