English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

LSB (Least Significant Bit) sequences are widely used as the initial inputsin some modern stream ciphers, such as the ZUC algorithm-the core of the 3GPPLTE International Encryption Standard. Therefore, analyzing the statisticalproperties (for example, autocorrelation, linear complexity and 2-adiccomplexity) of these sequences becomes an important research topic. In thispaper, we first reduce the autocorrelation distribution of the LSB sequence ofa $p$-ary $m$-sequence with period $p^n-1$ for any order $n\geq2$ to theautocorrelation distribution of a corresponding Costas sequence with period$p-1$, and from the computing of which by computer, we obtain the explicitautocorrelation distribution of the LSB sequence for each prime $p<100$. Inaddition, we give a lower bound on the 2-adic complexity of each of these LSBsequences for all primes $p < 20$, which proves to be large enough to resistthe analysis of RAA (Rational Approximation Algorithm) for FCSRs (Feedback withCarry Shift Registers). In particular, for a Mersenne prime $p=2^k-1$ (i.e.,$k$ is a prime such that $p$ is also a prime), our results hold for all itsbit-component sequences since they are shift equivalent to the LSB sequence.

Autocorrelation and Lower Bound on the 2-Adic Complexity of LSB Sequence of $p$-ary $m$-Sequence