Presentation Somo

8/11/2019 Presentation Somo

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Random Number Generator

(RNG) for Microcontrollers

Dr. S. Somokanta Singh

Manipur Institute of Management [email protected]


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Dr. S. Somokanta SinghMIMS, M.U.

Introduction

RNG Wisdom

Motivation for an RNG

Other RNG Methods

Requirements for a Good RNG

Approaches Taken

Testing

Implementation

Summary


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RNG Wisdom

Anyone who considers arithmeticalmethods of producing random dig i ts is ,

of course, in a state of sin. John von

Neumann (1903-1957).

The generation of random numbers is

too important to be left to chance.Robert R. Coveyou, Oak Ridge NationalLaboratory in Tennessee.


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Motivation For An RNG

For Microcontrollers More Interesting Robotic Behavior

Avoid Stuck-In-A-Corner Logic

Used In AI Techniques Genetic Algorithms

Neural Networks

Fuzzy Logic


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Other RNG Methods

Hardware-Based (true) RNGs

White-Noise Source

Transistor Circuits

Our desire is to have a pseudo random

number generator, as defined by


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Requirements - a Good RNG

Key Requirements (detailed list in paper).

N = F(), where

N is in the range 0 to 255

Large cycle of Ns before pattern repeats. All values of N are generated the same number of

times in the cycle.

Windows of consecutive Ns in cycle meet

Constraints for Average, Min, and Max values.

Small Code Size


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Approaches Taken

Table-Based Method

Define a table of 128 values.

Use EXOR to generate 128 other values.

Cycle through these 256 values 64

different ways.

Cycle length of 16,384.

Met the goodness criteria.

62 bytes of code + 128 bytes for table =

190 total bytes. 4 bytes of RAM.


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Approaches Taken

Equation-Based Method

2-byte seed value in RAM

seed = 181 * seed + 359

Return top 8 bits of seed.

Cycle length of 65,536.

Met the goodness criteria.

25 bytes of code, 4 bytes of RAM.


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Approaches Taken

Notes:

181 and 359 determined by a program searching

for values to meet the goodness criteria.

Table method also used a program to find right

128 table values.


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Generated Numbers

First 240 numbers:1 255 117 4 73 222 125 232 15 167 21 110 230 252 49 2735 65 133 50 218 156 132 185 223 239 99 114 197 223 22 226226 208 81 76 71 229 135 182 203 4 237 226 1 207 119 8560 170 216 82 145 187 134 223 211 228 179 190 152 202 84 116

50 209 28 68 182 28 128 52 248 145 181 6 139 210 172 63196 68 28 34 183 10 119 181 56 9 242 186 219 229 129 182243 2 216 237 149 132 106 98 148 78 108 218 134 5 210 217189 13 80 163 78 137 89 59 13 94 34 102 141 48 159 16835 99 131 69 227 27 68 64 161 59 20 94 241 104 232 3538 6 115 211 85 56 43 113 81 228 66 194 176 172 172 74196 244 31 77 162 226 13 206 30 88 171 146 203 251 237 29

254 47 135 179 203 23 236 87 6 153 81 206 66 87 170 156213 181 171 5 209 217 199 12 10 165 51 118 22 190 227 19971 136 138 67 178 39 158 237 43 126 81 138 69 50 152 15885 167 38 109 111 0 113 250 103 34 171 11 208 177 201 33


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Testing The Numbers

Met The Defined Goodness Criteria

Inspection

Graphical Plots Plot number pairs on 256x256 grid.


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Testing

1024 pairs

plotted


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Testing

Half the

pairs plotted


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Testing

All pairs

plotted


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Testing

All pairs

with another

set of

constants


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Implementation

25 Bytes of 68HC11 CodeRandom:

PSHB ; (1,3) Remember the current value of B* scratch = seed * multiplier

LDAA #MULTIPLIER ; (2,2) A = #181LDAB SEED_LOW ; (2,3) B = the low byte of the seed

MUL ; (1,10) D = A x BSTD RandomScratch ; (1,4) scratch = D

LDAA #MULTIPLIER ; (2,2) A = #181LDAB SEED_HIGH ; (2,3) B = the high byte of the seed

MUL ; (1,10) D = A x B* low byte of MUL result is added to the high byte of scratch

ADDB RandomScratch ; (2,3) B = B + scratch_highSTAB RandomScratch ; (2,3) scratch = seed * 181

*LDD RandomScratch ; (2,4) D = scratch

ADDD #ADDER ; (3,4) D = D + 359STD RandomSeed ; (2,4) remember new seed value

* (A = SEED_HIGH from ADDD instruction)PULB ; (1,4) Restore the value of BRTS ; (1,5) A holds the new 8-bit random number


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Summary

RNG Studied

RNG Goodness Criteria Developed

Two RNG Methods Developed Both Methods Were Critiqued

Equation-Based RNG Chosen For

Number Coverage and Code Size 68HC11 Code Implemented and

Tested

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