Enhancing secrecy with channel knowledge
This presentation is the property of its rightful owner.
Sponsored Links
1 / 48

Enhancing Secrecy With Channel Knowledge PowerPoint PPT Presentation


  • 64 Views
  • Uploaded on
  • Presentation posted in: General

Enhancing Secrecy With Channel Knowledge. Presenter: Pang-Chang Lan Advisor: C.-C. (Jay) Kuo May 2, 2014. Outline. Research Problem Statement Introduction to Achievable Rate and Capacity Physical Layer (PHY) Security Some Research Results Conclusions and Future work.

Download Presentation

Enhancing Secrecy With Channel Knowledge

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Enhancing secrecy with channel knowledge

Enhancing Secrecy With Channel Knowledge

Presenter: Pang-Chang Lan

Advisor: C.-C. (Jay) Kuo

May 2, 2014


Outline

Outline

Research Problem Statement

Introduction to Achievable Rate and Capacity

Physical Layer (PHY) Security

Some Research Results

Conclusions and Future work


Research problem statement

Research Problem Statement


Wireless environment

Wireless Environment

Ally

Enemy

Signaler

Open-access medium


Wiretap channel modeling

Wiretap Channel Modeling

receiver

transmitter

eavesdropper

The received signals are modeled as

where are channel coefficients and are Gaussian noises


Channel state information

Channel State Information

transmitter

receiver

eavesdropper

In convention, the channel state information (CSI) are assumed to be known to all the nodes

However, letting the eavesdropper know the CSI can be problematic by increasing her ability in eavesdropping


Reference signaling

Reference Signaling

Downlink reference signaling

transmitter

receiver

Amp.

Amp.

channel estimate

reference signal

channel

In wireless communications, we use reference signals to help estimate channel information


Conventional channel estimation

Conventional Channel Estimation

Channel state information at the transmitter (CSIT)

Channel state information at the receiver (CSIR)

uplink reference signals

downlink reference signals

transmitter

receiver

Not realistic

Channel state information at the eavesdropper (CSIE)

Uplink and downlink channel estimation

eavesdropper


Channel estimation for secrecy

Channel Estimation for Secrecy

Channel state information at the transmitter (CSIT)

Channel state information at the receiver (CSIR)

uplink reference signals

downlink reference signals

transmitter

receiver

Not realistic

Channel state information at the eavesdropper (CSIE)

Q: Is uplink reference signaling enough?

eavesdropper


Introduction to achievable rate and capacity

Introduction to Achievable Rate and Capacity


Rate without noises and channel uncertainty

Rate without Noises and Channel Uncertainty

channel

receiver

transmitter

infinitely long message

Let’s take a look at the point-to-point channel

If there are no channel uncertainty and noise, e.g., , we can deliver infinite information through the channel in a unit time, i.e.,


Random property

Random Property

Degenerate case

Randomized case

Message: 01011100101…

10110011001…

Message: 111111111…

We often model the as random variables

For example, let be a Bernoulli random variable


Channel uncertainty and noises

Channel Uncertainty and Noises

channel

noise

+

=

receiver

transmitter

However, channel uncertainty and noises make it impossible to deliver messages at a infinite rate

That is , where is the channel coefficient and is the additive noise

Reference signaling can help eliminate the channel uncertainty


Overcome the noise

Overcome the Noise

Assume a Gaussian channel, i.e., where

To overcome the noise, we can quantize the transmitted symbol

Since the transmit power, i.e., , is limited, the number of quantization levels is limited => rate is limited


Rate and capacity

Rate and Capacity

The whole transmission will be ruined

Capacity

With the noise, we know that the transmission rate cannot be infinite

Q: How large can the rate be? Or is there a capacity (maximum achievable rate)?

The notion of capacity


Channel coding

Channel Coding

50 years

1940s Hamming Codes

1990s Turbo Codes

Channel coding is essential for achieving the capacity

Channel coding: Ways to quantize and randomize the transmitted symbol to tolerate noises and convey as much information as possible

The channel coding design is generally not easy


Random coding

Random Coding

Random coding: randomly generate the quantization according to a specific distribution

In the theoretical development, random coding saves the struggle of designing a channel coding scheme

Random coding is generally not good in the practical use


Some assumptions

Some Assumptions

t

bits

+

+

+

+

=

We want to transmit at a rate of , i.e., each symbol represents bits

As the signals are sent through time, let where

is the time index

Therefore, we convey a message from a set, e.g.,


Codebook generation

Codebook Generation

codeword

receiver

transmitter

In random coding, we need to randomly generate a codebook

For each message candidate, there is a randomly generated codeword associated with it


Achievable rate

Achievable Rate

A rate is said to be achievable if there exists a channel coding scheme (including random coding) such that the message error probability, i.e., , is zero as

For example, with the CSI known to both the transmitter and the receiver, it turns out that the capacity of the channel

subject to the power constraint , is given by


Converse

Converse

  • Capacity proofs usually consist of two parts

    • Achievability

    • Converse

  • The converse part helps you identify that a certain achievable rate is in fact the maximum rate (capacity), i.e., any rate above it is not achievable

  • Usually, the converse part of the proof is difficult and may not be always obtained


Physical layer phy security

Physical Layer (PHY) Security


Physical layer security

Physical Layer Security

transmitter

receiver

eavesdropper

Scenario: The transmitter wants to send secret messages to the receiver without being wiretapped by the eavesdropper

In 1975, Wyner showed that channel coding is possible to protect the secret messages without using any cryptography methods

The corresponding maximum rate of the secret message is referred to as the “secrecy capacity”


Gaussian wiretap channel

Gaussian Wiretap Channel

receiver

transmitter

eavesdropper

The received signals are modeled as

subject to the power constraint

where are the channel coefficients and


Secrecy capacity

Secrecy Capacity

transmitter

receiver

eavesdropper

Suppose that the CSI are known to all the terminals. The secrecy capacity turns out to be

where

To have a positive secrecy capacity, the receiver should experience a better channel than the eavesdropper, i.e.,


Interpretation of secrecy capacity

Interpretation of Secrecy Capacity

This remaining portion is the secrecy capacity

This portion is used to overwhelm the eavesdropper

receiver

eavesdropper

Information theoretic points of view


Interpretation of secrecy capacity1

Interpretation of Secrecy Capacity

Transmitter’s 16QAM

constellation

  • transmitted symbol

Eavesdropper

Receiver

  • Modulation points of view

    • Suppose that the eavesdropper has a worse resolution on the transmitted symbol


Random modulation

Random Modulation

00

00

00

00

Use 4PSK to transmit the secret message while randomly choosing the quadrants to confuse the eavesdropper

For example, to transmit the 00 symbol, we have four candidates to select

2-bit degrees of freedom are used to confuse the eavesdropper


Realistic channel assumption

Realistic Channel Assumption

An essential assumption for achieving the secrecy capacity is for the transmitter to know the CSI from the eavesdropper

However, as a malicious node, the eavesdropper will not feed its channel information back

What we are interested in is “Secrecy with CSIT only”


Secrecy with csit only

Secrecy with CSIT Only

Channel state information at the transmitter (CSIT)

Channel state information at the receiver (CSIR)

uplink reference signals

transmitter

receiver

Channel state information at the eavesdropper (CSIE)

eavesdropper


Some research results

Some Research Results


Siso wiretap channel model

SISO Wiretap Channel Model

receiver

transmitter

eavesdropper

The received signals are modeled as

where , , and


Case 1 reversed training without csire

Case 1: Reversed Training without CSIRE

transmit

stop

Suppose that the transmitter knows but doesn’t know

We take the strategy of channel inversion with a channel quality threshold for transmission, i.e.,

where

and are first revealed to the receiver and eavesdropper


Resulting channel and achievable rate

Resulting Channel and Achievable Rate

The resulting received signals at the receiver and eavesdropper are

We want to find an achievable secrecy rate for this scheme as

where the mutual information is obtained by numerical integration


Case 2 reversed training with practical csire

Case 2: Reversed Training with Practical CSIRE

Here, we assume that the receiver and eavesdropper know their respective received SNR, i.e., and

So the transmitter only has to null the phase to the receiver. The resulting channel is given by

where is a uniform phase random variable


Achievable secrecy rate

Achievable Secrecy Rate

It turns out that the achievable secrecy rate is given by

where

and


Asymptotic bounds on the achievable rates

Asymptotic Bounds on the Achievable Rates

[1] A. Lapidoth, “On phase noise channels at high SNR,” in Proceedings of IEEE Information Theory Workshop 2002, Oct. 2002, pp. 1–4

Since the achievable rates above rely on the numerical integration, explicit asymptotic bounds are also useful for performance evaluation.

Based on the techniques in [1], we can derive the asymptotic lower bounds for the above achievable secrecy rates as


Vs with p 10 db and

vs. with P = 10 dB and


Enhancing secrecy with channel knowledge

vs. P with Optimal and


Miso wiretap channel model

MISOWiretap Channel Model

transmitter

receiver

Suppose that the transmitter has antennas, and the legitimate receiver and the eavesdropper have respectively one antenna

The MISOSE wiretap channel is modeled by

where , , and

eavesdropper


Case 1 reversed training without csir

Case 1: Reversed Training without CSIR

Suppose that the transmitter knows but doesn’t know

The transmitter applies the channel inversion strategy with a channel quality threshold, i.e.,

where

and are first revealed to the receiver and eavesdropper


Resulting channel and achievable rate1

Resulting Channel and Achievable Rate

The resulting received signals at the receiver and eavesdropper are

The achievable secrecy rate for this scheme can still be found by


Case 2 reversed training with practical csir

Case 2: Reversed Training with Practical CSIR

Here, we assume that the receiver and eavesdropper know their respective received SNR, i.e., and

So the transmitter only has to null the phase to the receiver. The resulting channel is given by

It turns out that the achievable secrecy rate is also given by


Vs with p 10 db and1

vs. with P = 10 dB and


Enhancing secrecy with channel knowledge

vs. P with Optimal and


Conclusions and future work

Conclusions and Future work


Conclusions

Conclusions

With CSIT only, we can achieve a higher secrecy rate than with full CSI at all the nodes

With multiple antennas at the transmitter, the gain on the achievable secrecy rate can be even increased

By setting a channel gain threshold , i.e., transmit only when ,

the secrecy rate can be effectively improved


Future work

Future Work

Design an efficient algorithm to find the optimal

Find the achievable rate for the multi-antenna receiver and eavesdropper

Work on the scenario with finite-precision CSIT. Will the imprecision of the CSIT affect the achievable rate a lot?


  • Login