In this paper, we develop parallel scrambling techniques for the distributed sample scrambling (DSS), which are directly applicable to the bit- and multibit-interleaved multiplexing environments. We first consider how to realize PSRGs, parallel samplings and parallel corrections for the multibit-parallel DSS (MPDSS), which are the fundamental problems in realizing the MPDSS scramblers and descramblers. The results are summarized in three sets of theorems, and a corollary is attached to each theorem to specifically handle the case of the parallel DSS (PDSS). The theorems and corollaries are supported by examples that demonstrate the relevant MPDSS scramblers and descramblers.