Physical Layer Security in Wireless Networks

An Information Theoretic Perspective

Vince Poor(poor@princeton.edu)

Thanks to:

Arsenia Chorti (ENSEA), Mahdi Shakiba Herfeh (ENSEA) and Miroslav G. Mitev (Essex)

M. S. Herfeh, A. Chorti & H. V. Poor, “Physical Layer Security: Authentication, Integrity andConfidentiality.” In Physical Layer Security, Khoa N. Le, Ed. (Springer Nature, 2021), to appear.

Today’s Security Architecture

Application

Transport

Network

Link

Physical

Secured

Why do we need PLS?

Standard Crypto Systems

• No known feasible attacks

• Widely employed and tested

• Trustworthy authentication

DC• Built on unproven assumptions

• PHY connection assumed established

• Computationally intensive

• Require significant infrastructure

Physical Layer Security

• Quantum secure

• On-the-fly secret key generation

• Fast and lightweight implementation

DC• Assumptions on Eve’s channel

• Bounds not categorized on finite blocks

• Testing – still in infancy

A Prime Example: IoT

Figure source: https://www.computer.org/

• IoT vulnerabilities to cyber attacks à Mostly concern personal privacy and security

IoT Security – A Major Concern

An Example of What Can Go Wrong[Soltan, Mittal, Poor, USENIX’18]

• Manipulation of demand via IoT: Botnets controlling high-wattage IoTdevices (air conditioners, refrigerators, etc.) can disrupt the power grid.

• A Mirai-sized (600,000 bots) botnet of water heaters can change thedemand instantly by 3GW – similar to having access to the largestcurrently deployed nuclear plant!

Compromised High Wattage IoT Devices

Target of the Attack

Power Grid

Compromised High Wattage IoT Devices

Adversary

Synchronous On/Off

PLS Can Offer

PLS

Node authentication

Messageintegrity

Message confidentiality

Secure session

initiation

Completeness of security protocols

Secure messageexchange

• Physical unclonable functions• Biometrics• Wireless identification

• Wiretap channel model• Secret key generation

• Physical unclonable functions• Wireless identification

The theme:

- A role for information theory in this area

Focus mainly on message confidentiality and privacy:

- Message confidentiality in data transmission systems

- Privacy in sensing systems

Other issues – some newer some older (briefly):

- Authentication, security in MANETs, attacks on sensor networks

Overview of Today’s Talk

Message Confidentiality

in

Transmission Systems

• Traditionally security is treated as a higher-layer issue (e.g.,

at the APP)

• Encryption can be complex (and add delay), and difficult

without infrastructure

• Information theoretic security examines the fundamental

ability of the medium (i.e., the PHY) to provide security

(primarily data confidentiality)

Information Theoretic SecurityRethinking Security Design

• Physical layer security provides security by exploiting imperfections in physical channels: noise, fading, …

• Joint encoding for reliability and security.

• Conventionally a higher layer issue: encryption, key distributions, …

• Difficult with massive number of devices (esp. with no infrastructure), low cost, low latency.

!X

Shannon (1949): For cipher, perfect secrecy requires a one-time pad.

[I.e., the entropy of the key must be at least the entropy of the source: H(K) ≥ H(M)]

Information Theoretic Security: Shannon’s Model

Alice Bob

Eve

Secret Key K

Message M M

?

X X

X

Information Theoretic Security: Wyner’s Model

Alice Bob

Eve

Message M M

?

X Y

Z

Noisy Channel

Noisy Channel

“The Wiretap Channel”

• Tradeoff: reliable rate R to Bob vs. the equivocation H(M|Z) at Eve

• Secrecy capacity = maximum R such that R = H(M|Z)

• Wyner (1975): Secrecy capacity > 0 iff. Z is degraded relative to Y

Physical Layer Security

• In general, the legitimate receiver needs an advantage overthe eavesdropper – either a secret shared with thetransmitter, or a better channel.

• There has been a resurgence of interest in these ideas.

Physical Layer Security

• In general, the legitimate receiver needs an advantage overthe eavesdropper – either a secret shared with thetransmitter, or a better channel.

• There has been a resurgence of interest in these ideas.

• The physical properties of radio propagation (diffusion &superposition) provide opportunities for this, via

- fading: provides natural degradedness over time

- interference: allows active countermeasures to eavesdropping

- spatial diversity (MIMO, relays): creates “secrecy degrees of freedom”

- random channels: sources of common randomness for key generation

Physical Layer Security

• In general, the legitimate receiver needs an advantage overthe eavesdropper – either a secret shared with thetransmitter, or a better channel.

• There has been a resurgence of interest in these ideas.

• The physical properties of radio propagation (diffusion &superposition) provide opportunities for this, via

- fading: provides natural degradedness over time

- interference: allows active countermeasures to eavesdropping

- spatial diversity (MIMO, relays): creates “secrecy degrees of freedom”

- random channels: sources of common randomness for key generation

• The first three of these phenomena lead to rich secrecy capacityregions for the fundamental channel models used to understandwireless networks.

• Interference Channels:

• Multiple-Access Channels:

• Relay Channels, MIMO Channels, etc.

Secrecy in Fundamental Channel Models

Alice1/Eve2

Bob

Message M1

M1,M2

X1

Y

Alice2/Eve1Message M2 X2

Z1

Z2

Alice1 Bob1/Eve2Message M1 M1,?X1

Alice2Message M2X2

Y1

Y2Bob2/Eve1 M2,?

Y1

Y2

Alice

Bob1

Bob2/Eve

M1,M2

M1,?

Messages M1, M2• Broadcast Channels:

Poor, Schaefer (2017) Wireless Physical Layer Security PNAS

Y1

Y2

Alice

Bob1

Bob2/Eve

M1,M2

M1,?

Messages M1, M2

E.g., the Gaussian Broadcast Channel

Y1

Y2

Alice

Bob1

Bob2/Eve

M1,M2

M1,?

Messages M1, M2

E.g., the Gaussian Broadcast Channel

Y1

Y2

Alice

Bob1

Bob2/Eve

M1,M2

M1,?

Messages M1, M2

E.g., the Fading Gaussian BC

Wiretap Channel and Secrecy Capacity

• Secrecy capacity: largest rate in the asymptotic regime of

• Blocklength

• Probability of error

• Information leakage

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P⇣W 6= W

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• Limitation: not suitable for low-latency applications as in IoT.

Channel

BobXn

ŴYn

W

Zn Leakage ≤ dEve

Alice

Encoder Channel DecoderSource

1, 2, … , MW Xn Yn Ŵ

• (n,M,ε) code: P(W≠Ŵ) ≤ ε

• Fundamental limit: M*(n,ε) = max{M: ∃ an (n,M,ε) code}

Finite Blocklength Information Theory

log M*(n,ε) = n C - √nV Q-1(ε) + O(log n)

C = E[i(X*,Y*)] (Shannon’s capacity); V = Var[i(X*,Y*)] (“dispersion”)

[Polyanskiy, et al. IT’10, etc.]

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.1

0.2

0.3

0.4

0.5

Blocklength, n

Rat

e R

, bi

ts/c

h.us

eCapacity

Converse

Best achievability

Normal approximation

Example: AWGN (SNR = 0 dB; ε = 10-3)

[Polyanskiy, et al. (2010)]

PHY Layer Security: Finite Blocklength

• secrecy code:

• Message

• Encoder ; decoder

• Average error probability:

• Secrecy constraint: information leakage

!X

• maximum secret rate at a given blocklength.

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W 2 {1, . . . ,M}<latexit sha1_base64="X0p1Ew3qIQr+meQx9STwv+hyi1k=">AAAB+nicbVDLSsNAFL3xWesr1aWbYBFclJKIoMuiGzdCBfuAJpTJdNoOnUzCzI1SYj/FjQtF3Pol7vwbp20W2npg4HDOPdw7J0wE1+i639bK6tr6xmZhq7i9s7u3b5cOmjpOFWUNGotYtUOimeCSNZCjYO1EMRKFgrXC0fXUbz0wpXks73GcsCAiA8n7nBI0UtcutXwu/cyr+L0YdeXWn3Ttslt1Z3CWiZeTMuSod+0vk6VpxCRSQbTueG6CQUYUcirYpOinmiWEjsiAdQyVJGI6yGanT5wTo/ScfqzMk+jM1N+JjERaj6PQTEYEh3rRm4r/eZ0U+5dBxmWSIpN0vqifCgdjZ9qD0+OKURRjQwhV3Nzq0CFRhKJpq2hK8Ba/vEyaZ1XP8Lvzcu0qr6MAR3AMp+DBBdTgBurQAAqP8Ayv8GY9WS/Wu/UxH12x8swh/IH1+QN6wZN7</latexit><latexit sha1_base64="X0p1Ew3qIQr+meQx9STwv+hyi1k=">AAAB+nicbVDLSsNAFL3xWesr1aWbYBFclJKIoMuiGzdCBfuAJpTJdNoOnUzCzI1SYj/FjQtF3Pol7vwbp20W2npg4HDOPdw7J0wE1+i639bK6tr6xmZhq7i9s7u3b5cOmjpOFWUNGotYtUOimeCSNZCjYO1EMRKFgrXC0fXUbz0wpXks73GcsCAiA8n7nBI0UtcutXwu/cyr+L0YdeXWn3Ttslt1Z3CWiZeTMuSod+0vk6VpxCRSQbTueG6CQUYUcirYpOinmiWEjsiAdQyVJGI6yGanT5wTo/ScfqzMk+jM1N+JjERaj6PQTEYEh3rRm4r/eZ0U+5dBxmWSIpN0vqifCgdjZ9qD0+OKURRjQwhV3Nzq0CFRhKJpq2hK8Ba/vEyaZ1XP8Lvzcu0qr6MAR3AMp+DBBdTgBurQAAqP8Ayv8GY9WS/Wu/UxH12x8swh/IH1+QN6wZN7</latexit><latexit sha1_base64="X0p1Ew3qIQr+meQx9STwv+hyi1k=">AAAB+nicbVDLSsNAFL3xWesr1aWbYBFclJKIoMuiGzdCBfuAJpTJdNoOnUzCzI1SYj/FjQtF3Pol7vwbp20W2npg4HDOPdw7J0wE1+i639bK6tr6xmZhq7i9s7u3b5cOmjpOFWUNGotYtUOimeCSNZCjYO1EMRKFgrXC0fXUbz0wpXks73GcsCAiA8n7nBI0UtcutXwu/cyr+L0YdeXWn3Ttslt1Z3CWiZeTMuSod+0vk6VpxCRSQbTueG6CQUYUcirYpOinmiWEjsiAdQyVJGI6yGanT5wTo/ScfqzMk+jM1N+JjERaj6PQTEYEh3rRm4r/eZ0U+5dBxmWSIpN0vqifCgdjZ9qD0+OKURRjQwhV3Nzq0CFRhKJpq2hK8Ba/vEyaZ1XP8Lvzcu0qr6MAR3AMp+DBBdTgBurQAAqP8Ayv8GY9WS/Wu/UxH12x8swh/IH1+QN6wZN7</latexit><latexit sha1_base64="X0p1Ew3qIQr+meQx9STwv+hyi1k=">AAAB+nicbVDLSsNAFL3xWesr1aWbYBFclJKIoMuiGzdCBfuAJpTJdNoOnUzCzI1SYj/FjQtF3Pol7vwbp20W2npg4HDOPdw7J0wE1+i639bK6tr6xmZhq7i9s7u3b5cOmjpOFWUNGotYtUOimeCSNZCjYO1EMRKFgrXC0fXUbz0wpXks73GcsCAiA8n7nBI0UtcutXwu/cyr+L0YdeXWn3Ttslt1Z3CWiZeTMuSod+0vk6VpxCRSQbTueG6CQUYUcirYpOinmiWEjsiAdQyVJGI6yGanT5wTo/ScfqzMk+jM1N+JjERaj6PQTEYEh3rRm4r/eZ0U+5dBxmWSIpN0vqifCgdjZ9qD0+OKURRjQwhV3Nzq0CFRhKJpq2hK8Ba/vEyaZ1XP8Lvzcu0qr6MAR3AMp+DBBdTgBurQAAqP8Ayv8GY9WS/Wu/UxH12x8swh/IH1+QN6wZN7</latexit>

PX|W : {1, . . . ,M} ! A<latexit sha1_base64="oLPhmXseA6rY/U43AFvI0bvwtdE=">AAACFHicbVDLSsNAFJ34rPUVdekmWATBUhIRFFdVN26ECvYBTQiT6aQdOnkwc6OUmI9w46+4caGIWxfu/BsnbRbaemDgcM69d+49XsyZBNP81ubmFxaXlksr5dW19Y1NfWu7JaNEENokEY9Ex8OSchbSJjDgtBMLigOP07Y3vMz99h0VkkXhLYxi6gS4HzKfEQxKcvXDhpt2HtrZmZ1aVbsXgaxe25ktWH8AWIjo3g4wDAjm6Xnm6hWzZo5hzBKrIBVUoOHqX2oiSQIaAuFYyq5lxuCkWAAjnGZlO5E0xmSI+7SraIgDKp10fFRm7CulZ/iRUC8EY6z+7khxIOUo8FRlvqKc9nLxP6+bgH/qpCyME6AhmXzkJ9yAyMgTMnpMUAJ8pAgmgqldDTLAAhNQOZZVCNb0ybOkdVSzFL85rtQvijhKaBftoQNkoRNUR1eogZqIoEf0jF7Rm/akvWjv2sekdE4renbQH2ifP3PKnxU=</latexit><latexit sha1_base64="oLPhmXseA6rY/U43AFvI0bvwtdE=">AAACFHicbVDLSsNAFJ34rPUVdekmWATBUhIRFFdVN26ECvYBTQiT6aQdOnkwc6OUmI9w46+4caGIWxfu/BsnbRbaemDgcM69d+49XsyZBNP81ubmFxaXlksr5dW19Y1NfWu7JaNEENokEY9Ex8OSchbSJjDgtBMLigOP07Y3vMz99h0VkkXhLYxi6gS4HzKfEQxKcvXDhpt2HtrZmZ1aVbsXgaxe25ktWH8AWIjo3g4wDAjm6Xnm6hWzZo5hzBKrIBVUoOHqX2oiSQIaAuFYyq5lxuCkWAAjnGZlO5E0xmSI+7SraIgDKp10fFRm7CulZ/iRUC8EY6z+7khxIOUo8FRlvqKc9nLxP6+bgH/qpCyME6AhmXzkJ9yAyMgTMnpMUAJ8pAgmgqldDTLAAhNQOZZVCNb0ybOkdVSzFL85rtQvijhKaBftoQNkoRNUR1eogZqIoEf0jF7Rm/akvWjv2sekdE4renbQH2ifP3PKnxU=</latexit><latexit sha1_base64="oLPhmXseA6rY/U43AFvI0bvwtdE=">AAACFHicbVDLSsNAFJ34rPUVdekmWATBUhIRFFdVN26ECvYBTQiT6aQdOnkwc6OUmI9w46+4caGIWxfu/BsnbRbaemDgcM69d+49XsyZBNP81ubmFxaXlksr5dW19Y1NfWu7JaNEENokEY9Ex8OSchbSJjDgtBMLigOP07Y3vMz99h0VkkXhLYxi6gS4HzKfEQxKcvXDhpt2HtrZmZ1aVbsXgaxe25ktWH8AWIjo3g4wDAjm6Xnm6hWzZo5hzBKrIBVUoOHqX2oiSQIaAuFYyq5lxuCkWAAjnGZlO5E0xmSI+7SraIgDKp10fFRm7CulZ/iRUC8EY6z+7khxIOUo8FRlvqKc9nLxP6+bgH/qpCyME6AhmXzkJ9yAyMgTMnpMUAJ8pAgmgqldDTLAAhNQOZZVCNb0ybOkdVSzFL85rtQvijhKaBftoQNkoRNUR1eogZqIoEf0jF7Rm/akvWjv2sekdE4renbQH2ifP3PKnxU=</latexit><latexit sha1_base64="oLPhmXseA6rY/U43AFvI0bvwtdE=">AAACFHicbVDLSsNAFJ34rPUVdekmWATBUhIRFFdVN26ECvYBTQiT6aQdOnkwc6OUmI9w46+4caGIWxfu/BsnbRbaemDgcM69d+49XsyZBNP81ubmFxaXlksr5dW19Y1NfWu7JaNEENokEY9Ex8OSchbSJjDgtBMLigOP07Y3vMz99h0VkkXhLYxi6gS4HzKfEQxKcvXDhpt2HtrZmZ1aVbsXgaxe25ktWH8AWIjo3g4wDAjm6Xnm6hWzZo5hzBKrIBVUoOHqX2oiSQIaAuFYyq5lxuCkWAAjnGZlO5E0xmSI+7SraIgDKp10fFRm7CulZ/iRUC8EY6z+7khxIOUo8FRlvqKc9nLxP6+bgH/qpCyME6AhmXzkJ9yAyMgTMnpMUAJ8pAgmgqldDTLAAhNQOZZVCNb0ybOkdVSzFL85rtQvijhKaBftoQNkoRNUR1eogZqIoEf0jF7Rm/akvWjv2sekdE4renbQH2ifP3PKnxU=</latexit>

g : B ! {1, . . . ,M}<latexit sha1_base64="kIkUZumVtJN/ZqOausLxVev1qS0=">AAACDnicbVC7SgNBFL0bXzG+opY2S0JAMIRdG8UqxMZGiGAekF3C7GSSDJl9MHNXCct+gY2f4C/YWChia23n3zh5FJp4YOBwzj3MvceLBFdoWd9GZmV1bX0ju5nb2t7Z3cvvHzRVGEvKGjQUoWx7RDHBA9ZAjoK1I8mI7wnW8kaXE791x6TiYXCL44i5PhkEvM8pQS1186XBheMTHFIiklrqSD4YIpEyvHcSu+z0QlTlayft5otWxZrCXCb2nBSrBefkCQDq3fyXztLYZwFSQZTq2FaEbkIkcipYmnNixSJCR2TAOpoGxGfKTabnpGZJKz2zH0r9AjSn6u9EQnylxr6nJyerq0VvIv7ndWLsn7sJD6IYWUBnH/VjYWJoTroxe1wyimKsCaGS611NOiSSUNQN5nQJ9uLJy6R5WrE1v7GL1RrMkIUjKMAx2HAGVbiCOjSAwgM8wyu8GY/Gi/FufMxGM8Y8cwh/YHz+AKvfnfU=</latexit><latexit sha1_base64="HC2Oz3F2nue3ZWVlbYjQxdKJwfE=">AAACDnicbVDLSsNAFJ34rPUVdekmtBQES0ncKK5K3bgRKtgHNKVMppN06GQSZm6UEPoFblz4I25cKOLWtbv+jdPHQlsPDBzOuYe593gxZwpse2ysrK6tb2zmtvLbO7t7++bBYVNFiSS0QSIeybaHFeVM0AYw4LQdS4pDj9OWN7ya+K17KhWLxB2kMe2GOBDMZwSDlnpmKbh0QwwDgnlWG7mSBQPAUkYPbuaU3X4Eqnzjjnpm0a7YU1jLxJmTYrXgnj6Pq2m9Z37rLElCKoBwrFTHsWPoZlgCI5yO8m6iaIzJEAe0o6nAIVXdbHrOyCpppW/5kdRPgDVVfycyHCqVhp6enKyuFr2J+J/XScC/6GZMxAlQQWYf+Qm3ILIm3Vh9JikBnmqCiWR6V4sMsMQEdIN5XYKzePIyaZ5VHM1vnWK1hmbIoWNUQCfIQeeoiq5RHTUQQY/oBb2hd+PJeDU+jM/Z6IoxzxyhPzC+fgC1SZ97</latexit><latexit sha1_base64="HC2Oz3F2nue3ZWVlbYjQxdKJwfE=">AAACDnicbVDLSsNAFJ34rPUVdekmtBQES0ncKK5K3bgRKtgHNKVMppN06GQSZm6UEPoFblz4I25cKOLWtbv+jdPHQlsPDBzOuYe593gxZwpse2ysrK6tb2zmtvLbO7t7++bBYVNFiSS0QSIeybaHFeVM0AYw4LQdS4pDj9OWN7ya+K17KhWLxB2kMe2GOBDMZwSDlnpmKbh0QwwDgnlWG7mSBQPAUkYPbuaU3X4Eqnzjjnpm0a7YU1jLxJmTYrXgnj6Pq2m9Z37rLElCKoBwrFTHsWPoZlgCI5yO8m6iaIzJEAe0o6nAIVXdbHrOyCpppW/5kdRPgDVVfycyHCqVhp6enKyuFr2J+J/XScC/6GZMxAlQQWYf+Qm3ILIm3Vh9JikBnmqCiWR6V4sMsMQEdIN5XYKzePIyaZ5VHM1vnWK1hmbIoWNUQCfIQeeoiq5RHTUQQY/oBb2hd+PJeDU+jM/Z6IoxzxyhPzC+fgC1SZ97</latexit><latexit sha1_base64="VrUuQzVFyl0znKS5PmV0oNzbfnE=">AAACDnicbVC7SgNBFJ31GeNr1dJmMAQsQti1UaxCbGyECOYB2SXMTmY3Q2YfzNxVwrJfYOOv2FgoYmtt5984m6TQxAMDh3PuYe49XiK4Asv6NlZW19Y3Nktb5e2d3b198+Cwo+JUUtamsYhlzyOKCR6xNnAQrJdIRkJPsK43vir87j2TisfRHUwS5oYkiLjPKQEtDcxqcOmEBEaUiKyZO5IHIyBSxg9OZtecYQyqduPkA7Ni1a0p8DKx56SC5mgNzC+dpWnIIqCCKNW3rQTcjEjgVLC87KSKJYSOScD6mkYkZMrNpufkuKqVIfZjqV8EeKr+TmQkVGoSenqyWF0teoX4n9dPwb9wMx4lKbCIzj7yU4EhxkU3eMgloyAmmhAqud4V0xGRhIJusKxLsBdPXiads7qt+a1daTTndZTQMTpBp8hG56iBrlELtRFFj+gZvaI348l4Md6Nj9noijHPHKE/MD5/AJlgnGw=</latexit>

P⇣W 6= W

⌘ ✏

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�<latexit sha1_base64="2UpktDjIXDw6QkA0AS30lOtYgkk=">AAAB8XicbZC7TsNAEEXH4RXCKzw6GosIiSqyaaC0oKGgCBJJELEVrdfjZJX12uyukSIrf0FDAUK0/AWfQMffsHkUkHCllY7undHOTJhxprTjfFulpeWV1bXyemVjc2t7p7q711JpLik2acpTeRcShZwJbGqmOd5lEkkScmyHg8tx3n5EqVgqbvUwwyAhPcFiRok21r3P8cGPkGvSrdacujORvQjuDGrewfWnBwCNbvXLj1KaJyg05USpjutkOiiI1IxyHFX8XGFG6ID0sGNQkARVUEwmHtnHxonsOJXmCW1P3N8dBUmUGiahqUyI7qv5bGz+l3VyHZ8HBRNZrlHQ6Udxzm2d2uP17YhJpJoPDRAqmZnVpn0iCdXmSBVzBHd+5UVondZdwzduzbuAqcpwCEdwAi6cgQdX0IAmUBDwBC/wainr2Xqz3qelJWvWsw9/ZH38ANhwkoE=</latexit><latexit sha1_base64="hahxMb32b62Aj9TJQ3lu1YNwsTI=">AAAB8XicbZC7TsNAEEXH4RXCKzw6GosIiSqyaaCMoKGgCBJJELYVrdfjZJX12uyukSIrf0FDAUK0/AWfQMffsHkUkHCllY7undHOTJhxprTjfFulpeWV1bXyemVjc2t7p7q711ZpLim2aMpTeRcShZwJbGmmOd5lEkkScuyEg8tx3nlEqVgqbvUwwyAhPcFiRok21r3P8cGPkGvSrdacujORvQjuDGqNg+vPpix7zW71y49SmicoNOVEKc91Mh0URGpGOY4qfq4wI3RAeugZFCRBFRSTiUf2sXEiO06leULbE/d3R0ESpYZJaCoTovtqPhub/2VeruPzoGAiyzUKOv0ozrmtU3u8vh0xiVTzoQFCJTOz2rRPJKHaHKlijuDOr7wI7dO6a/jGrTUuYKoyHMIRnIALZ9CAK2hCCygIeIIXeLWU9Wy9We/T0pI169mHP7I+fgAKs5Nm</latexit><latexit sha1_base64="hahxMb32b62Aj9TJQ3lu1YNwsTI=">AAAB8XicbZC7TsNAEEXH4RXCKzw6GosIiSqyaaCMoKGgCBJJELYVrdfjZJX12uyukSIrf0FDAUK0/AWfQMffsHkUkHCllY7undHOTJhxprTjfFulpeWV1bXyemVjc2t7p7q711ZpLim2aMpTeRcShZwJbGmmOd5lEkkScuyEg8tx3nlEqVgqbvUwwyAhPcFiRok21r3P8cGPkGvSrdacujORvQjuDGqNg+vPpix7zW71y49SmicoNOVEKc91Mh0URGpGOY4qfq4wI3RAeugZFCRBFRSTiUf2sXEiO06leULbE/d3R0ESpYZJaCoTovtqPhub/2VeruPzoGAiyzUKOv0ozrmtU3u8vh0xiVTzoQFCJTOz2rRPJKHaHKlijuDOr7wI7dO6a/jGrTUuYKoyHMIRnIALZ9CAK2hCCygIeIIXeLWU9Wy9We/T0pI169mHP7I+fgAKs5Nm</latexit><latexit sha1_base64="8WZk1MgupJfKQNNxF6qpvzGBZWs=">AAAB8XicbZA9T8MwEIYv5auUrwIji0WFxFQlLDBWsDAWiX6IJqoc59JadZxgO0hV1X/BwgBCrPwbNv4NbpsBWl7J0qP37uS7N8wE18Z1v53S2vrG5lZ5u7Kzu7d/UD08aus0VwxbLBWp6oZUo+ASW4Ybgd1MIU1CgZ1wdDOrd55QaZ7KezPOMEjoQPKYM2qs9eALfPQjFIb2qzW37s5FVsEroAaFmv3qlx+lLE9QGiao1j3PzUwwocpwJnBa8XONGWUjOsCeRUkT1MFkvvGUnFknInGq7JOGzN3fExOaaD1OQtuZUDPUy7WZ+V+tl5v4KphwmeUGJVt8FOeCmJTMzicRV8iMGFugTHG7K2FDqigzNqSKDcFbPnkV2hd1z/KdV2tcF3GU4QRO4Rw8uIQG3EITWsBAwjO8wpujnRfn3flYtJacYuYY/sj5/AGkDJDf</latexit>

R⇤(n, ✏, �) :<latexit sha1_base64="dyu12PUwZGuowFqbHHoaArjGN7s=">AAACAHicdZBNSwMxEIZn/bZ+VT148BJaBL8ou7VY9VT04lHFqtDWkk2nbWg2uyRZoZRe/CWCFw+KePVnePPfmG0VVPSFwMM7M0zm9SPBtXHdd2dkdGx8YnJqOjUzOze/kF5cutBhrBiWWShCdeVTjYJLLBtuBF5FCmngC7z0O0dJ/fIGleahPDfdCGsBbUne5Iwaa9XTK2fXm+tyu4qR5iK00EBh6MZBPZ11c/t7u/nCLnFzrlv08l4C+WJhp0A86yTKljLVrTsAOKmn36qNkMUBSsME1briuZGp9agynAnsp6qxxoiyDm1hxaKkAepab3BAn6xZp0GaobJPGjJwv0/0aKB1N/BtZ0BNW/+uJeZftUpsmnu1HpdRbFCy4aJmLIgJSZIGaXCFzIiuBcoUt38lrE0VZcZmlrIhfF1K/oeLfM6zfOplS4cw1BSsQgbWwYMilOAYTqAMDPpwD4/w5Nw6D86z8zJsHXE+Z5bhh5zXD5hUl0A=</latexit><latexit sha1_base64="dz7RVEy9cdzpYFf7gvFeIsuRsKs=">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</latexit><latexit sha1_base64="dz7RVEy9cdzpYFf7gvFeIsuRsKs=">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</latexit><latexit sha1_base64="6ME4DRxcE1+uAoSHTxHFzC6uXAY=">AAACAHicdZDLSgMxFIYzXmu9VV24cBMsQhUpM7W01VXRjcsq9gJtLZn0TBuayQxJRiilG1/FjQtF3PoY7nwbM20FFf0h8PGfczg5vxtyprRtf1hz8wuLS8uJleTq2vrGZmpru6aCSFKo0oAHsuESBZwJqGqmOTRCCcR3OdTdwUVcr9+BVCwQN3oYQtsnPcE8Rok2Vie1e317lBHHLQgV44GBLnBNDs86qbSdPS0VcvkCtrO2XXRyTgy5Yv4kjx3jxEqjmSqd1HurG9DIB6EpJ0o1HTvU7RGRmlEO42QrUhASOiA9aBoUxAfVHk0OGOMD43SxF0jzhMYT9/vEiPhKDX3XdPpE99XvWmz+VWtG2iu1R0yEkQZBp4u8iGMd4DgN3GUSqOZDA4RKZv6KaZ9IQrXJLGlC+LoU/w+1XNYxfOWky+ezOBJoD+2jDHJQEZXRJaqgKqJojB7QE3q27q1H68V6nbbOWbOZHfRD1tsnhdWVtw==</latexit>

Channel

BobXn

ŴYn

W

Zn Leakage ≤ dEve

Alice

[Yang, Schaefer, Poor, IT’19]

• Legitimate channel is deterministic, eavesdropper channel is BSC:

Semi-deterministic Wiretap Channel (BSC):

!X

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.1

0.2

0.3

0.4

0.5CS = 0.5

Second-order Approximation

Converse

Converse [Y.-Schaefer-Poor’16]

Achievability

Blocklength, n

Secrecy

rate,bit/(ch.use)

1

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R⇤(n, ✏, �) = Cs �

rV

nQ�1

✓�

1� ✏

◆+O

✓log n

n

◆

<latexit sha1_base64="2XYj1zXI74+cqD57yOAJUqzVM0k=">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</latexit><latexit sha1_base64="2XYj1zXI74+cqD57yOAJUqzVM0k=">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</latexit><latexit sha1_base64="2XYj1zXI74+cqD57yOAJUqzVM0k=">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</latexit><latexit sha1_base64="2XYj1zXI74+cqD57yOAJUqzVM0k=">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</latexit>

[Yang, et al. (2017)]

4078 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 65, NO. 7, JULY 2019

Fig. 2. Secrecy rate for the Gaussian wiretap channel with P/N1 = 3 dB, P/N2 = −3 dB, ε = δ = 10−3.

where CS is given in (114) and

Vi = log2 e2

P2 + 2P Ni

(P + Ni )2 , i ∈ {1, 2} (117)

Vc = V1 + V2 − P N1

P + N1

(1

N2+ 1

P + N2

)log2 e. (118)

Proof: See Appendix VI.

C. Numerical Results and Discussions

In this section, we compare the bounds proposed in thispaper with existing bounds in [25] and [35], and with theapproximations provided in Theorem 14 for a Gaussian wire-tap channel (with the O(·) terms omitted). The results areshown in Fig. 2.

Let us first explain how each bound was computed. Notethat, every achievability bound for the wiretap channel consistsof two parts: a reliability bound on the decoding performanceof the legitimate receiver and a secrecy bound on the informa-tion leakage to the eavesdropper (see, e.g., Theorem 7). Forthe reliability part, we have used Shannon’s channel codingachievability bound [49], which is the tightest achievabilitybound for Gaussian channels [7, Sec. III.J-4]. In particular,let MShannon(ε, n) be the number of codewords for a givenprobability of error ε and blocklength n implied by Shannon’sachievability bound. The quantity MShannon(ε, n) can be com-puted via the numerical routine in [50]. The maximal secrecyrate R∗

avg(n, ε, δ) can be lower-bounded by

R∗avg(n, ε, δ) ≥ 1

nlog

MShannon(ε, n)

L(119)

where L may be interpreted as the number of “dummy”messages that must be conveyed through the wiretap channelto achieve the desired secrecy. To compute an achievabilitybound on R∗

avg(n, ε, δ), it suffices to determine an upper bound

on L. Note that, each of the achievability bound plottedin Fig. 2 is computed using (119) and corresponds to arespective method for upper-bounding L.

1) Achievability (Theorem 7): The result is an applicationof the secrecy bound (45). To compute (45), we have chosenQZ to be a multivariate Gaussian distribution with i.i.d.N (0, P + N2) elements, and have chosen A to be the powersphere Sn = {xn : ‖xn‖2 = n P}. By the rotational symmetryof the set A and of the distributions PZ |X=x and QZ , the twosupremums on the right-hand side of (45) are both achievedby an arbitrary x ∈ A. In particular, we have set

x = x n ! [√

P, . . . ,√

P] (120)

in the computation. With these choices, (45) becomes

δ ≤ 1 − E[exp

(−|Bn − log γ |+

)]

+ 12

√γ

LE

[exp(−|Bn − log γ |)

](121)

where

Bn ! n2

log(

1 + PN2

)+ log e

2

n∑

i=1

(

1 − (√

P Zi − √N2)2

P + N2

)

(122)

with {Zi} i.i.d. CN (0, 1) distributed. The inequality (121)implies the following upper bound on L:

√L ≤ min

γ

√γ E

[exp(−|Bn − log γ |)

]

2(δ + E[exp

(−|Bn − log γ |+

)]− 1)

(123)

where the minimization is over all γ > 0 such that thedenominator in (123) is positive. Substituting (123) into (119)we obtain the desired result.

Gaussian Wiretap Channel(SNRBob = 3db; SNREve = - 3db)

[Yang, Schaefer, Poor, IT’19]

Key Generation from Common Randomness

• Passive Eavesdropper:

– Public discussion

– Channel reciprocity: joint source-channel model

– Relay assisted: trusted or oblivious

• Active Eavesdropper:

– Channel reciprocity: joint source-channel model

Lai, Liang, Du, Poor (2015)Key Generation from Random Channelsin Physical Layer Security inWireless Communications (CRC)

Privacy-Utility Tradeoffs

in

Sensing Systems

• Privacy is not secrecy:

Privacy vs. Secrecy

• Privacy is not secrecy:

• Denial of access (secrecy) makes a data source useless.

= Eve ?

Privacy vs. Secrecy

• Sensing systems generate considerable electronic data:

• Data’s utility depends on its accessibility.

• Accessibility endangers privacy.

• This fundamental tradeoff can becharacterized via information theory.

Privacy pEquivocation E

Utility UDistortion D

Utility-PrivacyTradeoff Region

Privacy-Utility Tradeoff

• Smart meter data is useful for price-aware usage, load balancing

• But, it leaks information about in-home activity

Example: Smart Meter Privacy

Giaconi, Gunduz, Poor (2021) Smart Meter Privacy, in Advanced Data Analytics forPower Systems (Cambridge)

P-U tradeoff leads to a spectral ‘reverse water-filling’ solution

The following theorem captures our main result.

Theorem 3: The utility-privacy tradeoff for smart metermeasurements modeled as a Gaussian source with memory isgiven by the leakage function λ(D) which results from choos-ing the distribution p (xn|xn) as the rate-distortion (withoutprivacy) optimal distribution.

Proof: The proof follows directly from noting that, for agiven jointly Gaussian distribution of the source and correlatedhidden sequence, pXnY n , the infimum in (8) and (9) is strictlyover the space of conditional distributions of the revealedsequence given the original source sequence as a result ofthe Markov chain relationship Y n − Xn − Xn. Expandingthe leakage as I(Y n; Xn) = h(Y n) − h(Y n|Xn), and usingthe fact for correlated Gaussian processes, Yk = αkXk + Zk,for all k, where {Zk} is a sequence independent of {Xk}and αk is a constant for each k, one can show that the jointlyGaussian distribution of Xn and Xn which minimizes (8) alsominimizes (9).

Remark 2: Theorem 3 simplifies the development of theRDL region for Gaussian sources with memory for which therate-distortion function is known. For Gaussian sources withmemory the rate-distortion function is known and lends itselfto a straightforward practical implementation that we discussin the following section.

F. Rate-Distortion for Gaussian Sources with Memory

In general, the rate distortion functions for sources withmemory are not straightforward to compute. However, forGaussian sources, the rate-distortion function R(D) (withoutthe additional privacy constraint) is known and can be obtainedvia a transformation of the correlated source sequence Xn

to its eigen-space in which the resulting sequence Xn isuncorrelated (and hence, independent for jointly Gaussiansources); let SX(ω), SY (ω), and SXY (ω) denote the two-sided power spectral densities (PSDs) of the {Xk} , {Yk},and {XkYk} processes, respectively [16]. Let φ denote theLagrangian parameter for the distortion constraint (4) in therate minimization problem. Explicitly denoting the dependenceon the water-level φ, the rate-distortion function Rφ (D) andthe average distortion function D (φ) are given by

Rφ (D) =

∫ π

−π

max

(

0,1

2log

SX(ω)

φ

)

dω

2π(10)

D (φ) =

∫ π

−π

min (SX(ω),φ)dω

2π. (11)

Note that the water-level φ is determined by the desiredaverage distortion D (φ) = D. Thus, R(D) for a Gaussiansource with memory can be expressed as an infinite sum of therate-distortion functions for independent Gaussian variables,one for each angular frequency ω ∈ [−π,π]. The “water-level” φ captures the average time-domain distortion constraintacross the spectrum such that the distortion for any ω is theminimum of the water-level and the PSD. The privacy leakageλ(D (φ)) is then the infinite sum of the information leakage

0 0 0

0.5

1

1.5

2

2.5

3

ωπ−π

S (ω)

φ

Fig. 1. The PSD of {Xk}. The area below the curve and the horizontal lineis equal to D.

about {Yk} for each ω, and is given by

λ (D (φ)) =

∫ π

−π

1

2log

(

SY (ω)

SXY (ω)g (ω) + SY (ω)

)

dω

2π(12)

where g (ω) ≡ (min (SX(ω),φ) − 1) .Remark 3: The transform domain “water-filling” solution

suggests that in practice the time-series data can be filteredfor a desired level of fidelity (distortion) and privacy (leak-age) using Fourier transforms. The privacy-preserving rate-distortion optimal scheme thus reveals only those frequencycomponents with power above the water-level φ. Furthermore,at every frequency only the portion of the signal energy whichis above the water level φ is preserved by the minimum-ratesequence from which the source can be generated with anaverage distortion D.

IV. ILLUSTRATION

The following example illustrates our results. We assumethat the private information to be hidden is the measurementsequence itself, i.e., Yk = Xk, for all k. For the metermeasurements modeled as a stationary Gaussian time series{Xk} , we choose Xk ∼ N (0, 1) for all k ∈ I, and anautocorrelation function

cm = E[XkXk+m] =

1 m = 0,0.3 m = ±1,0.4 m = ±2,0 otherwise.

The power spectral density PSD (frequency domain represen-tation of the autocorrelation function) of this process is givenby

S(ω) =∞∑

m=−∞

cm exp(imω) = 1+0.6 cos(ω)+0.8 cos(2ω),

− π ≤ ω ≤ π. (13)

In order to obtain the rate-distortion function Rφ(D) for thissource, for a given D we have to find the water-level φsatisfying (11).

Source Coding Solution:Hidden Gauss-Markov Model (protection of the hidden

intermittency state)

wasted energyversus

information leakageTradeoff:

A Control Approach:Energy Harvesting and Storage

º

ENERGY MANAGEMENT UNIT (EMU)

APPLIANCES

ENERGY HARVESTING (EH)

DEVICE

Char

ging

Disc

harg

ing

Harv

este

dEn

ergy

Output LoadInput Load

UTILITY PROVIDER

(UP)

RECHARGEABLE BATTERY (RB)

iX iY

iZ

SMAR

T M

ETER

(S

M)

Info

rmat

ion

Leak

age

Rat

e, I

(pX = pZ = ½)

Privacy-Utility Tradeoff:Binary Variables

Competitive Privacy: Privacy-Utility Tradeoffs for Interacting Agents

• Multiple interacting, but competing,agents (or groups of agents) withcoupled measurements.

• Each wants to estimate its ownparameters, or state.

• They can help each other by sharingdata, but wish to preserve privacy.

• Each has a privacy-utility tradeoff, butthey are competitive ones.

• How should they interact?

Motivating Examples

Electricity Grids: grid management

Radar: untrustworthy allies

Sensor Networks: resource localization

Yk = Hk ,mXm + Zk

m=1

M

∑ , k = 1,2,…,M

mth system state

• Noisy measurements at agent k:

• Utility for agent k: mean-square error for its own state Xk

• Privacy for agent k: leakage of information about Xk to other agents

Linear Measurement Model

How Should Agents Exchange Data?

• This is a classical problem in information theory – theWyner-Ziv problem (optimal distributed sourcecoding) – which tells how to exchange information.

• But, doesn’t say how much information to exchange.

• Because of the competitive nature, gametheory or prospect theory can illuminate this.

• Leads to a number of interesting solutions:– a basic problem is a prisoners’ dilemma

– with pricing, cooperation or multi-play games,more meaningful solutions arise

Poor (2018)Privacy in Networks of Interacting Agentsin Emerging Applications of Control and SystemTheory (Springer)

Other Issues

Other Issues

• Authentication

– Information theoretic bounds on the probabilities of successful impersonation and

substitution attacks [Lai, et al. IT’09]

• Attacks on MANETs

– Information theoretic guidance on how many malicious nodes can be tolerated

[Liang, et al. IT’11]

• Man-in-the-Middle and Spoofing Attacks on Sensor Nets

– Effects on CRLB in parameter estimation [Zhang, et al. SPM’18]

Authentication with Correlated Sequences

Impersonation attack: O transmits a message before S

Substitution attack: O replaces S’s message with its own

S R

O

s1L s2L

M

Theorem [Lai, et al. IT’09]: If the S-O channel is not less noisy than the S-R channel, then

Eav�

Eav�

Eav�

MANETs with Malicious Nodes

Secrecy Capacity Scaling[Liang, et al. IT’11]

Attacks on Sensor Nets[Zhang, et al. SPM’18]

3

studied in [3], [4], [7]–[9] and references therein. Investigations on cyberattacks on estimation systems

have been studied in [6], [7], [10]–[15], [17], [23] and references therein. The early work in [3], [4],

[6], [7], [7]–[9], [13]–[15], [23] set the tone for many later investigations and influenced most of the

discussions in this paper. In particular, the impact and mitigation of cyberattacks on systems solving

hypothesis testing problems was studied in [3], [4], [7], [9] and references therein. Distributed detection

in tree topologies in the presence of cyberattacks was considered in [8]. Investigations on cyberattacks

on estimation systems have been studied in [6], [7], [10]–[15], [17], [23] and references therein. The

problem of distributed spectrum sensing in a cognitive radio network under cyberattacks was studied in

[4], [5], [25]. Several cyberattack detection techniques were proposed for IoT localization systems in [6],

[12], [18], [19]. More recently, the data-injection attack in smart grids was considered in [13]–[15], [26]

and the references therein.

FusionCenter

QuantizerSensor 1

Physical phenomenon

QuantizerSensor 2

QuantizerSensor 3

QuantizerSensor N

Spoofing Attack

���

Man-in-the-

middle Attack

Fig. 1: Cyberattacks in IoT systems.

According to the place where they occur, cyberattacks in IoT systems can be categorized into two

classes, as illustrated in Fig. 1. We call any attack modifying a signal in the IoT system prior to

quantization a spoofing attack. It has been shown [12] that the same changes in the signals in the

IoT system produced by any spoofing attack can also be produced by changing the data going into

the sensors to be different from that coming from the physical phenomenon being monitored. We call

any attack modifying a signal in the IoT system after quantization a man-in-the-middle attack (MiMA).

The same changes in the signals in the IoT system produced by any MiMA [12] can also be produced

May 22, 2018 DRAFT

Man-in-the-middle attack:- TQA uses attacked data- SEA ignores attacked data

• Information theory can help understand some fundamental limits of

security and privacy in wireless networks

• These are theoretical constructs; although they sometimes point to

potential practical solutions, there are many needs to connect this kind ofanalysis to real networks, e.g.

- more finite-blocklength analysis

- scaling laws for large networks

- practical coding schemes to achieve fundamental limits

- other security primitives (signatures, certificates, etc.)

• Not all security has to be iron-clad: Quality of Security can be aparameter, just like Quality of Service

Closing Thoughts

Some References

Schaefer, Boche, Khisti, Poor (2017) Information Theoretic Security and Privacy ofInformation Systems (Cambridge)

Poor, Schaefer (2017) Wireless Physical Layer Security, PNAS.

Poor (2018) Privacy in Networks of Interacting Agents, in Emerging Applications ofControl and System Theory (Springer)

Yang, Schaefer, Poor (2019) Wiretap Channels: Nonasymptotic FundamentalLimits, IEEETransactions on Information Theory

Yagli, Dytso, Poor (2020) Information-Theoretic Bounds on the GeneralizationError and Privacy Leakage in Federated Learning, Proceedings SPAWC

Giaconi, Gunduz, Poor (2021) Smart Meter Privacy, in Advanced Data Analytics forPower Systems (Cambridge)

Herfeh, Chorti, Poor (2021) Physical Layer Security: Authentication, Integrity andConfidentiality, in Physical Layer Security (Springer)

Thank You!