AMC
On the arithmetic autocorrelation of the Legendre sequence
Richard Hofer Arne Winterhof
The Legendre sequence possesses several desirable features of pseudorandomness in view of different applications such as a high linear complexity (profile) for cryptography and a small (aperiodic) autocorrelation for radar, gps, or sonar. Here we prove the first nontrivial bound on its arithmetic autocorrelation, another figure of merit introduced by Mandelbaum for errorcorrecting codes.
keywords: Arithmetic autocorrelation Legendre sequence pseudorandom sequences pattern distribution cryptography
AMC
On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences
Alina Ostafe Igor E. Shparlinski Arne Winterhof
Recently, multisequences have gained increasing interest for applications in cryptography and quasi-Monte Carlo methods. We study the (generalized) joint linear complexity of a class of nonlinear pseudorandom multisequences introduced by the first two authors as well as the linear complexity of its coordinate sequences. We prove lower bounds which are much stronger than in the case of single sequences since the multidimensional case brings in new and favourable effects.
keywords: nonlinear pseudorandom number generators. Linear complexity

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