Incomplete character sums and a special class of permutations

S. D. Cohen; H. Niederreiter; I. E. Shparlinski; M. Zieve

Journal de théorie des nombres de Bordeaux (2001)

  • Volume: 13, Issue: 1, page 53-63
  • ISSN: 1246-7405

Abstract

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We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an ℛ -orthomorphism. Examples of ℛ -orthomorphisms are given.

How to cite

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Cohen, S. D., et al. "Incomplete character sums and a special class of permutations." Journal de théorie des nombres de Bordeaux 13.1 (2001): 53-63. <http://eudml.org/doc/248719>.

@article{Cohen2001,
abstract = {We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an $\mathcal \{R\}$-orthomorphism. Examples of $\mathcal \{R\}$-orthomorphisms are given.},
author = {Cohen, S. D., Niederreiter, H., Shparlinski, I. E., Zieve, M.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {incomplete character sum; permutation; pseudorandom sequence; orthomorphisms},
language = {eng},
number = {1},
pages = {53-63},
publisher = {Université Bordeaux I},
title = {Incomplete character sums and a special class of permutations},
url = {http://eudml.org/doc/248719},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Cohen, S. D.
AU - Niederreiter, H.
AU - Shparlinski, I. E.
AU - Zieve, M.
TI - Incomplete character sums and a special class of permutations
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 1
SP - 53
EP - 63
AB - We present a method of bounding incomplete character sums for finite abelian groups with arguments produced by a first-order recursion. This method is particularly effective if the recursion involves a special type of permutation called an $\mathcal {R}$-orthomorphism. Examples of $\mathcal {R}$-orthomorphisms are given.
LA - eng
KW - incomplete character sum; permutation; pseudorandom sequence; orthomorphisms
UR - http://eudml.org/doc/248719
ER -

References

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  3. [3] J. Gutierrez, H. Niederreiter, I.E. Shparlinski, On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period. Monatsh. Math.129 (2000), 31-36. Zbl1011.11053MR1741034
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  7. [7] H. Niederreiter, I.E. Shparlinski, On the distribution of inversive congruential pseudorandom numbers in parts of the period. Math. Comp., to appear. Zbl0983.11048MR1836919
  8. [8] H. Niederreiter, I.E. Shparlinski, On the distribution and lattice structure of nonlinear congruential pseudorandom numbers. Finite Fields Appl.5 (1999), 246-253. Zbl0942.11037MR1702905
  9. [9] H. Niederreiter, I.E. Shparlinski, Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus. Acta Arith.92 (2000), 89-98. Zbl0949.11036MR1739735
  10. [10] H. Niederreiter, I.E. Shparlinski, On the distribution of pseudorandom numbers and vectors generated by inversive methods. Applicable Algebra Engrg. Comm. Comput.10 (2000),189-202. Zbl0999.11040MR1751430
  11. [11] C.P. Schnorr, S. Vaudenay, Black box cryptanalysis of hash networks based on multipermutations. Advances in Cryptology - EUROCRYPT '94 (A. De Santis, ed.), Lecture Notes in Computer Science, Vol. 950, pp. 47-57, Springer, Berlin, 1995. Zbl0909.94013MR1479648
  12. [12] I.E. Shparlinski, Finite Fields: Theory and Computation. Kluwer Academic Publ., Dordrecht, 1999. Zbl0967.11052MR1745660
  13. [13] J.H. Van Lint, R.M. Wilson, A Course in Combinatorics. Cambridge Univ. Press, Cambridge, 1992. Zbl0769.05001MR1207813

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