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Pseudo-random generators using linear feedback shift registers with output extraction

Holger Nobach

Published 2024 in arXiv.org

ABSTRACT

The use of three extractors, fed by linear feedback shift registers (LFSR) for generating pseudo-random bit streams is investigated. Specifically, a standard LFSR is combined with a von Neumann extractor, a modified LFSR, extended by the all-zero state, is combined with an output logic, which translates every three bits from the LFSR into up to two output bits and a run extraction of the input bit stream into single output bits are investigated. The latter two achieve better efficiency in using bits from the primary bit stream, the last one reaches 50\%. Compared to other generator logics, the three extractors investigated are less performant in terms of their cryptographic strength. However, the focus of this report is on the quality of the pseudo-random bit stream in comparison to really random bits and on the efficiency of using the bits of the primary stream from the LFSR and generating valid output bits, while fulfilling a minimum cryptographic strength only, beyond that of the pure LFSR.

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