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Although much thought usually goes into the design of encryption algorithms and protocols, less consideration is often given to equally important issues such as the selection of cryptographically strong random numbers, so that an attacker may find it easier to break the random number generator than the security system it is used with. This paper provides a comprehensive guide to designing and implementing a practically strong random data accumulator and generator which requires no specialised hardware or access to privileged system services. The performance of the generator on a variety of systems is analysed, and measures which can make recovery of the accumulator/generator state information more difficult for an attacker are presented. The result is an easy-to-use random number generator which should be suitable even for demanding cryptographic applications.