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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 )

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 - UDT2018Organisateurs de la rencontre : Karpenkov, Oleg ; Nair, Radhakrishnan ; Verger-Gaugry, Jean-LouisDates : 01/10/2018 - 05/10/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1860.htmlCitation 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

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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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