Authors:
Eric Filiol
1
;
2
and
Pierre Filiol
3
Affiliations:
1
Thales Digital Factory, Thales Group, Paris, France
;
2
ENSIBS, Vannes, France
;
3
Lab-STICC, ENSTA Bretagne, Brest, France
Keyword(s):
NLFSR, Stream Cipher, Binary Sequence, Maximum Period, Graph Representation, Incidence Matrix.
Abstract:
NonLinear Feedback Shift Registers (NLFSRs) are key primitives to design pseudorandom generators in modern stream ciphers, especially when the feedback function is of low degree. Contrary to their linear counterparts (LFSRs) for which a general and comprehensive theory has been established, many fundamental problems related to NLFSRs remain open. In particular finding a systematic procedure of acceptable complexity for constructing NLFSRs with a guaranteed long period is still a general open problem and only a few results have been obtained so far. In this paper, we present the results of a exhaustive exploratory search and analysis of NLFSRs of low degree. We first model NLFSRs as graphs using their incidence matrix and express the maximum period property as graph properties. This enables to reduce the number of possible candidates greatly that can be tested finally for the maximum period property by HPC on GPGPUs and Massively Parallel Processor Array (MPPA).