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Scalable Compilers for Group Key Establishment : Two/Three Party to Group.

S. Sree Vivek, S. Sharmila Deva Selvi, Deepanshu Shukla, Chandrasekharan Pandu Rangan

Published Jan 1, 2009• 2 citations
OpenAlex

Abstract

Abstract. This work presents the first scalable, efficient and generic compilers to construct group key exchange (GKE) protocols from two/three party key exchange (2-KE/3-KE) protocols. We propose three different compilers where the first one is a 2-KE to GKE compiler (2-TGKE) for tree topology, the second one is also for tree topology but from 3-KE to GKE (3-TGKE) and the third one is a compiler that constructs a GKE from 3-KE for circular topology. Our compilers 2-TGKE and 3-TGKE are first of their kind and are efficient due to the underlying tree topology. For the circular topology, we design a compiler called 3-CGKE. 2-TGKE and 3-TGKE compilers require a total of O (n lg n) communication, when compared to the existing compiler for circular topology, where the communication cost is O ` n 2 ´. By extending the compilers 2-TGKE and 3-TGKE using the techniques in [18], scalable compilers for tree based authenticated group key exchange protocols (2-TAGKE/3-TAGKE), which are secure against active adversaries can be constructed. As an added advantage our compilers can be used in a setting where there is asymmetric distribution of computing power. Finally, we present a constant round authenticated group key exchange (2-TAGKE) obtained by applying Diffie-Hellman protocol and the technique in [18] to our compiler 2-TGKE. We prove the security of our compilers in a stronger Real or Random model and do not assume the existence of random oracles.

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Group key establishment (GKE): Two/three party key exchange to GKE

S. Sree Vivek, S. Sharmila Deva Selvi, Deepanshu Shukla +1 more

This work presents the first scalable, efficient and generic compilers to construct group key exchange (GKE) protocols from two/three party key exchange (2-KE/3-KE) protocols. We propose three different compilers where the first one is a 2-KE to GKE compiler (2-TGKE) for tree topology, the second one is also for tree topology but from 3-KE to GKE (3-TGKE) and the third one is a compiler that constructs a GKE from 3-KE for circular topology. Our compilers 2-TGKE and 3-TGKE are first of their kind and are efficient due to the underlying tree topology. For the circular topology, we design a compiler called 3-CGKE. By extending the compilers 2-TGKE and 3-TGKE using the techniques in [?], scalable compilers for tree based authenticated group key exchange protocols (2-TAGKE/3-TAGKE), that are secure against active adversaries can be constructed. As an added advantage our compilers can be used in a setting where there is asymmetric distribution of computing power and hence applicable for low power devices such as PDA's, palmtops, sensor network nodes and mobile phones.

IEEE International Conference on Advanced Networks and Telecommunications Systems•Dec 1, 2012•0 citations

Scalable key exchange transformation: from two-party to group

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A modular method which derives a scalable construction of a group key exchange (GKE) scheme from a two-party key exchange (KE) one is presented. By combining the method presented with the compiler by Katz and Yung [1] a scalable compiler can be obtained that transforms any two-party KE protocol secure against a passive eavesdropper to an authenticated GKE one secure against a stronger active adversary.

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Abstract. Task-specific groups are often formed in an ad-hoc manner within big structures, like companies. Take the following typical scenario: A high rank manager decides that a task force group for some project needs to be built. This order is passed down the hierarchy where it finally reaches a manager who calls some employees to form a group. The members should communicate in a secure way and for efficiency reasons symmetric systems are the common choice. To establish joint secret keys for groups, group key exchange (GKE) protocols were developed. If the users are part of e.g. a Public Key Infrastructure (PKI), which is usually the case within a company or a small network, it is possible to achieve authenticated GKE by modifying the protocol and particularly by including signatures. In this paper we recall a GKE due to Burmester and Desmedt which needs only O(log n) communication and computation complexity per user, rather than O(n) as in the more well-known Burmester-Desmedt protocol, and runs in a constant number of rounds. To achieve authenticated GKE one can apply compilers, however, the existing ones would need O(n) computation and communication thereby mitigating the advantages of the faster protocol. Our contribution is to extend an existing compiler so that it preserves the computation and communication complexity of the non-authenticated protocol. This is particularly important for tree based protocols.

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Abstract We revisit a generic compiler from a two-party key exchange (KE) protocol to a group KE (GKE) one by Just and Vaudenay. We then give two families of GKE protocols fromstaticassumptions, which are obtained from the general compiler. The first family of the GKE protocols is a constant-round GKE by using secure key derivation functions (KDFs). As special cases, we have such GKE fromstaticRing-LWE (R-LWE), where “static” means that the parameter size in the R-LWE does not depend on the number of group members,n, and also from the standard SI-DDH and CSI-DDH assumptions. The second family consists of two-round GKE protocols from isogenies, which are proven secure fromnewisogeny assumptions, the first (resp. second) of which is based on the SIDH (resp. CSIDH) two-party KE. The underlying newstaticassumptions are based on indistinguishability betweena product value of supersingular invariantsand a random value.

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Constant Round Group Key Exchange with Logarithmic Computational Complexity.

Junghyun Nam, Youngsook Lee, Dongho Won

Protocols for group key exchange (GKE) are cryptographic algorithms that describe how a group of parties communicating over a public network can come up with a common secret key. Due to their critical role in building secure multicast channels, a number of GKE protocols have been proposed over the years in a variety of settings. However despite many impressive achievements, it still remains a challenging problem to design a secure GKE protocol which scales very well for large groups. Our observation is that all provably-secure constant-round GKE protocols providing forward secrecy thus far are not fully scalable, but have a computational complexity that scales only linearly in group size. Motivated by this observation, we propose a new GKE protocol that not only offers full scalability in all directions but also attains provable security against active adversaries. Full scalability is achieved by using a complete binary tree structure where users are arranged on both internal and leaf nodes. Security is proved via reduction to the decisional Diffie-Hellman assumption in a well-defined formal model of communication and adversarial capabilities.

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Scalable Group Key Exchange for Securing Distributed Operating Systems

Junghyun Nam, Minkyu Park, Sangchul Han +2 more

Distributed operating systems are designed to run over a collection of computing nodes that are spatially disseminated and communicate through a computer network. The computing nodes interact collaboratively with each other in order to pursue a common purpose. Protecting group communication between the collaborating nodes against potential attacks is one of the major challenges faced by the designers of distributed operating systems. This challenge can be effectively addressed by a group key exchange (GKE) protocol which allows a group of communicating parties to build a secure multicast channel over an insecure network. In this work, we propose a scalable GKE protocol that achieves both constant round complexity and logarithmic computation complexity. Our GKE protocol achieves its scalability by employing a complete binary tree structure combined with a so-called ”nonce-chained authentication technique”. Besides the scalability, our protocol features provable security against active adversaries in a well-defined communication model.

Journal of information science and engineering•Sep 1, 2012•3 citations
Abstract. This work presents the first scalable, efficient and generic compilers to construct group key exchange (GKE) protocols from two/three party key exchange (2-KE/3-KE) protocols. We propose three different compilers where the first one is a 2-KE to GKE compiler (2-TGKE) for tree topology, the second one is also for tree topology but from 3-KE to GKE (3-TGKE) and the third one is a compiler that constructs a GKE from 3-KE for circular topology. Our compilers 2-TGKE and 3-TGKE are first of their kind and are efficient due to the underlying tree topology. For the circular topology, we design a compiler called 3-CGKE. 2-TGKE and 3-TGKE compilers require a total of O (n lg n) communication, when compared to the existing compiler for circular topology, where the communication cost is O ` n 2 ´. By extending the compilers 2-TGKE and 3-TGKE using the techniques in [18], scalable compilers for tree based authenticated group key exchange protocols (2-TAGKE/3-TAGKE), which are secure against active adversaries can be constructed. As an added advantage our compilers can be used in a setting where there is asymmetric distribution of computing power. Finally, we present a constant round authenticated group key exchange (2-TAGKE) obtained by applying Diffie-Hellman protocol and the technique in [18] to our compiler 2-TGKE. We prove the security of our compilers in a stronger Real or Random model and do not assume the existence of random oracles.
This work presents the first scalable, efficient and generic compilers to construct group key exchange (GKE) protocols from two/three party key exchange (2-KE/3-KE) protocols. We propose three different compilers where the first one is a 2-KE to GKE compiler (2-TGKE) for tree topology, the second one is also for tree topology but from 3-KE to GKE (3-TGKE) and the third one is a compiler that constructs a GKE from 3-KE for circular topology. Our compilers 2-TGKE and 3-TGKE are first of their kind and are efficient due to the underlying tree topology. For the circular topology, we design a compiler called 3-CGKE. By extending the compilers 2-TGKE and 3-TGKE using the techniques in [?], scalable compilers for tree based authenticated group key exchange protocols (2-TAGKE/3-TAGKE), that are secure against active adversaries can be constructed. As an added advantage our compilers can be used in a setting where there is asymmetric distribution of computing power and hence applicable for low power devices such as PDA's, palmtops, sensor network nodes and mobile phones.
Abstract. Task-specific groups are often formed in an ad-hoc manner within big structures, like companies. Take the following typical scenario: A high rank manager decides that a task force group for some project needs to be built. This order is passed down the hierarchy where it finally reaches a manager who calls some employees to form a group. The members should communicate in a secure way and for efficiency reasons symmetric systems are the common choice. To establish joint secret keys for groups, group key exchange (GKE) protocols were developed. If the users are part of e.g. a Public Key Infrastructure (PKI), which is usually the case within a company or a small network, it is possible to achieve authenticated GKE by modifying the protocol and particularly by including signatures. In this paper we recall a GKE due to Burmester and Desmedt which needs only O(log n) communication and computation complexity per user, rather than O(n) as in the more well-known Burmester-Desmedt protocol, and runs in a constant number of rounds. To achieve authenticated GKE one can apply compilers, however, the existing ones would need O(n) computation and communication thereby mitigating the advantages of the faster protocol. Our contribution is to extend an existing compiler so that it preserves the computation and communication complexity of the non-authenticated protocol. This is particularly important for tree based protocols.
Abstract We revisit a generic compiler from a two-party key exchange (KE) protocol to a group KE (GKE) one by Just and Vaudenay. We then give two families of GKE protocols fromstaticassumptions, which are obtained from the general compiler. The first family of the GKE protocols is a constant-round GKE by using secure key derivation functions (KDFs). As special cases, we have such GKE fromstaticRing-LWE (R-LWE), where “static” means that the parameter size in the R-LWE does not depend on the number of group members,n, and also from the standard SI-DDH and CSI-DDH assumptions. The second family consists of two-round GKE protocols from isogenies, which are proven secure fromnewisogeny assumptions, the first (resp. second) of which is based on the SIDH (resp. CSIDH) two-party KE. The underlying newstaticassumptions are based on indistinguishability betweena product value of supersingular invariantsand a random value.
Protocols for group key exchange (GKE) are cryptographic algorithms that describe how a group of parties communicating over a public network can come up with a common secret key. Due to their critical role in building secure multicast channels, a number of GKE protocols have been proposed over the years in a variety of settings. However despite many impressive achievements, it still remains a challenging problem to design a secure GKE protocol which scales very well for large groups. Our observation is that all provably-secure constant-round GKE protocols providing forward secrecy thus far are not fully scalable, but have a computational complexity that scales only linearly in group size. Motivated by this observation, we propose a new GKE protocol that not only offers full scalability in all directions but also attains provable security against active adversaries. Full scalability is achieved by using a complete binary tree structure where users are arranged on both internal and leaf nodes. Security is proved via reduction to the decisional Diffie-Hellman assumption in a well-defined formal model of communication and adversarial capabilities.
Distributed operating systems are designed to run over a collection of computing nodes that are spatially disseminated and communicate through a computer network. The computing nodes interact collaboratively with each other in order to pursue a common purpose. Protecting group communication between the collaborating nodes against potential attacks is one of the major challenges faced by the designers of distributed operating systems. This challenge can be effectively addressed by a group key exchange (GKE) protocol which allows a group of communicating parties to build a secure multicast channel over an insecure network. In this work, we propose a scalable GKE protocol that achieves both constant round complexity and logarithmic computation complexity. Our GKE protocol achieves its scalability by employing a complete binary tree structure combined with a so-called ”nonce-chained authentication technique”. Besides the scalability, our protocol features provable security against active adversaries in a well-defined communication model.