Pseudo Random Number Generation and Random Event Validation through Graphical Analysis

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Pseudo Random Number Generation and Random Event
Validation through Graphical Analysis
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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

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True vs Pseudo

• RNG
• No input criteria
• Cannot be predicted

• PRNG
• Input initial seed
• usually predictable
• In the form of a mathematical function

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The problem

• Computer systems need random numbers
• Provided by a PRNG
• Poor vs Good

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Good vs Poor

• R250
• Linear recursive method

• Von Neumanns Middle Square method
• Good PRNG using a bad seed

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Example

• Linear Recursive Method
• Xn1 (aXn b) m
• a 273 673 163 155 8
• b 138
• m 248
• Period

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• Approx. 1 year _at_ 10 000 000 random numbers
  per second
• Or
• 3 x 1014 random numbers

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Random Event Validation

• Look at existing PRNG
• Investigate Lotto numbers
• Build hardware RNG

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A graphical view

• Method of delayed coordinates plotted in a phase
  space
• Convert 1-D to 3-D by
• Xn sn-2 sn-3
• Yn sn-1 sn - 2
• Zn sn sn-1
• Higher dimensions are possible
• Acts as a comb

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What to expect

• True random data set - Random Cloud
• Random cloud for a good PRNG
• Poor PRNG will result in attractors

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True random
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Poor PRNG
ISNs from Windows 98 SE TPC/IP