Quasi-Random Number Sequences from a Long-Period TLP Generator with Remarks on Application to Cryptography

The background of the Lehmer hnear congruential algorithms that are in almost universal use for random sequence generatmn is reviewed; the reasomng is given for choosing the somewhat different Tausworthe linear recurrence (mod 2) type, using the bit selection algorithm of Lewis and Payne; and the initial statmtical evaluation is reported on. A review is gwen of the intmtwe process by which the Tausworthe approach, with a generating primitive trinomial of Mersenne prime exponent degree, was chosen. A discussmn is provided on the criteria on which conventional statistmal test methods are based. Then a summary of the statmtical tests on short subsequences of one generator of this type is given. It is proved that such a generator, cycling from a nonsingular seed matrix, yields a uniform dmtnbution of values over an enttre period. Finally, perturbation procedures for inhibiting sequence extrapolation and for making sequence members nonreproducible are outhned