Download Pseudo Random Number Generation and Random Event Validation

Pseudo Random Number
Generation and Random
Event Validation through
Graphical Analysis
What is randomness?
A function not affected by any input or
state
Independent of previous results
Example



Flipping an unbiased coin
Rolling die
Quantum effects
True vs Pseudo
RNG
No input criteria
PRNG
Input initial seed

Cannot be predicted
usually predictable
In the form of a
mathematical function
The problem
Computer systems need random numbers
Provided by a PRNG
Poor vs Good
Good vs Poor
R250
Linear recursive
method
Von Neumann’s
Middle Square
method
Good PRNG using a
bad seed
Example
Linear Recursive Method
Xn+1 = (aXn + b) % m
a = 273 673 163 155 8
b = 138
m = 248
Period…
Approx. 1 year @ 10 000 000
random numbers per second
Or
3 x 1014 random numbers
Random Event Validation
Look at existing PRNG
Investigate Lotto numbers
Build hardware RNG
A graphical view
Method of delayed coordinates plotted in a
phase space
Convert 1-D to 3-D by:
X[n] = s[n-2] – s[n-3]
Y[n] = s[n-1] – s[n - 2]
Z[n] = s[n] – s[n-1]
Higher dimensions are possible
Acts as a “comb”
What to expect
True random data set - Random Cloud
Random cloud for a good PRNG
Poor PRNG will result in attractors
True random
Poor PRNG
ISN’s from Windows 98 SE TPC/IP