Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2112.00394

Wiretap Secret Key Agreement Via Secure Omniscience

Praneeth Kumar Vippathalla, Chung Chan, Navin Kashyap, Qiaoqiao Zhou

Published Dec 1, 2021• 1 citation
arXivHTMLPDF

Abstract

In this paper, we explore the connection between secret key agreement and secure omniscience within the setting of the multiterminal source model with a wiretapper who has side information. While the secret key agreement problem considers the generation of a maximum-rate secret key through public discussion, the secure omniscience problem is concerned with communication protocols for omniscience that minimize the rate of information leakage to the wiretapper. The starting point of our work is a lower bound on the minimum leakage rate for omniscience, $R_{\mathop{\mathrm{L}}}$, in terms of the wiretap secret key capacity, $C_{\mathop{\mathrm{W}}}$. Our interest is in identifying broad classes of sources for which this lower bound is met with equality, in which case we say that there is a duality between secure omniscience and secret key agreement. We show that this duality holds in the case of certain finite linear source (FLS) models, such as two-terminal FLS models and pairwise independent network models on trees with a linear wiretapper. Duality also holds for any FLS model in which $C_{\mathop{\mathrm{W}}}$ is achieved by a perfect linear secret key agreement scheme. We conjecture that the duality in fact holds unconditionally for any FLS model. On the negative side, we give an example of a (non-FLS) source model for which duality does not hold if we limit ourselves to communication-for-omniscience protocols with at most two (interactive) communications. We also address the secure function computation problem and explore the connection between the minimum leakage rate for computing a function and the wiretap secret key capacity.

DOI
10.48550/arxiv.2112.00394

Related papers

Secret Key Agreement via Secure Omniscience

Praneeth Kumar Vippathalla, Chung Chan, Navin Kashyap +1 more

In this paper, we explore the connection between secret key agreement and secure omniscience within the setting of the multiterminal source model with an eavesdropper having side information. While the secret key agreement problem considers the generation of a maximum-rate secret key through public discussion, the secure omniscience problem is concerned with communication protocols for omniscience that minimize the rate of information leakage to the eavesdropper. The starting point of our work is a lower bound on the minimum leakage rate for omniscience,$R_{ \text {L}}$, in terms of the wiretap secret key capacity,$C_{ \text {W}}$. Our interest is in identifying broad classes of sources for which this lower bound is met with equality, in which case we say that there is a duality between secure omniscience and secret key agreement. We show that this duality holds in the case of certain finite linear source (FLS) models, such as two-terminal FLS models and pairwise independent network models on trees with a linear eavesdropper. Duality also holds for any FLS model in which$C_{ \text {W}}$is achieved by a perfect linear secret key agreement scheme. We conjecture that the duality in fact holds unconditionally for any FLS model. On the negative side, we give an example of a (non-FLS) source model for which duality does not hold if we limit ourselves to communication-for-omniscience protocols with at most two (interactive) communications. We also address the secure function computation problem and explore the connection between the minimum leakage rate for computing a function and the wiretap secret key capacity.

IEEE Transactions on Information Theory•Oct 24, 2023•0 citations

Secret Key Agreement and Secure Omniscience of Tree-PIN Source with Linear Wiretapper

Praneeth Kumar Vippathalla, Chung Chan, Navin Kashyap +1 more

While the wiretap secret key capacity remains unknown for general source models even in the two-user case, we obtained a single-letter characterization for a large class of multi-user source models with a linear wiretapper who can observe any linear combinations of the source. We introduced the idea of irreducible sources to show existence of an optimal communication scheme that achieves perfect omniscience with minimum leakage of information to the wiretapper. This implies a duality between the problems of wiretap secret key agreement and secure omniscience, and such duality potentially holds for more general sources.

arXiv:2102.01771•Feb 2, 2021•2 citations

Secure Information Exchange for Omniscience

Chung Chan, Navin Kashyap, Praneeth Kumar Vippathalla +1 more

We consider the problem of exchanging sensitive information in public and provide a general formulation that can unify and extend various existing scenarios of information exchange, such as the problems of private information extraction and information bottleneck. The formulation also gives rise to a new scenario called secure omniscience (SO), where users want to exchange all their private information with minimum leakage to a wiretapper with side information. Single-letter lower and upper bounds are obtained for the minimum leakage, and the bounds are shown to be tight under the finite linear source model with two users. The bounds are derived in terms of the solutions of the closely related problems of communication for omniscience (CO) and secret key agreement (SKA). However, we find examples where the bounds are not tight, and so the connections to CO and SKA are not precise. In particular, it is possible that any optimal CO scheme that minimizes communication does not minimize leakage, and any optimal SO scheme that minimizes leakage does not attain the capacity for SKA. Nevertheless, we identify a useful notion of information alignment that can modify an optimal CO scheme to reduce leakage for SO.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2020•5 citations

Secret Key Agreement and Secure Omniscience of Tree-PIN Source with Linear Wiretapper

Praneeth Kumar Vippathalla, Chung Chan, Navin Kashyap +1 more

In this paper, we obtain a single-letter characterization of the wiretap secret key capacity for a large class of multiterminal source models (namely, tree-PIN models) with a linear wiretapper that can observe arbitrary linear combinations of the source. For this class of sources, we also show a duality between the problems of wiretap secret key agreement and secure omniscience, which suggests that such duality potentially holds for more general sources.

IEEE International Symposium on Information Theory (ISIT)•Jul 12, 2021•5 citations

On the Optimality of Secret Key Agreement via Omniscience

Chung Chan, Manuj Mukherjee, Navin Kashyap +1 more

For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources, including the hypergraphical sources. We also extend our results to more general class of multiterminal sources with helpers and silent users.

arXiv:1702.07429•IEEE Transactions on Information Theory•Feb 5, 2018•22 citations

Secret Key Generation in the Multiterminal Source Model : Communication and Other Aspects

Manuj Mukherjee

This dissertation is primarily concerned with the communication required to achieve secret key (SK) capacity in a multiterminal source model. The multiterminal source model introduced by Csiszar and Narayan consists of a group of remotely located terminals with access to correlated sources and a noiseless public channel. The terminals wish to secure their communication by agreeing upon a group secret key. The key agreement protocol involves communicating over the public channel, and agreeing upon an SK secured from eavesdroppers listening to the public communication. The SK capacity, i.e., the maximum rate of an SK that can be agreed upon by the terminals, has been characterized by Csiszar and Narayan. Their capacity-achieving key generation protocol involved terminals communicating to attain omniscience, i.e., every terminal gets to recover the sources of the other terminals. While this is a very general protocol, it often requires larger rates of public communication than is necessary to achieve SK capacity. The primary focus of this dissertation is to characterize the communication complexity, i.e., the minimum rate of public discussion needed to achieve SK capacity. A lower bound to communication complexity is derived for a general multiterminal source, although it turns out to be loose in general. While the minimum rate of communication for omniscience is always an upper bound to the communication complexity, we derive tighter upper bounds to communication complexity for a special class of multiterminal sources, namely, the hypergraphical sources. This upper bound yield a complete characterization of hypergraphical sources where communication for omniscience is a rate-optimal protocol for SK generation, i.e., the communication complexity equals the minimum rate of communication for omniscience. Another aspect of the public communication touched upon by this dissertation is the necessity of omnivocality, i.e., all terminals communicating, to achieve the SK capacity. It is well known that in two-terminal sources, only one terminal communicating success to generate a maximum rate secret key. However, we are able to show that for three or more terminals, omnivocality is indeed required to achieve SK capacity if a certain condition is met. For the specific case of three terminals, we show that this condition is also necessary to ensure omnivocality is essential in generating a SK of maximal rate. However, this condition is no longer necessary when there are four or more terminals. A certain notion of common information, namely, the Wyner common information, plays a central role in the communication complexity problem. This dissertation thus includes a study of multiparty versions of the two widely used notions of common information, namely, Wyner common information and Gacs-Korner (GK) common information. While evaluating these quantities is difficult in general, we are able to derive explicit expressions for both types of common information in the case of hypergraphical sources. We also study fault-tolerant SK…

•Jan 1, 2017•0 citations
In this paper, we explore the connection between secret key agreement and secure omniscience within the setting of the multiterminal source model with a wiretapper who has side information. While the secret key agreement problem considers the generation of a maximum-rate secret key through public discussion, the secure omniscience problem is concerned with communication protocols for omniscience that minimize the rate of information leakage to the wiretapper. The starting point of our work is a lower bound on the minimum leakage rate for omniscience, RLR_{\mathop{\mathrm{L}}}RL​, in terms of the wiretap secret key capacity, CWC_{\mathop{\mathrm{W}}}CW​. Our interest is in identifying broad classes of sources for which this lower bound is met with equality, in which case we say that there is a duality between secure omniscience and secret key agreement. We show that this duality holds in the case of certain finite linear source (FLS) models, such as two-terminal FLS models and pairwise independent network models on trees with a linear wiretapper. Duality also holds for any FLS model in which CWC_{\mathop{\mathrm{W}}}CW​ is achieved by a perfect linear secret key agreement scheme. We conjecture that the duality in fact holds unconditionally for any FLS model. On the negative side, we give an example of a (non-FLS) source model for which duality does not hold if we limit ourselves to communication-for-omniscience protocols with at most two (interactive) communications. We also address the secure function computation problem and explore the connection between the minimum leakage rate for computing a function and the wiretap secret key capacity.
In this paper, we explore the connection between secret key agreement and secure omniscience within the setting of the multiterminal source model with an eavesdropper having side information. While the secret key agreement problem considers the generation of a maximum-rate secret key through public discussion, the secure omniscience problem is concerned with communication protocols for omniscience that minimize the rate of information leakage to the eavesdropper. The starting point of our work is a lower bound on the minimum leakage rate for omniscience,RLR_{ \text {L}}RL​, in terms of the wiretap secret key capacity,CWC_{ \text {W}}CW​. Our interest is in identifying broad classes of sources for which this lower bound is met with equality, in which case we say that there is a duality between secure omniscience and secret key agreement. We show that this duality holds in the case of certain finite linear source (FLS) models, such as two-terminal FLS models and pairwise independent network models on trees with a linear eavesdropper. Duality also holds for any FLS model in whichCWC_{ \text {W}}CW​is achieved by a perfect linear secret key agreement scheme. We conjecture that the duality in fact holds unconditionally for any FLS model. On the negative side, we give an example of a (non-FLS) source model for which duality does not hold if we limit ourselves to communication-for-omniscience protocols with at most two (interactive) communications. We also address the secure function computation problem and explore the connection between the minimum leakage rate for computing a function and the wiretap secret key capacity.
While the wiretap secret key capacity remains unknown for general source models even in the two-user case, we obtained a single-letter characterization for a large class of multi-user source models with a linear wiretapper who can observe any linear combinations of the source. We introduced the idea of irreducible sources to show existence of an optimal communication scheme that achieves perfect omniscience with minimum leakage of information to the wiretapper. This implies a duality between the problems of wiretap secret key agreement and secure omniscience, and such duality potentially holds for more general sources.
We consider the problem of exchanging sensitive information in public and provide a general formulation that can unify and extend various existing scenarios of information exchange, such as the problems of private information extraction and information bottleneck. The formulation also gives rise to a new scenario called secure omniscience (SO), where users want to exchange all their private information with minimum leakage to a wiretapper with side information. Single-letter lower and upper bounds are obtained for the minimum leakage, and the bounds are shown to be tight under the finite linear source model with two users. The bounds are derived in terms of the solutions of the closely related problems of communication for omniscience (CO) and secret key agreement (SKA). However, we find examples where the bounds are not tight, and so the connections to CO and SKA are not precise. In particular, it is possible that any optimal CO scheme that minimizes communication does not minimize leakage, and any optimal SO scheme that minimizes leakage does not attain the capacity for SKA. Nevertheless, we identify a useful notion of information alignment that can modify an optimal CO scheme to reduce leakage for SO.
For the multiterminal secret key agreement problem under a private source model, it is known that the maximum key rate, i.e., the secrecy capacity, can be achieved through communication for omniscience, but the omniscience strategy can be strictly suboptimal in terms of minimizing the public discussion rate. While a single-letter characterization is not known for the minimum discussion rate needed for achieving the secrecy capacity, we derive single-letter lower bounds that yield some simple conditions for omniscience to be discussion-rate optimal. These conditions turn out to be enough to deduce the optimality of omniscience for a large class of sources, including the hypergraphical sources. We also extend our results to more general class of multiterminal sources with helpers and silent users.
This dissertation is primarily concerned with the communication required to achieve secret key (SK) capacity in a multiterminal source model. The multiterminal source model introduced by Csiszar and Narayan consists of a group of remotely located terminals with access to correlated sources and a noiseless public channel. The terminals wish to secure their communication by agreeing upon a group secret key. The key agreement protocol involves communicating over the public channel, and agreeing upon an SK secured from eavesdroppers listening to the public communication. The SK capacity, i.e., the maximum rate of an SK that can be agreed upon by the terminals, has been characterized by Csiszar and Narayan. Their capacity-achieving key generation protocol involved terminals communicating to attain omniscience, i.e., every terminal gets to recover the sources of the other terminals. While this is a very general protocol, it often requires larger rates of public communication than is necessary to achieve SK capacity. The primary focus of this dissertation is to characterize the communication complexity, i.e., the minimum rate of public discussion needed to achieve SK capacity. A lower bound to communication complexity is derived for a general multiterminal source, although it turns out to be loose in general. While the minimum rate of communication for omniscience is always an upper bound to the communication complexity, we derive tighter upper bounds to communication complexity for a special class of multiterminal sources, namely, the hypergraphical sources. This upper bound yield a complete characterization of hypergraphical sources where communication for omniscience is a rate-optimal protocol for SK generation, i.e., the communication complexity equals the minimum rate of communication for omniscience. Another aspect of the public communication touched upon by this dissertation is the necessity of omnivocality, i.e., all terminals communicating, to achieve the SK capacity. It is well known that in two-terminal sources, only one terminal communicating success to generate a maximum rate secret key. However, we are able to show that for three or more terminals, omnivocality is indeed required to achieve SK capacity if a certain condition is met. For the specific case of three terminals, we show that this condition is also necessary to ensure omnivocality is essential in generating a SK of maximal rate. However, this condition is no longer necessary when there are four or more terminals. A certain notion of common information, namely, the Wyner common information, plays a central role in the communication complexity problem. This dissertation thus includes a study of multiparty versions of the two widely used notions of common information, namely, Wyner common information and Gacs-Korner (GK) common information. While evaluating these quantities is difficult in general, we are able to derive explicit expressions for both types of common information in the case of hypergraphical sources. We also study fault-tolerant SK…