Physical Randomness Extractors Kai-Min Chung Academia Sinica, - - PowerPoint PPT Presentation

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Physical Randomness Extractors Kai-Min Chung Academia Sinica, - - PowerPoint PPT Presentation

Jan 15, 2023 202 likes •397 views

Physical Randomness Extractors Kai-Min Chung Academia Sinica, Taiwan Xiaodi Wu Yaoyun Shi MIT/UC Berkeley University of Michigan Presented in QIP14 as plenary talk (joint with [MS14]) 1 Randomness Randomness is a vital resource

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SLIDE 1

Physical Randomness Extractors

Kai-Min Chung

Academia Sinica, Taiwan

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Yaoyun Shi University of Michigan Xiaodi Wu MIT/UC Berkeley Presented in QIP’14 as plenary talk (joint with [MS’14])

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SLIDE 2

Randomness

  • Randomness is a vital resource

– necessary in cryptography – pervasive in computer science

  • How can we be sure a source is truly random?

– Bias? Correlation? – and…

2

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SLIDE 3

Randomness

  • Randomness is a vital resource

– necessary in cryptography – pervasive in computer science

  • How can we be sure a source is truly random?

– Bias? Correlation? – and…

3

What are the minimal assumptions for generating (almost) uniform randomness?

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SLIDE 4

Classical Answer— Randomness Extractors

  • Extract pure randomness from “weak” sources.

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seed

Ext

source ≈uniform output Seeded Randomness Extractor

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SLIDE 5

Classical Answer— Randomness Extractors

  • Extract pure randomness from “weak” sources.

– sufficient min-entropy – at least two independent sources

5

Ext

source ≈uniform output

Necessary!

source

Require:

Two-source Randomness Extractor

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SLIDE 6

Classical Answer— Randomness Extractors

  • Extract pure randomness from “weak” sources.

– sufficient min-entropy – at least two independent sources

6

Ext

source ≈uniform output

Necessary!

source

Require:

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SLIDE 7

Classical Answer— Randomness Extractors

  • Extract pure randomness from “weak” sources.

– sufficient min-entropy – at least two independent sources

7

Ext

source ≈uniform output

Necessary!

source

Require:

Can independence assumption be avoided?

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SLIDE 8

Our Proposal— Physical Randomness Extractors

  • Requirements:

– source has sufficient min-entropy – spatial separate devices

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Phy−Ext

source ≈uniform output device device device

Necessary!

Accept/Reject

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SLIDE 9

Our Proposal— Physical Randomness Extractors

  • Requirements:

– source has sufficient min-entropy – spatial separate devices

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devices

Phy−Ext

source ≈uniform output devices devices

Necessary!

Accept/Reject

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SLIDE 10

Our Proposal— Physical Randomness Extractors

  • Requirements:

– source has sufficient min-entropy – spatial separate devices

10

devices

Phy−Ext

source ≈uniform output devices devices

Necessary!

No trust on devices Completeness: if devices honest ⟹ accept w.h.p. & output ≈ uniform Soundness: if devices malicious ⟹ either reject w.h.p. or (output|accept) ≈ uniform

Accept/Reject

No independence assumption:

  • allow source-device correlation
  • only need random-to-device source,

i.e., Hmin(source|devices) > k0

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SLIDE 11
  • Extract arbitrary N bits of randomness using source

with O(1)-bit entropy and O(1) devices with 0.001 error in 𝑃(N) time with additional features

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Phy−Ext

source ≈uniform output devices devices devices Accept/Reject

Our Result— Efficient Physical Randomness Extractor

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SLIDE 12

Physics Answer— Quantum Random Number Generator

  • Generate pure randomness by measuring q-bits in

superposition.

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device

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SLIDE 13

Physics Answer— Quantum Random Number Generator

  • Generate pure randomness by measuring q-bits in

superposition.

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device

0101000010110 … 𝜔 = 1 2 0 + 1 2 |1〉

However…

  • Noise

– inherent – bias outcome

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SLIDE 14

Physics Answer— Quantum Random Number Generator

  • Generate pure randomness by measuring q-bits in

superposition.

14

device

0101000010110 … 𝜔 = 1 2 0 + 1 2 |1〉

However…

  • Noise

– inherent – bias outcome

  • Adversary

– no entropy against Adv!

0101000010110 …

entanglement

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SLIDE 15

Physics Answer— Quantum Random Number Generator

  • Generate pure randomness by measuring q-bits in

superposition.

15

device

0101000010110 … 𝜔 = 1 2 0 + 1 2 |1〉

However…

  • Noise

– inherent – bias outcome

  • Adversary

– no entropy!

0101000010110 …

entanglement

Can we avoid trusting quantum devices?

Well, this is not new……

Device-independent Quantum Cryptography The Central Rule: Trust classical operations only, without assumption on inner-working of super-classical devices. Origins in the 90’s [Mayers-Yao’98] Develop rapidly very recently!

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SLIDE 16

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  • Extract arbitrary N bits of randomness using source

with O(1)-bit entropy and O(1) devices with 0.001 error in 𝑃(N) time with additional features

  • Prior to our work, only known how to extract a

single bit from Santha-Vazirani (SV) source with non-constructive (thus inefficient) extractors

[GMdlT+12]

Our Result— Efficient Physical Randomness Extractor

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SLIDE 17

17

  • Extract arbitrary N bits of randomness using source

with O(1)-bit entropy and O(1) devices with 0.001 error in 𝑃(N) time with additional features

– Robustness: accept w.h.p. w.r.t. honest devices with Ω(1) noise rate. – Simplicity: very simple construction and analysis via composition

  • Our key composition lemma already found application for

(unbounded) randomness expansion to simplify and improve [CY14] Available on arXiv:1402.4797

Our Result— Efficient Physical Randomness Extractor