Linear Models for High-Complexity Sequences

Author(s):Show less -

Cardell, Sara D. ; Fuster-Sabater, Amparo ; Gervasi, O ; Murgante, B ; Misra, S ; Borruso, G ; Torre, CM ; Rocha, AMAC ; Taniar, D ; Apduhan, BO ; Stankova, E ; Cuzzocrea, A

• Document type: Journal article
• Source: COMPUTATIONAL SCIENCE AND ITS APPLICATIONS - ICCSA 2017, PT I; v. 10404, p. 11-pg., 2017-01-01.

Abstract

Different binary sequence generators produce sequences whose period is a power of 2. Although these sequences exhibit good cryptographic properties, in this work it is proved that such sequences can be obtained as output sequences from simple linear structures. More precisely, every one of these sequences is a particular solution of a linear difference equation with binary coefficients. This fact allows one to analyze the structural properties of the sequences with such a period from the point of view of the linear difference equations. In addition, a new application of the Pascal's triangle to the cryptographic sequences has been introduced. In fact, it is shown that all these binary sequences can be obtained by XORing a finite number of binomial sequences that correspond to the diagonals of the Pascal's triangle reduced modulo 2. (AU)

• FAPESP's process: 15/07246-0 - Construction, decoding and implementation of F_q linear codes. Performanca of SPC product codes and cryptanalysis of the shrinking generators.
• Grantee: Sara Díaz Cardell
• Support Opportunities: Scholarships in Brazil - Post-Doctoral