the entropy generation rates of physical sources of randomness - - PowerPoint PPT Presentation

β–Ά
the entropy generation rates of
SMART_READER_LITE
LIVE PREVIEW

the entropy generation rates of physical sources of randomness - - PowerPoint PPT Presentation

Feb 22, 2024 578 likes β€’919 views

The im impact of dig igitization on the entropy generation rates of physical sources of randomness Joseph D. Hart 1,2,* , Thomas E. Murphy 2,3 , Rajarshi Roy 2,3,4 , Gerry Baumgartner 5 1 Dept. of Physics 2 Institute for Research in Electronics

slide-1
SLIDE 1

The im impact of dig igitization on the entropy generation rates of physical sources of randomness

Joseph D. Hart1,2,*, Thomas E. Murphy2,3, Rajarshi Roy2,3,4, Gerry Baumgartner5

1 Dept. of Physics 2 Institute for Research in Electronics & Applied Physics 3 Dept. of Electrical & Computer Engineering 4 Institute for Physical Science and Technology 5Laboratory for Telecommunication Science

*jhart12@umd.edu

slide-2
SLIDE 2

Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.

  • -John von Neumann

Why Physical RNG?

slide-3
SLIDE 3

Physical RNG

  • Algorithms can only produce pseudo-random

numbers

  • For true random numbers, we turn to physical

systems

  • Can be FASTER because not limited by CPU clock
  • Need to be post-processed to remove bias, etc.
  • Important differences between pseudo-RNG and

physical RNG should be reflected in evaluation metrics

slide-4
SLIDE 4

Electronic Physical RNG Today (Intel Ivy Bridge Processors)

  • 3 Gb/s raw RNG rate
  • Raw bits are not directly used (nor accessible)
  • Continuously re-seeds a pseudo-random generator
  • Instruction: RDRND
slide-5
SLIDE 5

Chaotic Semiconductor Laser

  • Fluctuations are fast and chaotic

(sensitive dependence on initial conditions)

Sakuraba, Ryohsuke, et al. Optics express 23.2 (2015): 1470-1490.

slide-6
SLIDE 6

Amplified Spontaneous Emission

  • C. R. Williams, J. C. Salevan, X. Li, R. Roy, and T. E.

Murphy, Optics Express 18, 23584–23597 (2010).

slide-7
SLIDE 7

Comparison of Optical RNG Methods – Recent Research

Whitewood ID Quantique PicoQuant

slide-8
SLIDE 8

NIST SP 800-22rev1a

  • Easy to implement
  • Publicly accessible standard
  • Even non-cryptographically secure Pseudo-RNG

methods (e.g., Mersenne Twister) will pass all tests

  • Only works on binary data (1s and 0s), not analog

data or waveforms

  • Most physical RNG methods require post-

processing to pass tests

slide-9
SLIDE 9

Post-Processing of Digitized Waveforms

  • Least Significant Bit Extraction:

What is the source of entropy? (waveform, digitizer, thermal noise?)

slide-10
SLIDE 10

Entropy estimates

  • Try to quantify the number of random bits allowed

to be harvested from a physical system

  • Works on raw data, not post-processed data
  • Can help reveal where the entropy is coming from
  • Can be slower, require more data than NIST SP 800-

22rev1a

slide-11
SLIDE 11

Dynamical systems approach to entropy generation

  • Kolmogorov-Sinai (or metric) entropy
  • Analog of Shannon entropy for dynamical system
  • Allows for direct comparison of dynamical

processes, stochastic processes, and mixed processes

𝐼 = βˆ’ 1 π‘’πœ ෍ π‘ž 𝑗1, … , 𝑗𝑒 log2 π‘ž 𝑗1, … , 𝑗𝑒

slide-12
SLIDE 12

Discretization of analog signals

12

slide-13
SLIDE 13

Time-delay embedding

  • Reconstruct phase-space of dynamical system from

measurement of one variable

Takens, Floris. Detecting strange attractors in

  • turbulence. Springer Berlin Heidelberg, 1981.

𝐲 𝑒 = (𝑦 𝑒 , 𝑦 𝑒 βˆ’ π‘ˆ , … , 𝑦(𝑒 βˆ’ 𝑒 βˆ’ 1 π‘ˆ)

Lorenz attractor

slide-14
SLIDE 14

Numerically Estimating Entropy

Box Counting Method

Cohen and Procaccia, β€œComputing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems”,

  • Phys. Rev. A 31, 1872 (1985)

Cohen - Procaccia

slide-15
SLIDE 15

Entropy of chaotic systems

For small Ξ΅ π‘Œπ‘’+1 = 4π‘Œπ‘’(1 βˆ’ π‘Œπ‘’)

  • P. Gaspard and X. Wang,

Physics Reports, Volume 235, 1993

β„Ž 𝜁 = β„ŽπΏπ‘‡ = 1 ln(2) ෍

πœ‡π‘—>0

πœ‡π‘—

slide-16
SLIDE 16

(Ξ΅-Ο„) entropy of noise

β„Ž 𝜁 ~ βˆ’ log2 𝜁

Gaussian random variable

  • P. Gaspard and X. Wang,

Physics Reports, Volume 235, 1993

slide-17
SLIDE 17

Noisy chaotic systems

π‘Žπ‘’+1 = π‘Œπ‘’ + 𝑏𝑆𝑒 π‘Œπ‘’+1 = 4π‘Œπ‘’(1 βˆ’ π‘Œπ‘’)

𝑏

R is random Gaussian variable

  • P. Gaspard and X. Wang,

Physics Reports, Volume 235, 1993

slide-18
SLIDE 18

Case study:

Amplified Spontaneous Emission (ASE)

  • C. R. Williams, J. C. Salevan, X. Li, R. Roy, and T. E.

Murphy, Optics Express 18, 23584–23597 (2010).

slide-19
SLIDE 19

ASE

slide-20
SLIDE 20

Signal and Noise

  • Least-significant bits contribute considerable

entropy (not optical!)

Electronic Noise ASE

slide-21
SLIDE 21

Entropy Rate - ASE

  • Entropy rolls off with sample rate

50GS/s 5GS/s

slide-22
SLIDE 22

Entropy Rate - ASE

  • Entropy rolls off with sample rate

50GS/s 5GS/s 2 bits 8 bits

slide-23
SLIDE 23

NIST SP 800-90B Entropy Estimates

  • Most Common Value Estimate
  • Collision Estimateβ€”based on mean time until first

repeated value

  • Markov Estimateβ€”measures dependencies

between consecutive values

  • Compression Estimateβ€”estimates how much the

dataset can be compressed

  • Other more complicated tests…
slide-24
SLIDE 24

50 GSamples/s Instrumentation Limit IID Entropy Rate

Entropy rate as a function of measurement resolution (Ξ΅)

8 2 6 4 10

Ξ΅ [bits]

300 100 200

Entropy [Gbits/s]

slide-25
SLIDE 25

IID Entropy Rate 50 GSamples/s Instrumentation Limit

Entropy rate as a function of measurement resolution (Ξ΅)

8 2 6 4 10

Ξ΅ [bits]

300 100 200

Entropy [Gbits/s]

slide-26
SLIDE 26

IID Entropy Rate 50 GSamples/s Instrumentation Limit

Entropy rate as a function of measurement resolution (Ξ΅)

8 2 6 4 10

Ξ΅ [bits]

300 100 200

Entropy [Gbits/s]

slide-27
SLIDE 27

IID Entropy Rate 50 GSamples/s Instrumentation Limit

Entropy rate as a function of measurement resolution (Ξ΅)

8 2 6 4 10

Ξ΅ [bits]

300 100 200

Entropy [Gbits/s]

slide-28
SLIDE 28

IID Entropy Rate 50 GSamples/s 1 GSample/s Instrumentation Limit

Entropy rate as a function of measurement resolution (Ξ΅)

8 2 6 4 10

Ξ΅ [bits]

300 100 200

Entropy [Gbits/s]

8 2 6 4 10

Ξ΅ [bits]

6 2 4

slide-29
SLIDE 29

Instrumentation Limit IID Entropy Rate

Capturing Temporal Correlations

10 100 1

Sampling Frequency [Gsamples/s]

10 100 1

Sampling Frequency [Gsamples/s]

100 10 1 100 10 1

Entropy rate [Gbits/s]

slide-30
SLIDE 30

Chaotic Laser

  • Fluctuations are fast and chaotic (sensitive

dependence on initial conditions)

slide-31
SLIDE 31

Entropy rateβ€”laser chaos

  • Significant portion of entropy comes from

background noise (especially at high resolution)

slide-32
SLIDE 32

Conclusions:

  • Important to look at entropy as a function of

measurement resolution and sampling frequency

  • Different physical processes can generate entropy,

even within the same experiment

  • Measurement determines which physical entropy

generation processes you observe

  • Entropy estimates should consider analog data, not

post-processed bit stream

slide-33
SLIDE 33

To learn more about:

Aaron M. Hagerstrom, Thomas E. Murphy, and Rajarshi Roy. "Harvesting entropy and quantifying the transition from noise to chaos in a photon-counting feedback loop." Proceedings of the National Academy of Sciences 112.30 (2015): 9258-9263.

Entropy generation in noisy chaotic systems: Amplified spontaneous emission:

Williams, Caitlin RS, et al. "Fast physical random number generator using amplified spontaneous emission." Optics express 18.23 (2010): 23584-23597. Li, Xiaowen, et al. "Scalable parallel physical random number generator based on a superluminescent LED." Optics letters 36.6 (2011): 1020-1022.