On the linear complexity of the Naor–Reingold sequence with elliptic curves

Cruz, M.; Gómez, Domingo; Sadornil, Daniel

doi:10.1016/j.ffa.2010.05.005

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…For Naor-Reingold sequences with elliptic curves, Proposition 1 and the results of [5] says that the sequence passes the 2-lattice test, for almost all choices of a 1 , . .…”

Section: Lattice Profile Of Ec-lcgmentioning

confidence: 94%

On lattice profile of the elliptic curve linear congruential generators

2014

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Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (abbr. EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG.

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“…For Naor-Reingold sequences with elliptic curves, Proposition 1 and the results of [5] says that the sequence passes the 2-lattice test, for almost all choices of a 1 , . .…”

Section: Lattice Profile Of Ec-lcgmentioning

confidence: 94%

On lattice profile of the elliptic curve linear congruential generators

2014

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“…This is because we have centered in the case of small n. This is the most interesting case and it also has been treated in [1,8] for elliptic curves. An interesting open question is to find lower bounds on the linear complexity for values of n near log l of the elliptic curves Naor-Reingold sequence.…”

Section: Remarks Conclusion and Future Workmentioning

confidence: 99%

On the linear complexity of the Naor–Reingold sequence

Gómez

Gutiérrez

Ibeas

2011

Information Processing Letters

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“…Several number-theoretic properties and complexity measures have been studied for the Naor-Reingold pseudo-random functions over finite fields as well as over elliptic curves: distribution (see [12,13] and references therein), period (see [14]), linear complexity (see [15][16][17][18]) and non-linear complexity (see [19]). Recently [20], the authors of the present paper proved lower bounds on the degree of polynomials interpolating the Naor-Reingold pseudo-random function at several points for fixed keys (over a finite field and over the group of points on an elliptic curve over a finite field).…”

Section: Introductionmentioning

confidence: 99%