Date of Award
Master of Engineering (Research)
Richard A. Guinee
Random numbers have conventionally been used in a range of applications such as numerical analysis, lotteries and computer simulation and as cryptographic keys. The algorithms used for the production of random numbers are termed pseudorandom, as the numbers produced are not truly random as they emanate from a deterministic periodic source that is they are predictable if a subset of the sequence is known. However, for most applications these pseudorandom number sources are entirely suitable.
For cryptographic key sources, however, the random number sequences must be statistically good and difficult to predict. Linear feedback shift registers are presented in this thesis as random number generators that are based on pseudorandom binary sequences. The initial generator discussed comprises of a single stage maximal length shift register whose randomness attributes are investigated by examination of its autocorrelation function. This topology is extended to a dual geared form that employs two linear feedback shift registers combined so as to produce a compound non-maximal length sequences with enhanced statistical properties. Following from this Gold and Kasami sequences are investigated as possible dual geared random number generators due to their bounded low value cross correlation functions.
The dual geared structure enhances the randomness characteristics of the number streams produced and uses delayed versions of the combined generator output sequence as tap points in the random number creation so as to spread the taps over the entire register sequence length rather than the physically available register stages. The auotcorrelation function of the resultant random number stream approaches that of white noise and indicates the uniformity of the numbers produced.
The statistical quality of the random number sequences produced is gauged using a set of standard statistical tests for randomness. Generators that pass these tests may be considered as adequate key sources for cryptographic applications where data security is a concern.
Rea, Susan, "Uniform Random Number Generation Using Pseudorandom Binary Sequences" (2001). Theses [online].
Available at: https://sword.cit.ie/allthe/625