Research efforts have extensively shown the significant roles of unpredictable phenomena originated in nature, such as chaos, as an inspiring discipline to generate random numbers. In the current study, focusing on encryption purposes, the main strategy is to provide a keystream using Pseudo Random Number Generators (PRNGs) derived from synchronized chaotic systems. Numerous Investigations performed on the synchronized configuration of Chua’s circuit have proven the advantage of its application as a prominent chaotic system. However, the less than ideal alignment between the core objective of the research, that is offering a secure communication optionally necessitating an arbitrary distance of the correspondents, and the standard version of synchronized Chua’s circuits not fulfilling this condition pragmatically, made the authors tackle the problem analytically by using the governing equations of the circuits and creating the so-called quasi-synchronized condition between the receiving and the transmitting sides. At last, eight different mathematical schemes are designed to manipulate the numerical data provided by the Chua’s equations to generate binary sequences for encryption purposes and then the main attempt has been dedicated to the evaluation of the results and finding the optimal PRNGs by conventional standards in cryptography provided by National Institute of Standards and Technology. Finally, three of the designed schemes are chosen as the successful methods, passing randomness criteria.