The Sender-Excited Secret Key Agreement Model: Capacity and Error Exponents Tzu-Han Chou, Vincent Y. F. Tan , Stark C. Draper Department of Electrical and Computer Engineering, University of Wisconsin-Madison Allerton (Sep 2011) Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 1 / 18
Joint work with Stark C. Draper Tzu-Han Chou UW-Madison Qualcomm Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 2 / 18
Introduction Consider the fundamental limits of the secret key generation problem Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 3 / 18
Introduction Consider the fundamental limits of the secret key generation problem There is a noiseless public discussion channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 3 / 18
Introduction Consider the fundamental limits of the secret key generation problem There is a noiseless public discussion channel Source is randomly excited by the sender Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 3 / 18
Introduction Consider the fundamental limits of the secret key generation problem There is a noiseless public discussion channel Source is randomly excited by the sender Motivated by Key generation [Maurer, Ahlswede and Csiszár] Key generation with external excitation [Chou, Draper and Sayeed] Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 3 / 18
Introduction Consider the fundamental limits of the secret key generation problem There is a noiseless public discussion channel Source is randomly excited by the sender Motivated by Key generation [Maurer, Ahlswede and Csiszár] Key generation with external excitation [Chou, Draper and Sayeed] Channels with action-dependent states [Weissman] Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 3 / 18
Introduction Consider the fundamental limits of the secret key generation problem There is a noiseless public discussion channel Source is randomly excited by the sender Motivated by Key generation [Maurer, Ahlswede and Csiszár] Key generation with external excitation [Chou, Draper and Sayeed] Channels with action-dependent states [Weissman] Main contributions: Secret key capacity Inner bound for rate-reliability-secrecy-exponent region Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 3 / 18
Wiretap Channel [Wyner, Csiszár and Körner] Z n ✲ Eve ˆ M ∈ [ 2 nR ] S n Y n M ✲ ✲ ✲ ✲ Enc p ( y , z | s ) Dec Alice Bob Want to transmit message reliably to Bob but keep Eve ignorant P ( ˆ M � = M ) → 0 and 1 n I ( M ; Z n ) → 0 Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 4 / 18
Wiretap Channel [Wyner, Csiszár and Körner] Z n ✲ Eve ˆ M ∈ [ 2 nR ] S n Y n M ✲ ✲ ✲ ✲ Enc p ( y , z | s ) Dec Alice Bob Want to transmit message reliably to Bob but keep Eve ignorant P ( ˆ M � = M ) → 0 and 1 n I ( M ; Z n ) → 0 Wiretap channel capacity C wiretap = U − S − ( Y , Z ) { I ( U ; Y ) − I ( U ; Z ) } max Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 4 / 18
Wiretap Channel [Wyner, Csiszár and Körner] Z n ✲ Eve ˆ M ∈ [ 2 nR ] S n Y n M ✲ ✲ ✲ ✲ Enc p ( y , z | s ) Dec Alice Bob Want to transmit message reliably to Bob but keep Eve ignorant P ( ˆ M � = M ) → 0 and 1 n I ( M ; Z n ) → 0 Wiretap channel capacity C wiretap = U − S − ( Y , Z ) { I ( U ; Y ) − I ( U ; Z ) } max Channel-type model Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 4 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ❄ Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ✻ Φ ✻ Φ ❄ Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ✻ Φ ✻ Φ ❄ ❄ K A K B ❄ Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ✻ Φ ✻ Φ ❄ ❄ K A K B ❄ Public Channel Secret keys are generated from dependent sources X , Y , Z Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ✻ Φ ✻ Φ ❄ ❄ K A K B ❄ Public Channel Secret keys are generated from dependent sources X , Y , Z P ( K A � = K B ) → 0 and 1 n I ( K A ; Z n , Φ) → 0 Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ✻ Φ ✻ Φ ❄ ❄ K A K B ❄ Public Channel Secret keys are generated from dependent sources X , Y , Z P ( K A � = K B ) → 0 and 1 n I ( K A ; Z n , Φ) → 0 Secret key capacity C SK = W − U − X − ( Y , Z ) { I ( U ; Y | W ) − I ( U ; Z | W ) } max Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Secret Key Generation [Maurer, Ahlswede & Csiszár] p ( x , y , z ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ✻ Φ ✻ Φ ❄ ❄ K A K B ❄ Public Channel Secret keys are generated from dependent sources X , Y , Z P ( K A � = K B ) → 0 and 1 n I ( K A ; Z n , Φ) → 0 Secret key capacity C SK = W − U − X − ( Y , Z ) { I ( U ; Y | W ) − I ( U ; Z | W ) } max Source-type model Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 5 / 18
Key Generation with External Excitation [Chou et al.] p ( x , y , z | s ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve Φ ✻ Φ ✻ Φ ❄ ❄ K A K B ❄ Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 6 / 18
Key Generation with External Excitation [Chou et al.] s n Wireless channels ⇒ ❄ auxiliary randomness p ( x , y , z | s ) Due to multipath fading X n Y n Z n ❄ ❄ ❄ Transmissions are Alice Bob Eve bi-directional ⇒ X , Y , Z Φ ✻ Φ ✻ Φ ❄ ❄ generated by transmitting K A K B prearranged sounding ❄ Public Channel signals. Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 6 / 18
Key Generation with External Excitation [Chou et al.] s n Wireless channels ⇒ ❄ auxiliary randomness p ( x , y , z | s ) Due to multipath fading X n Y n Z n ❄ ❄ ❄ Transmissions are Alice Bob Eve bi-directional ⇒ X , Y , Z Φ ✻ Φ ✻ Φ ❄ ❄ generated by transmitting K A K B prearranged sounding ❄ Public Channel signals. External excitation via a deterministic sounding signal s n Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 6 / 18
Key Generation with External Excitation [Chou et al.] s n Wireless channels ⇒ ❄ auxiliary randomness p ( x , y , z | s ) Due to multipath fading X n Y n Z n ❄ ❄ ❄ Transmissions are Alice Bob Eve bi-directional ⇒ X , Y , Z Φ ✻ Φ ✻ Φ ❄ ❄ generated by transmitting K A K B prearranged sounding ❄ Public Channel signals. External excitation via a deterministic sounding signal s n Secret key capacity C SK = p ( w , u | s ) , p ( x | u , s ) , p ( s ) { I ( U ; Y | W , S ) − I ( U ; Z | W , S ) } max Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 6 / 18
Our model: Sender-Excited Secret Key Agreement p ( x , y , z | s ) X n Y n Z n ❄ ❄ ❄ Alice Bob Eve ✻ ✻ Φ ❄ Φ ❄ Φ K A K B ❄ Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 7 / 18
Our model: Sender-Excited Secret Key Agreement p ( x , y , z | s ) M X n Y n Z n ❄ ❄ ❄ ❄ Alice Bob Eve ✻ ✻ Φ ❄ Φ ❄ Φ K A K B ❄ Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 7 / 18
Our model: Sender-Excited Secret Key Agreement S n ( M ) ❄ p ( x , y , z | s ) M X n Y n Z n ❄ ❄ ❄ ❄ Alice Bob Eve ✻ ✻ Φ ❄ Φ ❄ Φ K A K B ❄ Public Channel Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 7 / 18
Our model: Sender-Excited Secret Key Agreement S n ( M ) ❄ p ( x , y , z | s ) M X n Y n Z n ❄ ❄ ❄ ❄ Alice Bob Eve ✻ ✻ Φ ❄ Φ ❄ Φ K A K B ❄ Public Channel A ( 2 nR M , 2 nR Φ , n , Γ) code consists of a uniform M ∈ [ 2 nR M ] and Vincent Tan (UW-Madison) Sender-Excited Secret Key Agreement Model Allerton 2011 7 / 18
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