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A critical issue with generating pseudo-random sequences for any cryptographic application is security. One of the common techniques used to generate pseudo-random sequences has been the use of Congruential Generators (CGs). One of the well-known forms of these generators is called the Linear Congruential Generator (LCG). However these generators are known to be cryptographically weak. A highly secure pseudo-random bit sequence generation scheme (Hex-Coupled System) using coupled LCGs is proposed in this book. This book introduces other schemes of coupling CGs that generate pseudo-random sequences and two novel algorithms to generate parameters for LCGs and QCGs (Quadratic Congruential Generators). It also includes the results for the proposed coupled CGs that pass all the pseudo-randomness tests recommended by the NIST (National Institute of Standards and Technology). In summary, this book offers a wide variety of pseudo-random algorithms for numerous applications based on the need for low cost, efficient and secure pseudo-random bit sequences. Examples of the applications where these algorithms can be used, are RFID tags, simulation, encryption schemes, smart cards, etc.