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

A Bound For Multiparty Secret Key Agreement And Implications For A Problem Of Secure Computing

Himanshu Tyagi, Shun Watanabe

Published Dec 5, 2014• 0 citations
OpenAlex

Abstract

Abstract. We consider secret key agreement by multiple parties observ-ing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a single-shot upper bound on the length of the secret keys that can be generated, with-out making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of “how far ” is the joint distribution of the initial observations of the parties and the eaves-dropper from a distribution that renders the observations of the parties conditionally independent across some partition, when conditioned on the eavesdropper’s side information. The closeness of the two distribu-tions is measured in terms of the exponent of the probability of error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypoth-esis testing. When the underlying data consists of an independent and identically distributed sequence, an application of our bound recovers

Related papers

Converses for Secret Key Agreement and Secure Computing

Himanshu Tyagi, Shun Watanabe

We consider information theoretic secret key agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the secret key length, which is derived using a reduction of binary hypothesis testing to multiparty secret key agreement. Building on this basic result, we derive new converses for multiparty secret key agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to secret key agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses.

arXiv:1404.5715•Apr 23, 2014•5 citations

Secret key agreement: General capacity and second-order asymptotics

Masahito Hayashi, Himanshu Tyagi, Shun Watanabe

We revisit the problem of secret key agreement using interactive public communication for two parties. When the underlying observations are independent and identically distributed, we establish the second-order asymptotic term in the maximum length of a secret key. Furthermore, for general observations, we establish the secret key capacity. Underlying our proofs is a new secret key agreement scheme and a recently established upper bound on secret key lengths.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2014•12 citations

New bounds on the information-theoretic key agreement of multiple terminals

Amin Gohari, Venkat Anantharam

We study the problem of information-theoretically secure secret key agreement under the well-known source model and channel model. In both of these models the parties wish to create a shared secret key that is secure from an eavesdropper with unlimited computational resources. In the channel model, the first party can choose a sequence of inputs to a discrete memoryless channel, which has outputs at the other parties and at the eavesdropper. After each channel use, the parties can engage in arbitrarily many rounds of interactive authenticated communication over a public channel. At the end, each party should be able to generate the key. In the source model, the parties wishing to generate a secret key (as well as the eavesdropper) receive a certain number of independent identically distributed copies of jointly distributed random variables after which the parties are allowed interactive authenticated public communication, at the end of which each party should be able to generate the key. We derive new lower and upper bounds on the secret key rate under the source model and the channel model, and introduce a technique for proving that a given expression bounds the secrecy rate from above in the channel model. Our lower bounds strictly improve what is essentially the best known lower bound in both the source model and the channel model. Our upper bound in the channel model strictly improves the current state of art upper bound. We do not know whether our new upper bound in the source model represents an strict improvement but it includes the current best known bound as a special case.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2008•14 citations

One-Shot Variable-Length Secret Key Agreement Approaching Mutual Information

Cheuk Ting Li, Venkat Anantharam

This paper studies an information-theoretic oneshot variable-length secret key agreement problem with public discussion. Let X and Y be jointly distributed random variables, each taking values in some measurable space. Alice and Bob observe X and Y respectively, can communicate interactively through a public noiseless channel, and want to agree on a key length and a key that is approximately uniformly distributed over all bit sequences with the agreed key length. The public discussion is observed by an eavesdropper, Eve. The key should be approximately independent of the public discussion, conditional on the key length. We show that the optimal expected key length is close to the mutual information I(X; Y ) within a logarithmic gap. Moreover, an upper bound and a lower bound on the optimal expected key length can be written down in terms of I(X; Y ) only. This means that the optimal one-shot performance is always within a small gap of the optimal asymptotic performance regardless of the distribution of the pair (X, Y ). This one-shot result may find applications in situations where the components of an i.i.d. pair source (Xn, Y n) are observed sequentially and the key is output bit by bit with small delay, or in situations.

Allerton Conference on Communication, Control, and Computing•Oct 1, 2018•7 citations

One-Shot Variable-Length Secret Key Agreement Approaching Mutual Information

Cheuk Ting Li, Venkat Anantharam

This paper studies an information-theoretic one-shot variable-length secret key agreement problem with public discussion. Let X and Y be jointly distributed random variables, each taking values in some measurable space. Alice and Bob observe X and Y respectively, can communicate interactively through a public noiseless channel, and want to agree on a key length and a key that is approximately uniformly distributed over all bit sequences with the agreed key length. The public discussion is observed by an eavesdropper, Eve. The key should be approximately independent of the public discussion, conditional on the key length. We show that the optimal expected key length is close to the mutual information I(X;Y) within a logarithmic gap. Moreover, an upper bound and a lower bound on the optimal expected key length can be written down in terms of I(X;Y) only. This means that the optimal one-shot performance is always within a small gap of the optimal asymptotic performance regardless of the distribution of the pair (X,Y). This one-shot result may find applications in situations where the components of an i.i.d. pair source (Xn,Yn) are observed sequentially and the key is output bit by bit, or in situations where the random source is not an i.i.d. or ergodic process.

arXiv:1809.01793•IEEE Transactions on Information Theory•Jun 9, 2021•7 citations

Converses For Secret Key Agreement and Secure Computing

Himanshu Tyagi, Shun Watanabe

We consider information theoretic secret key (SK) agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the SK length, which is derived using a reduction of binary hypothesis testing to multiparty SK agreement. Building on this basic result, we derive new converses for multiparty SK agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to SK agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses.

IEEE Transactions on Information Theory•Jul 17, 2015•70 citations
Abstract. We consider secret key agreement by multiple parties observ-ing correlated data and communicating interactively over an insecure communication channel. Our main contribution is a single-shot upper bound on the length of the secret keys that can be generated, with-out making any assumptions on the distribution of the underlying data. Heuristically, we bound the secret key length in terms of “how far ” is the joint distribution of the initial observations of the parties and the eaves-dropper from a distribution that renders the observations of the parties conditionally independent across some partition, when conditioned on the eavesdropper’s side information. The closeness of the two distribu-tions is measured in terms of the exponent of the probability of error of type II for a binary hypothesis testing problem, thus bringing out a structural connection between secret key agreement and binary hypoth-esis testing. When the underlying data consists of an independent and identically distributed sequence, an application of our bound recovers
We consider information theoretic secret key agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the secret key length, which is derived using a reduction of binary hypothesis testing to multiparty secret key agreement. Building on this basic result, we derive new converses for multiparty secret key agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to secret key agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses.
We study the problem of information-theoretically secure secret key agreement under the well-known source model and channel model. In both of these models the parties wish to create a shared secret key that is secure from an eavesdropper with unlimited computational resources. In the channel model, the first party can choose a sequence of inputs to a discrete memoryless channel, which has outputs at the other parties and at the eavesdropper. After each channel use, the parties can engage in arbitrarily many rounds of interactive authenticated communication over a public channel. At the end, each party should be able to generate the key. In the source model, the parties wishing to generate a secret key (as well as the eavesdropper) receive a certain number of independent identically distributed copies of jointly distributed random variables after which the parties are allowed interactive authenticated public communication, at the end of which each party should be able to generate the key. We derive new lower and upper bounds on the secret key rate under the source model and the channel model, and introduce a technique for proving that a given expression bounds the secrecy rate from above in the channel model. Our lower bounds strictly improve what is essentially the best known lower bound in both the source model and the channel model. Our upper bound in the channel model strictly improves the current state of art upper bound. We do not know whether our new upper bound in the source model represents an strict improvement but it includes the current best known bound as a special case.
This paper studies an information-theoretic oneshot variable-length secret key agreement problem with public discussion. Let X and Y be jointly distributed random variables, each taking values in some measurable space. Alice and Bob observe X and Y respectively, can communicate interactively through a public noiseless channel, and want to agree on a key length and a key that is approximately uniformly distributed over all bit sequences with the agreed key length. The public discussion is observed by an eavesdropper, Eve. The key should be approximately independent of the public discussion, conditional on the key length. We show that the optimal expected key length is close to the mutual information I(X; Y ) within a logarithmic gap. Moreover, an upper bound and a lower bound on the optimal expected key length can be written down in terms of I(X; Y ) only. This means that the optimal one-shot performance is always within a small gap of the optimal asymptotic performance regardless of the distribution of the pair (X, Y ). This one-shot result may find applications in situations where the components of an i.i.d. pair source (Xn, Y n) are observed sequentially and the key is output bit by bit with small delay, or in situations.
This paper studies an information-theoretic one-shot variable-length secret key agreement problem with public discussion. Let X and Y be jointly distributed random variables, each taking values in some measurable space. Alice and Bob observe X and Y respectively, can communicate interactively through a public noiseless channel, and want to agree on a key length and a key that is approximately uniformly distributed over all bit sequences with the agreed key length. The public discussion is observed by an eavesdropper, Eve. The key should be approximately independent of the public discussion, conditional on the key length. We show that the optimal expected key length is close to the mutual information I(X;Y) within a logarithmic gap. Moreover, an upper bound and a lower bound on the optimal expected key length can be written down in terms of I(X;Y) only. This means that the optimal one-shot performance is always within a small gap of the optimal asymptotic performance regardless of the distribution of the pair (X,Y). This one-shot result may find applications in situations where the components of an i.i.d. pair source (Xn,Yn) are observed sequentially and the key is output bit by bit, or in situations where the random source is not an i.i.d. or ergodic process.
We consider information theoretic secret key (SK) agreement and secure function computation by multiple parties observing correlated data, with access to an interactive public communication channel. Our main result is an upper bound on the SK length, which is derived using a reduction of binary hypothesis testing to multiparty SK agreement. Building on this basic result, we derive new converses for multiparty SK agreement. Furthermore, we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to SK agreement. Finally, we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data, using an interactive public communication that by itself does not give away the value of the function. In many cases, we strengthen and improve upon previously known converse bounds. Our results are single-shot and use only the given joint distribution of the correlated observations. For the case when the correlated observations consist of independent and identically distributed (in time) sequences, we derive strong versions of previously known converses.