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:2406.13608 · IEEE International Symposium on Information Theory (ISIT)

Wiretapped Commitment Over Binary Channels

Anuj Kumar Yadav, Manideep Mamindlapally, Amitalok J. Budkuley

Published Jul 7, 2024• 1 citation
arXivHTMLPDF

Abstract

We propose the problem of wiretapped commitment, where two parties, say committer Alice and receiver Bob, engage in a commitment protocol using a noisy channel as a resource, in the presence of an eavesdropper, say Eve. Noisy versions of Alice's transmission over the wiretap channel are received by both Bob and Eve. We seek to determine the maximum commitment throughput in the presence of eavesdropper, i.e., wiretapped commitment capacity, where in addition to the standard security requirements for two-party commitment, one seeks to ensure that Eve doesn't learn about the commit string. A key interest in this work is to explore the effect of collusion (or lack of it) between the eavesdropper Eve and either Alice or Bob. Toward the same, we present results on the wiretapped commitment capacity under the so-called Y-private regime (when Alice or Bob cannot collude with Eve) and the 2-private regime (when Alice or Bob may collude with Eve).

DOI
10.1109/isit57864.2024.10619661

Related papers

The oblivious transfer capacity of the wiretapped binary erasure channel

Manoj Mishra, Bikash Kumar Dey, Vinod M. Prabhakaran +1 more

We consider oblivious transfer between Alice and Bob in the presence of an eavesdropper Eve when there is a broadcast channel from Alice to Bob and Eve. In addition to the secrecy constraints of Alice and Bob, Eve should not learn the private data of Alice and Bob. When the broadcast channel consists of two independent binary erasure channels, we derive the oblivious transfer capacity for both 2-privacy (where the eavesdropper may collude with either party) and 1-privacy (where there are no collusions).

arXiv:1404.6614•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2014•15 citations

Capacity Results for the Wiretapped Oblivious Transfer

Tianyou Pei, Wei Kang, Nan Liu

In this paper, we study the problem of the 1-of-2 string oblivious transfer (OT) between Alice and Bob in the presence of a passive eavesdropper Eve. The eavesdropper Eve is not allowed to get any information about the private data of Alice or Bob. When Alice and Bob are honest-but-curious users, we propose a protocol that satisfies 1-private (neither Alice nor Bob colludes with Eve) OT requirements for the binary erasure symmetric broadcast channel, in which the channel provides dependent erasure patterns to Bob and Eve. We find that when the erasure probabilities of the channel are within a certain range, the derived lower and upper bounds on the wiretapped OT capacity meet. Our results generalize and improve upon the results on 1-private wiretapped OT capacity by Mishra et al. Finally, we propose a protocol for a larger class of wiretapped channels and derive a lower bound on the wiretapped OT capacity.

arXiv:2207.06363•IEEE Transactions on Information Theory•Oct 28, 2024•2 citations

Wiretapped Oblivious Transfer

Manoj Mishra, Bikash Kumar Dey, Vinod M. Prabhakaran +1 more

In this paper, we study the problem of obtaining 1-of-2 string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users' inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice-Bob and Alice-Eve), we derive the 1-of-2 string OT capacity for both 2-privacy (when Eve can collude with either Alice or Bob) and 1-privacy (when no such collusion is allowed). We generalize these capacity results to 1-of-N string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice-Bob and Alice-Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice-Bob and Bob-Eve) and 1-of-2 string OT is desired between Alice and Bob with 1-privacy. For this setup, we derive an upper and lower bound on the 1-of-2 string OT capacity which match in one of two possible parameter regimes.

arXiv:1604.05668•IEEE Transactions on Information Theory•Jan 17, 2017•7 citations

Commitment over Compound Binary Symmetric Channels

Anuj Kumar Yadav, Manideep Mamindlapally, Amitalok J. Budkuley +1 more

In the commitment problem, two mutually distrustful parties Alice and Bob interact in a two-phase protocol, viz., commit and reveal phase, to achieve commitment over a bit string that Alice possesses. The protocol successfully achieves commitment if, firstly, Alice can commit to sharing a string with Bob, with the guarantee that this string remains hidden from Bob until she chooses to reveal it to him. Secondly, when Alice does reveal a string, Bob is able to detect precisely whether the revealed string is different from the one Alice committed to sharing. Information-theoretically secure commitment is impossible if Alice and Bob communicate only noiselessly; however, communication using a noisy channel can be a resource to realize commitment. Even though a noisy channel may be available, it is possible that the corresponding channel law is imprecisely known or poorly characterized. We define and study a compound-binary symmetric channel (compound-BSC) which models such a scenario. A compound-BSC is a BSC whose transition probability is fixed but unknown to either party; the set of potential values which this transition probability can take, though, is known to both parties a priori. In this work, we completely characterize the maximum commitment throughput or commitment capacity of a compound-BSC. We provide an optimal, computationally-efficient scheme for our achievability, and we derive a converse for general alphabet compound DMCs, which is then specialized for compound-BSCs.

National Conference on Communications•Jul 27, 2021•8 citations

Commitment Capacity under Cost Constraints

Manideep Mamindlapally, Anuj Kumar Yadav, Manoj Mishra +1 more

We study the problem of commitment over channels under cost constraints. Commitment is a widely studied cryptographic primitive, where two mutually distrustful parties, say Alice and Bob, interact over two phases of a protocol, viz., commit phase followed by reveal phase, to achieve commitment on a bit string available to Alice. Commitment (over the string) is said to occur if (i) Alice commits to the string which remains securely hidden from Bob at the end of the commit phase involving Alice's transmission to Bob, and (ii) Alice reveals a string to Bob and Bob is able to successfully detect whether the string is the committed one or not. When Alice and Bob are computationally unbounded, i.e., under the information-theoretic setting, it is well known that even a single bit commitment is impossible when the channel available to Alice and Bob is noiseless. Noisy channels, however, offer the potential of non-zero commitment rate, and thus, are a valuable resource. We study information-theoretically secure commitment over noisy discrete memoryless channels (DMCs). The largest commitment throughput over noisy channels is called the commitment capacity or simply capacity. In this work, we completely characterize via a single-letter expression, the commitment capacity of DMCs under general cost constraints; this generalizes the previously known result in the absence of such cost constraints. We show that cost constrained commitment capacity of any given DMC can significantly differ from its unconstrained value. We also present a dual capacity characterization in terms of output distributions. Interestingly, we show that every input distribution achieving the capacity results in the same output distribution; the latter is the unique optimizer of our dual capacity expression.

IEEE International Symposium on Information Theory (ISIT)•Jul 12, 2021•8 citations

On the oblivious transfer capacity of the degraded wiretapped binary erasure channel

Manoj Mishra, Bikash Kumar Dey, Vinod M. Prabhakaran +1 more

We study oblivious transfer (OT) between Alice and Bob in the presence of an eavesdropper Eve over a degraded wiretapped binary erasure channel from Alice to Bob and Eve. In addition to the privacy goals of oblivious transfer between Alice and Bob, we require privacy of Alice and Bob's private data from Eve. In previous work we derived the OT capacity (in the honest-but-curious model) of the wiretapped binary independent erasure channel where the erasure processes of Bob and Eve are independent. Here we derive a lower bound on the OT capacity in the same secrecy model when the wiretapped binary erasure channel is degraded in favour of Bob.

arXiv:1504.04499•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•1 citation
We propose the problem of wiretapped commitment, where two parties, say committer Alice and receiver Bob, engage in a commitment protocol using a noisy channel as a resource, in the presence of an eavesdropper, say Eve. Noisy versions of Alice's transmission over the wiretap channel are received by both Bob and Eve. We seek to determine the maximum commitment throughput in the presence of eavesdropper, i.e., wiretapped commitment capacity, where in addition to the standard security requirements for two-party commitment, one seeks to ensure that Eve doesn't learn about the commit string. A key interest in this work is to explore the effect of collusion (or lack of it) between the eavesdropper Eve and either Alice or Bob. Toward the same, we present results on the wiretapped commitment capacity under the so-called Y-private regime (when Alice or Bob cannot collude with Eve) and the 2-private regime (when Alice or Bob may collude with Eve).
We consider oblivious transfer between Alice and Bob in the presence of an eavesdropper Eve when there is a broadcast channel from Alice to Bob and Eve. In addition to the secrecy constraints of Alice and Bob, Eve should not learn the private data of Alice and Bob. When the broadcast channel consists of two independent binary erasure channels, we derive the oblivious transfer capacity for both 2-privacy (where the eavesdropper may collude with either party) and 1-privacy (where there are no collusions).
In this paper, we study the problem of the 1-of-2 string oblivious transfer (OT) between Alice and Bob in the presence of a passive eavesdropper Eve. The eavesdropper Eve is not allowed to get any information about the private data of Alice or Bob. When Alice and Bob are honest-but-curious users, we propose a protocol that satisfies 1-private (neither Alice nor Bob colludes with Eve) OT requirements for the binary erasure symmetric broadcast channel, in which the channel provides dependent erasure patterns to Bob and Eve. We find that when the erasure probabilities of the channel are within a certain range, the derived lower and upper bounds on the wiretapped OT capacity meet. Our results generalize and improve upon the results on 1-private wiretapped OT capacity by Mishra et al. Finally, we propose a protocol for a larger class of wiretapped channels and derive a lower bound on the wiretapped OT capacity.
In this paper, we study the problem of obtaining 1-of-2 string oblivious transfer (OT) between users Alice and Bob, in the presence of a passive eavesdropper Eve. The resource enabling OT in our setup is a noisy broadcast channel from Alice to Bob and Eve. Apart from the OT requirements between the users, Eve is not allowed to learn anything about the users' inputs. When Alice and Bob are honest-but-curious and the noisy broadcast channel is made up of two independent binary erasure channels (connecting Alice-Bob and Alice-Eve), we derive the 1-of-2 string OT capacity for both 2-privacy (when Eve can collude with either Alice or Bob) and 1-privacy (when no such collusion is allowed). We generalize these capacity results to 1-of-N string OT and study other variants of this problem. When Alice and/or Bob are malicious, we present a different scheme based on interactive hashing. This scheme is shown to be optimal for certain parameter regimes. We present a new formulation of multiple, simultaneous OTs between Alice-Bob and Alice-Cathy. For this new setup, we present schemes and outer bounds that match in all but one regime of parameters. Finally, we consider the setup where the broadcast channel is made up of a cascade of two independent binary erasure channels (connecting Alice-Bob and Bob-Eve) and 1-of-2 string OT is desired between Alice and Bob with 1-privacy. For this setup, we derive an upper and lower bound on the 1-of-2 string OT capacity which match in one of two possible parameter regimes.
In the commitment problem, two mutually distrustful parties Alice and Bob interact in a two-phase protocol, viz., commit and reveal phase, to achieve commitment over a bit string that Alice possesses. The protocol successfully achieves commitment if, firstly, Alice can commit to sharing a string with Bob, with the guarantee that this string remains hidden from Bob until she chooses to reveal it to him. Secondly, when Alice does reveal a string, Bob is able to detect precisely whether the revealed string is different from the one Alice committed to sharing. Information-theoretically secure commitment is impossible if Alice and Bob communicate only noiselessly; however, communication using a noisy channel can be a resource to realize commitment. Even though a noisy channel may be available, it is possible that the corresponding channel law is imprecisely known or poorly characterized. We define and study a compound-binary symmetric channel (compound-BSC) which models such a scenario. A compound-BSC is a BSC whose transition probability is fixed but unknown to either party; the set of potential values which this transition probability can take, though, is known to both parties a priori. In this work, we completely characterize the maximum commitment throughput or commitment capacity of a compound-BSC. We provide an optimal, computationally-efficient scheme for our achievability, and we derive a converse for general alphabet compound DMCs, which is then specialized for compound-BSCs.
We study the problem of commitment over channels under cost constraints. Commitment is a widely studied cryptographic primitive, where two mutually distrustful parties, say Alice and Bob, interact over two phases of a protocol, viz., commit phase followed by reveal phase, to achieve commitment on a bit string available to Alice. Commitment (over the string) is said to occur if (i) Alice commits to the string which remains securely hidden from Bob at the end of the commit phase involving Alice's transmission to Bob, and (ii) Alice reveals a string to Bob and Bob is able to successfully detect whether the string is the committed one or not. When Alice and Bob are computationally unbounded, i.e., under the information-theoretic setting, it is well known that even a single bit commitment is impossible when the channel available to Alice and Bob is noiseless. Noisy channels, however, offer the potential of non-zero commitment rate, and thus, are a valuable resource. We study information-theoretically secure commitment over noisy discrete memoryless channels (DMCs). The largest commitment throughput over noisy channels is called the commitment capacity or simply capacity. In this work, we completely characterize via a single-letter expression, the commitment capacity of DMCs under general cost constraints; this generalizes the previously known result in the absence of such cost constraints. We show that cost constrained commitment capacity of any given DMC can significantly differ from its unconstrained value. We also present a dual capacity characterization in terms of output distributions. Interestingly, we show that every input distribution achieving the capacity results in the same output distribution; the latter is the unique optimizer of our dual capacity expression.
We study oblivious transfer (OT) between Alice and Bob in the presence of an eavesdropper Eve over a degraded wiretapped binary erasure channel from Alice to Bob and Eve. In addition to the privacy goals of oblivious transfer between Alice and Bob, we require privacy of Alice and Bob's private data from Eve. In previous work we derived the OT capacity (in the honest-but-curious model) of the wiretapped binary independent erasure channel where the erasure processes of Bob and Eve are independent. Here we derive a lower bound on the OT capacity in the same secrecy model when the wiretapped binary erasure channel is degraded in favour of Bob.