We consider a group of m+1 trusted nodes that aim to create a shared secret key K over a network in the presence of a passive eavesdropper, Eve. We assume a linear non-coherent network coding broadcast channel (over a finite field F_q) from one of the honest nodes (i.e., Alice) to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free public channel which is also overheard by Eve. For this setup, we propose upper and lower bounds for the secret key generation capacity assuming that the field size q is very large. For the case of two trusted terminals (m = 1) our upper and lower bounds match and we have complete characterization for the secrecy capacity in the large field size regime.We consider a group of m+1 trusted nodes that aim to create a shared secret key K over a network in the presence of a passive eavesdropper, Eve. We assume a linear non-coherent network coding broadcast channel (over a finite field F_q) from one of the honest nodes (i.e., Alice) to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free public channel which is also overheard by Eve. For this setup, we propose upper and lower bounds for the secret key generation capacity assuming that the field size q is very large. For the case of two trusted terminals (m = 1) our upper and lower bounds match and we have complete characterization for the secrecy capacity in the large field size regime.

arXiv:1206.3133Jun 14, 20120 citations

Group secret key generation over broadcast erasure channels

Mahdi Jafari Siavoshani, Christina Fragouli, Suhas N. Diggavi +2 more

We consider a group of m trusted nodes that aim to create a shared secret key K over a wireless channel in the presence an eavesdropper Eve. We assume an erasure broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free public channel which is observed by Eve. For this setup we characterize the secret key generation capacity and propose an achievability scheme that is computationally efficient and employs techniques from network coding. Surprisingly, whether we have m = 2 nodes, or an arbitrary number m of nodes, we can establish a shared secret key among them at the same rate, independently of m.1We consider a group of m trusted nodes that aim to create a shared secret key K over a wireless channel in the presence an eavesdropper Eve. We assume an erasure broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free public channel which is observed by Eve. For this setup we characterize the secret key generation capacity and propose an achievability scheme that is computationally efficient and employs techniques from network coding. Surprisingly, whether we have m = 2 nodes, or an arbitrary number m of nodes, we can establish a shared secret key among them at the same rate, independently of m.1

Asilomar Conference on Signals, Systems and Computers (ACSSC)Nov 1, 201027 citations

Group secret key agreement over state-dependent wireless broadcast channels

Mahdi Jafari Siavoshani, Shaunak Mishra, Christina Fragouli +1 more

We consider a group of $m$ trusted and authenticated nodes that aim to create a shared secret key $K$ over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for "linear deterministic" wireless broadcast channels. This model generalizes the packet erasure model studied in literature for wireless broadcast channels. For "state-dependent Gaussian" wireless broadcast channels, we propose an achievability scheme based on a multi-layer wiretap code. Finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem. We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.We consider a group of $m$ trusted and authenticated nodes that aim to create a shared secret key $K$ over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for "linear deterministic" wireless broadcast channels. This model generalizes the packet erasure model studied in literature for wireless broadcast channels. For "state-dependent Gaussian" wireless broadcast channels, we propose an achievability scheme based on a multi-layer wiretap code. Finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem. We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.

arXiv:1604.02380Apr 8, 20161 citation

Group secret key agreement over state-dependent wireless broadcast channels

Mahdi Jafari Siavoshani, Shaunak Mishra, Suhas N. Diggavi +1 more

We consider a group of m trusted nodes that aim to create a shared secret key K, using a state-dependent wireless broadcast channel that exists from one of the honest nodes to the rest of the nodes including a passive eavesdropper Eve. All of the trusted nodes can also discuss over a cost-free and unlimited rate public channel which is also observed by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for linear deterministic wireless broadcast channels as well as in the high-SNR regime for wireless channels with large dynamic range over channel states.We consider a group of m trusted nodes that aim to create a shared secret key K, using a state-dependent wireless broadcast channel that exists from one of the honest nodes to the rest of the nodes including a passive eavesdropper Eve. All of the trusted nodes can also discuss over a cost-free and unlimited rate public channel which is also observed by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for linear deterministic wireless broadcast channels as well as in the high-SNR regime for wireless channels with large dynamic range over channel states.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 201112 citations

Multi-Party Secret Key Agreement Over State-Dependent Wireless Broadcast Channels

Mahdi Jafari Siavoshani, Shaunak Mishra, Christina Fragouli +1 more

We consider a group of m trusted and authenticated nodes that aim to create a shared secret key K over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state-dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for “linear deterministic” wireless broadcast channels. This model generalizes the packet erasure model studied in the literature for wireless broadcast channels. Here, the main idea is to convert a deterministic channel into multiple independent erasure channels by using superposition coding. For “state-dependent Gaussian” wireless broadcast channels, by using insights from the deterministic problem, we propose an achievability scheme based on a multi-layer wiretap code. By using the wiretap code, we can mimic the phenomenon of converting the wireless channel into multiple independent erasure channels. Then, finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem over these channels (layers). We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.We consider a group of m trusted and authenticated nodes that aim to create a shared secret key K over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state-dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for “linear deterministic” wireless broadcast channels. This model generalizes the packet erasure model studied in the literature for wireless broadcast channels. Here, the main idea is to convert a deterministic channel into multiple independent erasure channels by using superposition coding. For “state-dependent Gaussian” wireless broadcast channels, by using insights from the deterministic problem, we propose an achievability scheme based on a multi-layer wiretap code. By using the wiretap code, we can mimic the phenomenon of converting the wireless channel into multiple independent erasure channels. Then, finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem over these channels (layers). We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.

IEEE Transactions on Information Forensics and SecuritySep 22, 20168 citations

Secrecy Generation for Multiaccess Channel Models

Imre Csiszár, Prakash Narayan

Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a setAof terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint fromA. These bounds coincide in special cases, but not in general. We also consider models in which different sets of terminals share multiple keys, one for the terminals in each set with secrecy required from the eavesdropper as well as from the terminals not in this set. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.Shannon theoretic secret key generation by several parties is considered for models in which a secure noisy channel with multiple input and output terminals and a public noiseless channel of unlimited capacity are available for accomplishing this goal. The secret key is generated for a setAof terminals of the noisy channel, with the remaining terminals (if any) cooperating in this task through their public communication. Single-letter lower and upper bounds for secrecy capacities are obtained when secrecy is required from an eavesdropper that observes only the public communication and perhaps also a set of terminals disjoint fromA. These bounds coincide in special cases, but not in general. We also consider models in which different sets of terminals share multiple keys, one for the terminals in each set with secrecy required from the eavesdropper as well as from the terminals not in this set. Partial results include showing links among the associated secrecy capacity region for multiple keys, the transmission capacity region of the multiple access channel defined by the secure noisy channel, and achievable rates for a single secret key for all the terminals.

IEEE Transactions on Information TheoryAug 29, 201220 citations

We consider a group of

m

trusted and authenticated nodes that aim to create a shared secret key

K

over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for "linear deterministic" wireless broadcast channels. This model generalizes the packet erasure model studied in literature for wireless broadcast channels. For "state-dependent Gaussian" wireless broadcast channels, we propose an achievability scheme based on a multi-layer wiretap code. Finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem. We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.