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H 1 On the cross-combined measure of families of binary lattices and sequences

Auteurs : Gyarmati, Katalin (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The cross-combined measure (which is a natural extension of crosscorrelation measure) is introduced and important constructions of large families of binary lattices with nearly optimal cross-combined measures are presented. These results are important in the study of large families of pseudorandom binary lattices but they are also strongly related to the one dimensional case: An easy method is showed obtaining strong constructions of families of binary sequences with nearly optimal cross-correlation measures based on the previous constructions of lattices. The important feature of this result is that so far there exists only one type of constructions of very large families of binary sequences with small cross-correlation measure, and this only type of constructions was based on one-variable irreducible polynomials. Since it is very complicated to construct one-variable irreducible polynomials over $\mathbb{F}_p$, it became necessary to show other types of constructions where the generation of sequences are much faster. Using binary lattices based on two-variable irreducible polynomials this problem can be avoided, however a slightly weaker upper bound is obtained for the cross-correlation measure than in the original construction. (But, contrary to one-variable polynomials, using Schöneman-Eisenstein criteria it is very easy to construct two-variable irreducible polynomials over $\mathbb{F}_p$.)

    Keywords : pseudorandomness ; cross-combined; cross-correlation; combined measure; correlation measure; binary lattice; binary sequence

    Codes MSC :
    11K45 - Pseudo-random numbers; Monte Carlo methods
    94A60 - Cryptography

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 10/10/2018
      Date de captation : 04/10/2018
      Collection : Number Theory
      Sous collection : Research talks
      Format : MP4
      Domaine : Number Theory
      Durée : 00:29:32
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-10-04_Gyarmati.mp4

    Informations sur la rencontre

    Nom de la rencontre : 6th International conference on uniform distribution theory - UDT2018 / 6e Colloque international sur la théorie de la répartition uniforme - UDT2018
    Organisateurs de la rencontre : Karpenkov, Oleg ; Nair, Radhakrishnan ; Verger-Gaugry, Jean-Louis
    Dates : 01/10/2018 - 05/10/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1860.html

    Citation Data

    DOI : 10.24350/CIRM.V.19455203
    Cite this video as: Gyarmati, Katalin (2018). On the cross-combined measure of families of binary lattices and sequences. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19455203
    URI : http://dx.doi.org/10.24350/CIRM.V.19455203


    Voir aussi

    Bibliographie

    1. Gyarmati, K. (2018). On the cross-combined measure of families of binary lattices and sequences. In J. Kaczorowski, J. Pieprzyk, & J. Pomykala (Eds.), Number-Theoretic Methods in Cryptology. NuTMiC 2017 (pp. 217-238). Springer, Cham - http://dx.doi.org/10.1007/978-3-319-76620-1_13

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