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Pseudorandom number generators (PRNGs) are an essential tool in many areas, including simulation studies of stochastic processes, modeling, randomized algorithms, and games. The performance of any PRNGs depends on the quality of the generated random sequences; they must be generated quickly and have good statistical properties. Several statistical test suites have been developed to evaluate a single stream of random numbers, such as TestU01, DIEHARD, the tests from the SPRNG package, and a set of tests designed to evaluate bit sequences developed at NIST. TestU01 provides batteries of test that are sets of the mentioned suites. The predefined batteries are SmallCrush (10 tests, 16 p-values) that runs quickly, Crush (96 tests, 187 p-values) and BigCrush (106 tests, 2254 p-values) batteries that take longer to run. Most pseudorandom generators use recursion to produce sequences of numbers that appear to be random. The linear congruential generator is one of the well-known pseudorandom generators, the next number in the random sequences is determined by the previous one. The recurrences start with a value called the seed. Each time a recurrence starts with the same seed the same sequence is produced. This thesis develops a new pseudorandom number generation scheme that produces random sequences with good statistical properties via scrambling linear congruential generators. The scrambling technique is based on a simplified version of Feistel network, which is a symmetric structure used in the construction of cryptographic block ciphers. The proposed research seeks to improve the quality of the linear congruential generators’ output streams and to break up the regularities existing in the generators.