1. Quasi-Random Number Sequences from a Long Period TLP Generator with Remarks on Application to Cryptography By Herbert S. Bright and Richard L. Enison Presented by Saunders Roesser

2. The Problem Generation of successful random number sequences that pass all statistical testing criteria. Generation in an Application domain.

3. Background Physical Generations are unsuitable for modern computers Linear Congruential formulas: –X i+1 = ax i + c (mod m) Additive Formulas –Xi = a 1 X x-1 + a 2 x i-2 +…..+a p x i-p + c (mod m) Don’t work unless you have large primes.

4. TLP Sequence Tausworthe-Lewis-Payne distribution Sequence for generation of random numbers. Trinomial: x 521 +x 32 +1 Generate 64-bit numbers Period is 2 521 -1 Better then linear congruential generators

5. Statistical Testing Criteria Equidistribution/Frequency Test –The number of time a given number falls into a given interval Serial Test –The number of times a sequence appears in a certain number of numbers Gap Test –The distribution of gaps in the sequence of various lengths.

6. More Tests Runs Test –Plots the distribution of maximal ascending runs of various lengths Coupon Collector’s Test –Choose a small interger, divide the number into intervals then plot the distribution runs of various lengths required to have all intervals represented

7. More Tests Permutation Test –Order relations between the members of the sequence in groups of k. Serial Correlation Test –Computer the correlation coefficient between consecutive members of the sequence. Others..

8. Results At the time, all present generators failed the battery of tests. Hope came from recursive function theory. TLP Generator showed good results in string tests Passed equidistributivity tests, along with other tests.

9. Other Physical Random Number Generators Dice Ionizing radiation Gas discharge tubes Leaky capacitors Physical noise generators