DNA sequencing has faced a huge demand since it was first introduced as a service to the public. This service is often offloaded to the sequencing companies who will have access to full knowledge of individuals' sequences, a major violation of privacy. To address this challenge, we propose a solution, which is based on separating the process of reading the fragments of sequences, which is done at a sequencing machine, and assembling the reads, which is done at a trusted local data collector. To confuse the sequencer, in a pooled sequencing scenario, in which multiple sequences are going to be sequenced simultaneously, for each target individual, we add fragments of one non-target individual, with a known DNA sequence at the data collector. Then coverage depth of the individuals, defined as the number of DNA fragments per DNA site, are selected proportional to the powers of two. This layered structured solution allows us to ensure privacy, using only one sequencing machine, in contrast to our previous solution, where we relied on the existence of multiple non-colluding sequencing machines.