lecture slides lecture 4 lecture4

7/27/2019 Lecture Slides Lecture 4 Lecture4

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Lecture 4

Noise as a random number

generator


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Plan of the Lecture

Extracting randomness from physical noise

1 Technical definition of noise

2-3 Thermal noise

4 Randomness from noise


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MATHEMATICS OF N

Many frequencies


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Frequency spectra

1 1 2 1


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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

M=10

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

M=40

Adding frequencies

0


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NoiseMore frequencies in the spectrum more noisy

0 1000 2000 3000 4000 5000 6000 7000 8000 9-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Little correlation (short memory) hard to predict

In fact, many natural source of noise have a continuous spectru


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Spectral bandwidth vs. memor

Correlation time

Coherence time

Spectrin freq


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THERMAL

Theory


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A resistor

RI

Really zero?


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Contact with a thermal bat

R

Temperature T


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Thermal noise

V

0

V

t

time


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Johnson-Nyquist noise

The thermal noise of the resistor is named af

John Johnson, who reported it, and Harry Nywho did the theoretical description (Bell Labs

From Johnsons paper:

The mean-square potential fIuctuation over the

conductor is proportionalto the electrical resistaand the absolute temperature of the conductor.

independentof the size, shape or material of th

conductor.


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The formula

RPower dissipated

by the resistor

At equilibrium, they must be equal

Ban

the Cable = 1D

waveguide for E,B

Boltzmanns c


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More rigorous derivation


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Predictions in graphs

Frequency s

1kW

1.6 10-13V2

=(0.4 mV)2

T=300K, Df=10kHz


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NOISE IN TH


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Devices

R

Amplifier

Oscilloscope

time


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Observation


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RANDOMNESS FROM


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Statistics of noise

The observed distribution is enough, because we have a c

source of noise: we checked that the noise is the one expected for th

we trust physics that it is a phenomenon too comple

One could put up an antenna and capture unknown signals

look random to us. But they may not be random for others,

unwanted structure in them.


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Observed distribution

R=1kW

T=300K

time Counts (103


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Possible processing (1)

Try to get directly fair coin sequences out o

0 1 000

1

1

0

1

More than one bit need to adapt carefully the in

for each sequence to have the s

(2)


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Possible processing (2)

Remark: for a trusted source, one can be less conservativ

compute randomness from the average (Shannon) entro

C l ti f fi it b d


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Correlations from finite bandwPreviously we assumed that each value of V is independent of t

As we know, no problem in principle: just estimate P of each se

compute Hmin. But in practice, this is not feasible.


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Wikipedia pages: http://en.wikipedia.org/wiki/Hardware_random_number_generat

Suggested Readings

S f L t 4
http://en.wikipedia.org/wiki/Hardware_random_number_generatorhttp://en.wikipedia.org/wiki/Hardware_random_number_generator


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Summary of Lecture 4

Noise = large spectrum of frequencies

Thermal noise

Extracting randomness, effects of correlation

Extracting randomness from physical noise

lecture slides lecture 4 lecture4

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