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1.
Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography
and Monte-Carlo methods.
The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom
number generation.
Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudorandom number generator
was proven by Gutierrez, Shparlinski and the first author. For most nonlinear generators a much stronger lower bound is expected.
Here, we obtain a much stronger lower bound on the linear complexity profile of nonlinear congruential pseudorandom number
generators with Dickson polynomials. 相似文献
2.
3.
We estimate discrete Fourier transform, ambiguity, and Hamming-auto-correlation of \(m\) -ary sequences in terms of their (periodic) correlation measure of order 4. Roughly speaking, we show that every pseudorandom sequence, that is, any sequence with small correlation measure up to a sufficiently large order, cannot have a large discrete Fourier transform, ambiguity, or Hamming-autocorrelation. Conversely, there are sequences, for example the two-prime generator, with large correlation measure of order 4 but small discrete Fourier transform, ambiguity, autocorrelation, and Hamming-autocorrelation. 相似文献
4.
Inversive methods are attractive alternatives to the linear method for pseudorandom number generation. A particularly attractive method is the digital explicit inversive method recently introduced by the authors. We establish some new results on the statistical properties of parallel streams of pseudorandom numbers generated by this method. In particular, we extend the results of the first author on the statistical properties of pseudorandom numbers generated by the explicit inversive congruential method introduced by Eichenauer-Herrmann. These results demonstrate that the new method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties. 相似文献
5.
We continue the study of the linear complexity of binary sequences, independently introduced by Sidel’nikov and Lempel, Cohn,
and Eastman. These investigations were originated by Helleseth and Yang and extended by Kyureghyan and Pott. We determine
the exact linear complexity of several families of these sequences using well-known results on cyclotomic numbers. Moreover,
we prove a general lower bound on the linear complexity profile for all of these sequences. 相似文献
6.
In this paper we study the non-existence problem of (nearly) perfect (almost) m-ary sequences via their connection to (near) Butson–Hadamard (BH) matrices and (near) conference matrices. We refine the idea of Brock on the unsolvability of certain equations in the case of cyclotomic number fields whose ring of integers is not a principal ideal domain and get many new non-existence results for near BH matrices and near conference matrices. We also apply previous results on vanishing sums of roots of unity and self conjugacy condition to derive non-existence results for near BH matrices and near conference matrices. 相似文献
7.
Edwin D. El-Mahassni Igor E. Shparlinski Arne Winterhof 《Monatshefte für Mathematik》2006,59(1):297-307
The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom
number generation. In this paper we present a new bound on the s-dimensional discrepancy of nonlinear congruential pseudorandom numbers over the residue ring
\Bbb ZM{\Bbb Z}_M
modulo M for an “almost squarefree” integer M. It is useful to recall that almost all integers are of this type. Moreover, if the generator is associated with a permutation
polynomial over
\Bbb ZM{\Bbb Z}_M
we obtain a stronger bound “on average” over all initial values. This bound is new even in the case when M = p is prime. 相似文献
8.
We estimate the linear complexity profile of m-ary sequences in terms of their correlation measure, which was introduced by Mauduit and Sárközy. For prime m this is a direct extension of a result of Brandstätter and the second author. For composite m, we define a new correlation measure for m-ary sequences, relate it to the linear complexity profile and estimate it in terms of the original correlation measure. We apply our results to sequences of discrete logarithms modulo m and to quaternary sequences derived from two Legendre sequences. 相似文献
9.
Arne Winterhof 《Designs, Codes and Cryptography》2002,25(1):63-72
Recently, Coppersmith and Shparlinski proved several results on the interpolation of the discrete logarithm in the finite prime field
by polynomials modulo p and modulo p-1, respectively. In this paper most of these results are extended to arbitrary
. 相似文献
10.
We prove a bound on sums of products of multiplicative characters of shifted Fermat quotients modulo p. From this bound we derive results on the pseudorandomness of sequences of modular discrete logarithms of Fermat quotients modulo p: bounds on the well-distribution measure, the correlation measure of order ?, and the linear complexity. 相似文献