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

Generalized Common Information: Common Information Extraction and Private Sources Synthesis.

Lei Yu, Houqiang Li, Chang Wen Chen

Published Oct 28, 2016• 1 citation
OpenAlex

Abstract

In literature, two different common informations were defined by G\'acs and K\orner and by Wyner, respectively. In this paper, we define a generalized version of common information, information-correlation function, by exploiting conditional maximal correlation as a commonness or privacy measure, which encompasses the notions of G\'acs-K\orner's and Wyner's common informations as special cases. Furthermore, we also study the problems of common information extraction and private sources synthesis, and show that information-correlation function is the optimal rate under a given conditional maximal correlation constraint for the centralized setting versions of these problems. As a side product, some properties on conditional maximal correlation have been derived as well.

Related papers

Generalized Common Informations: Measuring Commonness by the Conditional Maximal Correlation

Lei Yu, Houqiang Li, Chang Wen Chen

In literature, different common informations were defined by Gács and Körner, by Wyner, and by Kumar, Li, and Gamal, respectively. In this paper, we define two generalized versions of common informations, named approximate and exact information-correlation functions, by exploiting the conditional maximal correlation as a commonness or privacy measure. These two generalized common informations encompass the notions of Gács-Körner's, Wyner's, and Kumar-Li-Gamal's common informations as special cases. Furthermore, to give operational characterizations of these two generalized common informations, we also study the problems of private sources synthesis and common information extraction, and show that the information-correlation functions are equal to the minimum rates of commonness needed to ensure that some conditional maximal correlation constraints are satisfied for the centralized setting versions of these problems. As a byproduct, the conditional maximal correlation has been studied as well.

arXiv:1610.09289•Oct 28, 2016•14 citations

Assisted Common Information With an Application to Secure Two-Party Sampling

Vinod M. Prabhakaran, Manoj Prabhakaran

An important subclass of secure multiparty computation is secure sampling: two parties output samples of a pair of jointly distributed random variables such that neither party learns more about the other party's output than what its own output reveals. The parties make use of a setup - correlated random variables with a different distribution - as well as unlimited noiseless communication. An upperbound on the rate of producing samples of a desired distribution from a given setup is presented. The region of tension developed in this paper measures how well the dependence between a pair of random variables can be resolved by a piece of common information. The bounds on rate are a consequence of a monotonicity property; a protocol between two parties can only lower the tension between their views. Connections are drawn between the region of tension and the notion of common information. A generalization of the Gács-Körner common information, called the assisted common information, which takes into account almost common information ignored by Gács-Körner common information is defined. The region of tension is shown to be related to the rate regions of both the assisted common information and the Gray-Wyner systems (and, a fortiori, Wyner's common information).

arXiv:1206.1282•IEEE Transactions on Information Theory•Apr 7, 2014•39 citations

Assisted common information: Further results

Vinod M. Prabhakaran, Manoj Prabhakaran

Abstract—We presented assisted common information as a generalization of Gács-Körner (GK) common information at ISIT 2010. The motivation for our formulation was to improve upperbounds on the efficiency of protocols for secure two-party sampling (which is a form of secure multi-party computation). Our upperbound was based on a monotonicity property of a rate-region (called the assisted residual information region) associated with the assisted common information formulation. In this note we present further results. We explore the connection of assisted common information with the Gray-Wyner system. We show that the assisted residual information region and the Gray-Wyner region are connected by a simple relationship: the assisted residual information region is the increasing hull of the Gray-Wyner region under an affine map. Several known relationships between GK common information and Gray-Wyner system fall out as consequences of this. Quantities which arise in other source coding contexts acquire new interpretations. In previous work we showed that assisted common information can be used to derive upperbounds on the rate at which a pair of parties can securely sample correlated random variables, given correlated random variables from another distribution. Here we present an example where the bound derived using assisted common information is much better than previously known bounds, and in fact is tight. This example considers correlated random variables defined in terms of standard variants of oblivious transfer, and is interesting on its own as it answers a natural question about these cryptographic primitives. I.

•Jan 1, 2011•7 citations

Assisted common information: Further results

Vinod M. Prabhakaran, Manoj M. Prabhakaran

We presented assisted common information as a generalization of Gacs-Korner (GK) common information at last year's ISIT. The motivation for our formulation was to improve upperbounds on the efficiency of protocols for secure two-party sampling (which is a form of secure multi-party computation). Our upperbound was based on a monotonicity property of a rate region (called the assisted residual information region) associated with the assisted common information formulation. In this note we present further results. We explore the connection of assisted common information with the Gray-Wyner system. We show that the assisted residual information region and the Gray-Wyner region are connected by a simple relationship: the assisted residual information region is the increasing hull of the Gray-Wyner region under an affine map. Several known relationships between GK common information and Gray-Wyner system fall out as consequences of this. Quantities which arise in other source coding contexts acquire new interpretations. In previous work we showed that assisted common information can be used to derive upperbounds on the rate at which a pair of parties can securely sample correlated random variables, given correlated random variables from another distribution. Here we present an example where the bound derived using assisted common information is much better than previously known bounds, and in fact is tight. This example considers correlated random variables defined in terms of standard variants of oblivious transfer, and is interesting on its own as it answers a natural question about these cryptographic primitives.

arXiv:1105.6163•IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2011•7 citations

Assisted common information

Vinod M. Prabhakaran, Manoj Prabhakaran

Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each party must learn nothing more about the other party's output than what its own output reveals. To aid in this, they have available a set up - correlated random variables whose distribution is different from the desired distribution - as well as unlimited noiseless communication. In this paper we present an upperbound on how efficiently a given set up can be used to produce samples from a desired distribution. The key tool we develop is a generalization of the concept of common information of two dependent random variables [Gács-Körner, 1973]. Our generalization - a three-dimensional region - remedies some of the limitations of the original definition which captured only a limited form of dependence. It also includes as a special case Wyner's common information [Wyner, 1975]. To derive the cryptographic bounds, we rely on a monotonicity property of this region: the region of the “views” of Alice and Bob engaged in any protocol can only monotonically expand and not shrink. Thus, by comparing the regions for the target random variables and the given random variables, we obtain our upperbound.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2010•9 citations

Exact Common Information and Exact Channel Synthesis for Correlated Gaussian Sources

Lei Yu

In this paper, we resolve two conjectures posed by Yu and Tan in 2020 (in two separate papers published in the IEEE Trans. Inf. Theory). Specifically, we establish that: 1) the exact common information for a pair of $ρ$-correlated Gaussian sources is given by the conjectured expression $\frac{1}{2}\log\frac{1+ρ}{1-ρ}+\fracρ{1+ρ}$; and 2) the admissible region for the shared randomness rate and the communication rate in exact channel synthesis is exactly the conjectured one. These results yield two important consequences. First, for any $ρ>0$, the exact common information of a correlated Gaussian pair strictly exceeds Wyner's common information. Second, for $ρ>0$, the exact channel synthesis of such a pair requires strictly higher rates than the total-variation version. The proof combines an exact optimal-transport representation of the worst-case Gaussian cross-entropy, Fathi's Gaussian transport inequality, and a determinant inequality arising from the covariance structure of the conditional means.

arXiv:2608.26012•Aug 26, 2026•0 citations
In literature, two different common informations were defined by G'acs and K\orner and by Wyner, respectively. In this paper, we define a generalized version of common information, information-correlation function, by exploiting conditional maximal correlation as a commonness or privacy measure, which encompasses the notions of G'acs-K\orner's and Wyner's common informations as special cases. Furthermore, we also study the problems of common information extraction and private sources synthesis, and show that information-correlation function is the optimal rate under a given conditional maximal correlation constraint for the centralized setting versions of these problems. As a side product, some properties on conditional maximal correlation have been derived as well.
In literature, different common informations were defined by Gács and Körner, by Wyner, and by Kumar, Li, and Gamal, respectively. In this paper, we define two generalized versions of common informations, named approximate and exact information-correlation functions, by exploiting the conditional maximal correlation as a commonness or privacy measure. These two generalized common informations encompass the notions of Gács-Körner's, Wyner's, and Kumar-Li-Gamal's common informations as special cases. Furthermore, to give operational characterizations of these two generalized common informations, we also study the problems of private sources synthesis and common information extraction, and show that the information-correlation functions are equal to the minimum rates of commonness needed to ensure that some conditional maximal correlation constraints are satisfied for the centralized setting versions of these problems. As a byproduct, the conditional maximal correlation has been studied as well.
An important subclass of secure multiparty computation is secure sampling: two parties output samples of a pair of jointly distributed random variables such that neither party learns more about the other party's output than what its own output reveals. The parties make use of a setup - correlated random variables with a different distribution - as well as unlimited noiseless communication. An upperbound on the rate of producing samples of a desired distribution from a given setup is presented. The region of tension developed in this paper measures how well the dependence between a pair of random variables can be resolved by a piece of common information. The bounds on rate are a consequence of a monotonicity property; a protocol between two parties can only lower the tension between their views. Connections are drawn between the region of tension and the notion of common information. A generalization of the Gács-Körner common information, called the assisted common information, which takes into account almost common information ignored by Gács-Körner common information is defined. The region of tension is shown to be related to the rate regions of both the assisted common information and the Gray-Wyner systems (and, a fortiori, Wyner's common information).
Abstract—We presented assisted common information as a generalization of Gács-Körner (GK) common information at ISIT 2010. The motivation for our formulation was to improve upperbounds on the efficiency of protocols for secure two-party sampling (which is a form of secure multi-party computation). Our upperbound was based on a monotonicity property of a rate-region (called the assisted residual information region) associated with the assisted common information formulation. In this note we present further results. We explore the connection of assisted common information with the Gray-Wyner system. We show that the assisted residual information region and the Gray-Wyner region are connected by a simple relationship: the assisted residual information region is the increasing hull of the Gray-Wyner region under an affine map. Several known relationships between GK common information and Gray-Wyner system fall out as consequences of this. Quantities which arise in other source coding contexts acquire new interpretations. In previous work we showed that assisted common information can be used to derive upperbounds on the rate at which a pair of parties can securely sample correlated random variables, given correlated random variables from another distribution. Here we present an example where the bound derived using assisted common information is much better than previously known bounds, and in fact is tight. This example considers correlated random variables defined in terms of standard variants of oblivious transfer, and is interesting on its own as it answers a natural question about these cryptographic primitives. I.
We presented assisted common information as a generalization of Gacs-Korner (GK) common information at last year's ISIT. The motivation for our formulation was to improve upperbounds on the efficiency of protocols for secure two-party sampling (which is a form of secure multi-party computation). Our upperbound was based on a monotonicity property of a rate region (called the assisted residual information region) associated with the assisted common information formulation. In this note we present further results. We explore the connection of assisted common information with the Gray-Wyner system. We show that the assisted residual information region and the Gray-Wyner region are connected by a simple relationship: the assisted residual information region is the increasing hull of the Gray-Wyner region under an affine map. Several known relationships between GK common information and Gray-Wyner system fall out as consequences of this. Quantities which arise in other source coding contexts acquire new interpretations. In previous work we showed that assisted common information can be used to derive upperbounds on the rate at which a pair of parties can securely sample correlated random variables, given correlated random variables from another distribution. Here we present an example where the bound derived using assisted common information is much better than previously known bounds, and in fact is tight. This example considers correlated random variables defined in terms of standard variants of oblivious transfer, and is interesting on its own as it answers a natural question about these cryptographic primitives.
Secure multi-party computation is a central problem in modern cryptography. An important sub-class of this are problems of the following form: Alice and Bob desire to produce sample(s) of a pair of jointly distributed random variables. Each party must learn nothing more about the other party's output than what its own output reveals. To aid in this, they have available a set up - correlated random variables whose distribution is different from the desired distribution - as well as unlimited noiseless communication. In this paper we present an upperbound on how efficiently a given set up can be used to produce samples from a desired distribution. The key tool we develop is a generalization of the concept of common information of two dependent random variables [Gács-Körner, 1973]. Our generalization - a three-dimensional region - remedies some of the limitations of the original definition which captured only a limited form of dependence. It also includes as a special case Wyner's common information [Wyner, 1975]. To derive the cryptographic bounds, we rely on a monotonicity property of this region: the region of the “views” of Alice and Bob engaged in any protocol can only monotonically expand and not shrink. Thus, by comparing the regions for the target random variables and the given random variables, we obtain our upperbound.
In this paper, we resolve two conjectures posed by Yu and Tan in 2020 (in two separate papers published in the IEEE Trans. Inf. Theory). Specifically, we establish that: 1) the exact common information for a pair of ρρρ-correlated Gaussian sources is given by the conjectured expression 12log⁡1+ρ1−ρ+ρ1+ρ\frac{1}{2}\log\frac{1+ρ}{1-ρ}+\fracρ{1+ρ}21​log1−ρ1+ρ​+1+ρρ​; and 2) the admissible region for the shared randomness rate and the communication rate in exact channel synthesis is exactly the conjectured one. These results yield two important consequences. First, for any ρ>0ρ>0ρ>0, the exact common information of a correlated Gaussian pair strictly exceeds Wyner's common information. Second, for ρ>0ρ>0ρ>0, the exact channel synthesis of such a pair requires strictly higher rates than the total-variation version. The proof combines an exact optimal-transport representation of the worst-case Gaussian cross-entropy, Fathi's Gaussian transport inequality, and a determinant inequality arising from the covariance structure of the conditional means.