Shrinking generators and statistical leakage

AbstractShrinking is a newly proposed technique for combining a pair of pseudo random binary sequences, (a,s), to form a new sequence, z, with better randomness, where randomness here stands for difficulty of prediction. The ones in the second sequence s are used to point out the bits in the sequence a to be included in z. The generator that performs this process is known as the shrinking generator (SG). In this paper, it is shown for the existing combining method that deviation from randomness in the statistics of a leads to the leakage of this statistics into z. We also show that it is sufficient for constructing a statistically balanced SG to at least have one statistically balanced generator. A new shrinking rule that yields statistically balanced output, even if a and s are not balanced, is then proposed. Self-shrinking in which a single pseudo random bit generator (PRBG) shrinks itself is also investigated and a modification of the existing shrinking rule is proposed. Simulation results show the robustness of the proposed methods. For self-shrinking, in particular, results show that the proposed shrinking rule yields sequences with balanced statistics even for extremely biased generators. This suggests possible application of the new rule to strengthen running key generators

Computational Analysis of Interleaving PN-Sequences with Different Polynomials

Binary PN-sequences generated by LFSRs exhibit good statistical properties; however, due to their intrinsic linearity, they are not suitable for cryptographic applications. In order to break such a linearity, several approaches can be implemented. For example, one can interleave several PN-sequences to increase the linear complexity. In this work, we present a deep randomness study of the resultant sequences of interleaving binary PN-sequences coming from different characteristic polynomials with the same degree. We analyze the period and the linear complexity, as well as many other important cryptographic properties of such sequences.This work was supported in part by the Spanish State Research Agency (AEI) of the Ministry of Science and Innovation (MICINN), project P2QProMeTe (PID2020-112586RB-I00/AEI/ 10.13039/501100011033). It was also supported by Comunidad de Madrid (Spain) under project CYNAMON (P2018/TCS-4566), co-funded by FSE and European Union FEDER funds. The work of the second author was partially supported by Spanish grant VIGROB-287 of the University of Alicante

Sequences with long range exclusions

Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive, strictly increasing function. We review an other, graph theoretic, formulation and then the known results covering various combinations of $f$ and the alphabet size. In the second part of the paper we turn to the fine structure of the allowed sequences in the particular case where $f$ is a suitable polynomial. The generation of sequences leads naturally to consider the problem of their maximal length, which turns out highly random asymptotically in the alphabet size.Comment: 18 pages, 3 figures. Replaces earlier version, submission 1204.3439, major updat