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Physical Layer Security over Wiretap Channelswith Random Parameters
Ziv Goldfeld, Paul Cuff and Haim Permuter
Ben Gurion University and Princeton University
2017 International Symposium on Cyber Security Cryptography andMachine Learning Conference
June 29-30, 2017
Physical Layer Security
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 2
Physical Layer Security
Rooted in Information Theory.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 2
Physical Layer Security
Rooted in Information Theory.
Alternative approach to cryptography:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 2
Physical Layer Security
Rooted in Information Theory.
Alternative approach to cryptography:
◮ Exploit the noisy channel for secrecy (no shared key).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 2
Physical Layer Security
Rooted in Information Theory.
Alternative approach to cryptography:
◮ Exploit the noisy channel for secrecy (no shared key).
◮ Computationally unlimited eavesdroppers.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 2
Physical Layer Security
Rooted in Information Theory.
Alternative approach to cryptography:
◮ Exploit the noisy channel for secrecy (no shared key).
◮ Computationally unlimited eavesdroppers.
Appropriate for securing low complexity devices such as IoT.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 2
Some Background
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 3
Basic Information Measures
(X, Y ) ∼ PX,Y discrete RVs
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 4
Basic Information Measures
(X, Y ) ∼ PX,Y discrete RVs
Entropy: H(X) = H(PX) = −∑
x∈XPX(x) log PX(x).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 4
Basic Information Measures
(X, Y ) ∼ PX,Y discrete RVs
Entropy: H(X) = H(PX) = −∑
x∈XPX(x) log PX(x).
Conditional Entropy: H(X|Y ) =∑
y∈YPY (y)H(PX|Y =y).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 4
Basic Information Measures
(X, Y ) ∼ PX,Y discrete RVs
Entropy: H(X) = H(PX) = −∑
x∈XPX(x) log PX(x).
Conditional Entropy: H(X|Y ) =∑
y∈YPY (y)H(PX|Y =y).
Mutual Information: I(X; Y ) = H(X) − H(X|Y )= H(Y ) − H(Y |X).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 4
Physical Layer Communication - IT Perspective
A mathematical model for a physical communication channel.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 5
Physical Layer Communication - IT Perspective
A mathematical model for a physical communication channel.
Channel Examples:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 5
Physical Layer Communication - IT Perspective
A mathematical model for a physical communication channel.
Channel Examples:
◮ Gaussian Channel:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 5
X
Z ∼ N (0, σ2)
Y = X + Z
Physical Layer Communication - IT Perspective
A mathematical model for a physical communication channel.
Channel Examples:
◮ Gaussian Channel:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 5
X
Z ∼ N (0, σ2)
Y = X + Z
◮ Binary Symmetric Channel:
0
1
0
1
X Y
α
1 − α
α
1 − α
Physical Layer Communication - IT Perspective
A mathematical model for a physical communication channel.
Channel Examples:
◮ Gaussian Channel:
Questions we ask:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 5
X
Z ∼ N (0, σ2)
Y = X + Z
◮ Binary Symmetric Channel:
0
1
0
1
X Y
α
1 − α
α
1 − α
Physical Layer Communication - IT Perspective
A mathematical model for a physical communication channel.
Channel Examples:
◮ Gaussian Channel:
Questions we ask:
◮ What is the maximal rate [bits/ch. use] of reliable communication?
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 5
X
Z ∼ N (0, σ2)
Y = X + Z
◮ Binary Symmetric Channel:
0
1
0
1
X Y
α
1 − α
α
1 − α
Physical Layer Communication - IT Perspective
A mathematical model for a physical communication channel.
Channel Examples:
◮ Gaussian Channel:
Questions we ask:
◮ What is the maximal rate [bits/ch. use] of reliable communication?
◮ How to design codes at that rate?
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 5
X
Z ∼ N (0, σ2)
Y = X + Z
◮ Binary Symmetric Channel:
0
1
0
1
X Y
α
1 − α
α
1 − α
Physical Layer Communication - Formal Definition
MEnc
XnPY |X
Y nDec
M̂
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 6
Physical Layer Communication - Formal Definition
MEnc
XnPY |X
Y nDec
M̂
Message: nR information bits.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 6
Physical Layer Communication - Formal Definition
MEnc
XnPY |X
Y nDec
M̂
Message: nR information bits.
(n,R)-Code: Block Encoding and Decoding functions.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 6
Physical Layer Communication - Formal Definition
MEnc
XnPY |X
Y nDec
M̂
Message: nR information bits.
(n,R)-Code: Block Encoding and Decoding functions.
Channel: P(
Y n = yn∣
∣Xn = xn)
=n∏
i=1PY |X(yi|xi).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 6
Physical Layer Communication - Formal Definition
MEnc
XnPY |X
Y nDec
M̂
Message: nR information bits.
(n,R)-Code: Block Encoding and Decoding functions.
Channel: P(
Y n = yn∣
∣Xn = xn)
=n∏
i=1PY |X(yi|xi).
Capacity: C , sup{
R∣
∣
∣∃(n, R) − codes s.t. P(
M 6= M̂)
→n
0}
.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 6
Physical Layer Communication - Formal Definition
MEnc
XnPY |X
Y nDec
M̂
Message: nR information bits.
(n,R)-Code: Block Encoding and Decoding functions.
Channel: P(
Y n = yn∣
∣Xn = xn)
=n∏
i=1PY |X(yi|xi).
Capacity: C , sup{
R∣
∣
∣∃(n, R) − codes s.t. P(
M 6= M̂)
→n
0}
.
Reminder: I(X; Y ) = H(Y ) − H(Y |X)Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 6
Theorem (Shannon 1948)
The capacity of a channel PY |X is C = maxPX
I(X; Y ).
State-Dependent Wiretap Channels
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 7
State-Dependent Channels[Gelfand-Pinsker 1980]
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State StSNR at time t
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State St 1 1 0 1 0 0 . . .
SNR at time t
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State St 1 1 0 1 0 0 . . .
SNR at time t Low
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State St 1 1 0 1 0 0 . . .
SNR at time t Low Low
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State St 1 1 0 1 0 0 . . .
SNR at time t Low Low High
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State St 1 1 0 1 0 0 . . .
SNR at time t Low Low High Low
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State St 1 1 0 1 0 0 . . .
SNR at time t Low Low High Low High
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
State-Dependent Channel:
State: S ∼ Bernoulli(
12
)
, S = {0, 1}.
AGN Channel: Y = X + ZS
Z0 ∼ N (0, σ20), Z1 ∼ N (0, σ
21), σ0 ≪ σ1.
Time t 1 2 3 4 5 6 . . .
State St 1 1 0 1 0 0 . . .
SNR at time t Low Low High Low High High . . .
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 8
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
Encoder knows the state sequence non-causally.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 9
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
Encoder knows the state sequence non-causally.
Enhance communication rates via coherent transmission.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 9
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
State-Dependent Channels[Gelfand-Pinsker 1980]
Encoder knows the state sequence non-causally.
Enhance communication rates via coherent transmission.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 9
M
(nR bits)Encoder
XnPY |X,S
Sn ∼ P nS
Y n
DecoderM̂
Theorem (Gelfand-Pinsker 1980)
CGP = maxPU,X|S
[
I(U ; Y ) − I(U ; S)]
Joint distribution: PU,X|SPY |X,S
The Gelfand-Pinsker Channel - Encoding
Pad nR message bits with nR̃ redundancy bits.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 10
The Gelfand-Pinsker Channel - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 10
The Gelfand-Pinsker Channel - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Codebook: (Message ,Padding) → Codeword Un.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 10
The Gelfand-Pinsker Channel - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Codebook: (Message ,Padding) → Codeword Un.
Correlating Un with Sn: R̃ > I(U ;S).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 10
The Gelfand-Pinsker Channel - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Codebook: (Message ,Padding) → Codeword Un.
Correlating Un with Sn: R̃ > I(U ;S).
Reliability: R+ R̃ < I(U ;Y ).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 10
Wiretap ChannelsDegraded [Wyner 1975], General [Csiszár-Körner 1978]
M
(nR bits)Encoder
XnPY,Z|X
Y n
Zn
Decoder
Eve
M̂
M
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 11
Wiretap ChannelsDegraded [Wyner 1975], General [Csiszár-Körner 1978]
M
(nR bits)Encoder
XnPY,Z|X
Y n
Zn
Decoder
Eve
M̂
M
Secrecy-Capacity:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 11
Wiretap ChannelsDegraded [Wyner 1975], General [Csiszár-Körner 1978]
M
(nR bits)Encoder
XnPY,Z|X
Y n
Zn
Decoder
Eve
M̂
M
Secrecy-Capacity:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 11
Reliable Communication.
Wiretap ChannelsDegraded [Wyner 1975], General [Csiszár-Körner 1978]
M
(nR bits)Encoder
XnPY,Z|X
Y n
Zn
Decoder
Eve
M̂
M
Secrecy-Capacity:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 11
Reliable Communication.
Zn contains no information about M .
Wiretap ChannelsDegraded [Wyner 1975], General [Csiszár-Körner 1978]
M
(nR bits)Encoder
XnPY,Z|X
Y n
Zn
Decoder
Eve
M̂
M
Secrecy-Capacity:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 11
Reliable Communication.
Zn contains no information about M .
Theorem (Csiszár-Körner 1978)
CWTC = maxPU,X
[
I(U ; Y ) − I(U ; Z)]
Joint distribution: PU,XPY,Z|X
Wiretap Channels - Encoding
Pad nR message bits with nR̃ redundancy bits.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 12
Wiretap Channels - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 12
Wiretap Channels - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Codebook: (Message ,Padding) → Codeword Un.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 12
Wiretap Channels - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Codebook: (Message ,Padding) → Codeword Un.
Security: R̃ > I(U ;Z).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 12
Wiretap Channels - Encoding
Pad nR message bits with nR̃ redundancy bits.
00101101000110100010101100 01001011101010
Message Padding
Transmitted together in one block
Codebook: (Message ,Padding) → Codeword Un.
Security: R̃ > I(U ;Z).
Reliability: R+ R̃ < I(U ;Y ).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 12
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 13
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Secrecy Capacity: Reliable and Secure Communication.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 13
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Secrecy Capacity: Reliable and Secure Communication.
Tension: Utilize state knowledge to simultaneously
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 13
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Secrecy Capacity: Reliable and Secure Communication.
Tension: Utilize state knowledge to simultaneously
◮ Enhance reliable communication rate (coherent transmission).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 13
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Secrecy Capacity: Reliable and Secure Communication.
Tension: Utilize state knowledge to simultaneously
◮ Enhance reliable communication rate (coherent transmission).
◮ Boost security performance (e.g., via secret key agreement).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 13
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Naive Approach:
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 14
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Naive Approach: Combine wiretap coding with GP coding.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 14
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Naive Approach: Combine wiretap coding with GP coding.
00101101000110100010101100 01001011101010
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 14
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Naive Approach: Combine wiretap coding with GP coding.
00101101000110100010101100 01001011101010
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 14
Theorem (Chen-Han Vinck 2006)
CGP−WTC ≥ maxPU,X|S
[
I(U ; Y )−max{
I(U ;Z), I(U ;S)}
]
Joint distribution: PSPU,X|SPY,Z|X,S
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Naive Approach: Combine wiretap coding with GP coding.
00101101000110100010101100 01001011101010
⋆ Always preforms wiretap codingZiv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 14
Theorem (Chen-Han Vinck 2006)
CGP−WTC ≥ maxPU,X|S
[
I(U ; Y )−max{
I(U ;Z), I(U ;S)}
]
Joint distribution: PSPU,X|SPY,Z|X,S
The Gelfand-Pinsker Wiretap Channel
M
(nR bits)Encoder
Xn
PY,Z|X,S
Eve
Sn
Y n
Zn
DecoderM̂
M
Naive Approach: Combine wiretap coding with GP coding.
00101101000110100010101100 01001011101010
⋆ Always preforms wiretap coding =⇒ Suboptimal vs. strong EveZiv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 14
Theorem (Chen-Han Vinck 2006)
CGP−WTC ≥ maxPU,X|S
[
I(U ; Y )−max{
I(U ;Z), I(U ;S)}
]
Joint distribution: PSPU,X|SPY,Z|X,S
Improved Two-Layered Coding Scheme
Theorem (ZG-Cuff-Permuter 2016)
CGP−WTC ≥ maxPU,V,X|S :
I(U ;Y )≥I(U ;S)
min
{
I(V ; Y |U) − I(V ; Z|U),I(U, V ; Y ) − I(U, V ; S)
}
Joint distribution PSPU,V,X|SPY,Z|X,S .
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 15
Improved Two-Layered Coding Scheme
Theorem (ZG-Cuff-Permuter 2016)
CGP−WTC ≥ maxPU,V,X|S :
I(U ;Y )≥I(U ;S)
min
{
I(V ; Y |U) − I(V ; Z|U),I(U, V ; Y ) − I(U, V ; S)
}
Joint distribution PSPU,V,X|SPY,Z|X,S .
Two-Layered Coding Scheme (Superposition Code):
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 15
Improved Two-Layered Coding Scheme
Theorem (ZG-Cuff-Permuter 2016)
CGP−WTC ≥ maxPU,V,X|S :
I(U ;Y )≥I(U ;S)
min
{
I(V ; Y |U) − I(V ; Z|U),I(U, V ; Y ) − I(U, V ; S)
}
Joint distribution PSPU,V,X|SPY,Z|X,S .
Two-Layered Coding Scheme (Superposition Code):
Inner Layer: No wiretap coding - Supports key-agreement strategies.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 15
Improved Two-Layered Coding Scheme
Theorem (ZG-Cuff-Permuter 2016)
CGP−WTC ≥ maxPU,V,X|S :
I(U ;Y )≥I(U ;S)
min
{
I(V ; Y |U) − I(V ; Z|U),I(U, V ; Y ) − I(U, V ; S)
}
Joint distribution PSPU,V,X|SPY,Z|X,S .
Two-Layered Coding Scheme (Superposition Code):
Inner Layer: No wiretap coding - Supports key-agreement strategies.
Outer Layer: Wiretap coding (when channel favors legit users).
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 15
Improved Two-Layered Coding Scheme
Theorem (ZG-Cuff-Permuter 2016)
CGP−WTC ≥ maxPU,V,X|S :
I(U ;Y )≥I(U ;S)
min
{
I(V ; Y |U) − I(V ; Z|U),I(U, V ; Y ) − I(U, V ; S)
}
Joint distribution PSPU,V,X|SPY,Z|X,S .
Two-Layered Coding Scheme (Superposition Code):
Inner Layer: No wiretap coding - Supports key-agreement strategies.
Outer Layer: Wiretap coding (when channel favors legit users).
Generalization: Captures all past results as special cases.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 15
Improved Two-Layered Coding Scheme
Theorem (ZG-Cuff-Permuter 2016)
CGP−WTC ≥ maxPU,V,X|S :
I(U ;Y )≥I(U ;S)
min
{
I(V ; Y |U) − I(V ; Z|U),I(U, V ; Y ) − I(U, V ; S)
}
Joint distribution PSPU,V,X|SPY,Z|X,S .
Two-Layered Coding Scheme (Superposition Code):
Inner Layer: No wiretap coding - Supports key-agreement strategies.
Outer Layer: Wiretap coding (when channel favors legit users).
Generalization: Captures all past results as special cases.
Strict Improvement: Explicit example & Analytic derivation.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 15
Summary
The Gelfand-Pinsker wiretap channel
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Summary
The Gelfand-Pinsker wiretap channel
◮ Combination of two fundamental IT setups.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Summary
The Gelfand-Pinsker wiretap channel
◮ Combination of two fundamental IT setups.
◮ Simultaneously exploit state for reliability and security.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Summary
The Gelfand-Pinsker wiretap channel
◮ Combination of two fundamental IT setups.
◮ Simultaneously exploit state for reliability and security.
Novel superposition coding scheme
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Summary
The Gelfand-Pinsker wiretap channel
◮ Combination of two fundamental IT setups.
◮ Simultaneously exploit state for reliability and security.
Novel superposition coding scheme
◮ Recovers all past results.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Summary
The Gelfand-Pinsker wiretap channel
◮ Combination of two fundamental IT setups.
◮ Simultaneously exploit state for reliability and security.
Novel superposition coding scheme
◮ Recovers all past results.
◮ Strictly outperforms previous benchmark.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Summary
The Gelfand-Pinsker wiretap channel
◮ Combination of two fundamental IT setups.
◮ Simultaneously exploit state for reliability and security.
Novel superposition coding scheme
◮ Recovers all past results.
◮ Strictly outperforms previous benchmark.
Available on ArXiV: https://arxiv.org/abs/1608.00743v1.
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Summary
The Gelfand-Pinsker wiretap channel
◮ Combination of two fundamental IT setups.
◮ Simultaneously exploit state for reliability and security.
Novel superposition coding scheme
◮ Recovers all past results.
◮ Strictly outperforms previous benchmark.
Available on ArXiV: https://arxiv.org/abs/1608.00743v1.
Thank you!
Ziv Goldfeld, Paul Cuff and Haim Permuter Ben Gurion University and Princeton University
Physical Layer Security over Wiretap Channels with Random Parameters 16
Some BackgroundState-Dependent Wiretap Channels