Triangle Network Secrecy

Question

1. What have the authors contributed in "Triangle network secrecy" ?

2. What is the way to decrypt a message?

3. What is the property of the c packets?

4. How do the authors secure a message in the second phase?

Accepted Answer

The source and the relay can each generate unlimited private randomness ; the relay and the destination can publicly provide strictly causal channel state information.. The authors prove that the optimal value of the outer bound LP is no larger than that of the scheme LP, which implies that the solution of the achievable scheme LP is the capacity.. Because the derivation of the inner and outer bound are both lengthy, the authors describe in this paper the achievability scheme, outline the outer bound, and provide the full derivations online [ 1 ].

Accepted Answer

The encrypted message packets that travel on the S−U−D path can potentially be encrypted with three types of key: key that only S−U share (say KSU ); key that only U−D share (say KUD), and key that S and D share (say KSD).

Accepted Answer

These packets are not independent, they are created by expanding the c packets through multiplication with the generator matrix of an MDS code of dimension c× (c1 + c2), but they have the property that all received packets will forman independent set (I5).

Accepted Answer

To securely send the message in the second phase, the authors first “expand” the secret key by using coding, to create a larger number (to be determined) of new (no longer independent) keys.

Accepted Answer

the k1 packets sent through the S−D channel also contribute to the encryption (from I6), resulting in an overall key rate of k2δ2E(1− δ2) + k1(1− δ1).

Accepted Answer

there are r3 + c3(1 − δ3) packets that D receives from U and S can also generate (I3, I4, I5), which adds to a rate of (k1 + c1)δ1E(1− δ1) + r3 + c3(1− δ3).

Accepted Answer

The encrypted packets W ′2 areW ′2 = W2 ⊕ [ K (1) 2 K (2) 2 ] [G(1)2 G(2) 2 ] ︸︷︷︸ G2(18)where G2 is a (k1(1 − δ1) + k2δ2E(1 − δ2)) × m2(1 − δ2) generator of an MDS code.

Accepted Answer

U − D channel: Using the k3 private random packets, the c3 common randomness packets (I5), as well as the r3 packets sent using ARQ (I4) results in a secret key rate (k3 + c3)δ3E(1 − δ3) + r3 δ3E(1−δ3)1−δ3δ3E .

Accepted Answer

Inequality (11) limits the length of the message sending phase on the U − D channel, the constraint follows from the fact that U does not have access to W .

Accepted Answer

The authors use the following two ideas:(I1) Time-sharing between two phases: in a first phase – for a time fraction k – the authors create a secret key between S and D; in the second phase – for a time fraction m – the authors use the created key to encrypt and send the message.

Accepted Answer

The authors have three variables: R, the secret message rate that the authors maximize, k, the fraction of time that the authors use to create a secret key from private randomness, and m the fraction of time the authors use to send the message.

Accepted Answer

All three channels are erasure channels with erasure probabilities δk and δkE , denoting the erasure probabilities toward the network node (U or D) and toward Eve (in case she is present on the given channel).

Accepted Answer

Their scheme combines key generation methods that exploit the common randomness (through (I4) and (I5)) and the key generation that uses private randomness (as seen in the case of a point-to-point channel).

Accepted Answer

The authors here describe their LP formulation for maximizing the secret message rate: based on their previous work the authors start from the single channel network, and gradually build up to the triangle network.

Accepted Answer

To avoid wasting the common randomness the authors introduce two techniques:(I4) The authors send part of the common random packets using ARQ (ensuring that each packet the source sends is received).

Triangle Network Secrecy

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Most frequently asked questions

1. What have the authors contributed in "Triangle network secrecy" ?

2. What is the way to decrypt a message?

3. What is the property of the c packets?

4. How do the authors secure a message in the second phase?

5. What is the key rate of the k1 packets sent through the SD channel?

6. What is the rate of k2 packets that D receives from U and S?

7. what is the key rate of a k2 packet?

8. what is the secret key rate of k3 packets?

9. What is the constraint on the U D channel?

10. What is the simplest way to create a secret key?

11. What is the LP formula for a secret message?

12. What are the erasure probabilities of the channels?

13. What is the scheme for generating keys?

14. What is the secret message capacity of the triangle network?

15. How do the authors avoid wasting the common randomness?

Figures

Citations

国際会議参加報告:2014 IEEE International Symposium on Information Theory

Secret message capacity of a line network

LP formulations for secrecy over erasure networks with feedback

LP formulations for secrecy over erasure networks with feedback

Wireless Network Security: Building on Erasures

References

The wire-tap channel

Broadcast channels with confidential messages

Secret key agreement by public discussion from common information

On the Secrecy Capacity of Fading Channels

Secure Communication Over Fading Channels

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