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Computationally Sound Symbolic Security Reduction Analysis of Group Key Exchange Protocol using Bilinear Pairings.

Zijian Zhang, Liehuang Zhu, Lejian Liao

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Canetti and Herzog have proposed a universally composable symbolic analysis (UCSA) of mutual authentication and key exchange protocols within universally composable security framework. It is fully automated and computationally sound symbolic analysis. Furthermore, Canetti and Gajek have analyzed Diffie-Hellman based key exchange protocols as an extension of their work. It deals with forward secrecy in case of fully adaptive party corruptions. However, their work only addresses two-party protocols that use public key encryptions, digital signatures and Diffie-Hellman exchange. We make the following contributions. First, we extend UCSA approach to analyze group key exchange protocols that use bilinear pairings exchange and digital signatures to resist insider attack under fully adaptive party corruptions with respect to forward secrecy. Specifically, we propose an formal algebra, and property of bilinear pairings in the execution of group key exchange protocol among arbitrary number of participants. This provides computationally sound and fully automated analysis. Second, we reduce the security of multiple group key exchange sessions among arbitrary number of participants to the security of a single group key exchange session among three participants. This improves the efficiency of security analysis.

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Canetti and Herzog have proposed a universally composable symbolic analysis (UCSA) of mutual authentication and key exchange protocols within universally composable security framework. It is fully automated and computationally sound symbolic analysis. Furthermore, Canetti and Gajek have analyzed Diffie-Hellman based key exchange protocols as an extension of their work. It deals with forward secrecy in case of fully adaptive party corruptions. However, their work only addresses two-party protocols that use public key encryptions, digital signatures and Diffie-Hellman exchange. We make the following contributions. First, we extend UCSA approach to analyze group key exchange protocols that use bilinear pairings exchange and digital signatures to resist insider attack under fully adaptive party corruptions with respect to forward secrecy. Specifically, we propose an formal algebra, and property of bilinear pairings in the execution of group key exchange protocol among arbitrary number of participants. This provides computationally sound and fully automated analysis. Second, we reduce the security of multiple group key exchange sessions among arbitrary number of participants to the security of a single group key exchange session among three participants. This improves the efficiency of security analysis.
The computational soundness of symbolic analysis is always argued,because the cryptographic primitives are viewed as black boxes,and the specific security properties of those cryptographic primitives have not been considered yet.Moreover,this kind of approaches is ineffective,when it is used to analyze group key exchange protocols with a large number of participants.This paper considers those problems above,and proposes computationally sound and effective symbolic analysis of group key exchange protocols.More specifically,we design a pattern function for symbolic expression,so as to define the concrete security properties that modular exponentiation operation needs satisfy.Based on that,we prove the symbolic analysis of Burmester-Desmedt protocol is computationally sound in universally composable security framework.Furthermore,we use mathematical inductive method to prove the security of Burmester-Desmedt protocol is unrelated to the number of participants.The number of the participants does not affect symbolic analysis.As a result,the efficiency of symbolic analysis is improved.
Authenticated key-exchange protocols allow two participants A and B , communicating over a public network and each holding an authentication means to exchange a shared secret value. Methods designed to deal with this cryptographic problem ensure A (resp. B ) that no other participants aside from B (resp. A ) can learn any information about the agreed value and often also ensure A and B that their respective partner has actually computed this value. A natural extension to this cryptographic method is to consider a pool of participants exchanging a shared secret value and to provide a formal treatment for it. Starting from the famous two-party Diffie--Hellman (DH) key-exchange protocol and from its authenticated variants, security experts have extended it to the multiparty setting for over a decade and, in the past few years, completed a formal analysis in the framework of modern cryptography. The present paper synthesizes this body of work on the provably-secure authenticated group DH key exchange.
Recently some efforts were made towards capturing the security requirements from digital signature schemes as an ideal functionality within a composable security framework. This modeling of digital signatures potentially has some significant analytical advantages (such as enabling component-wise analysis of complex systems that use signature schemes, as well as symbolic and automatable analysis of such systems). However, it turns out that formulating ideal functionalities that capture the properties expected from signature schemes in a way that is both sound and enjoys the above advantages is not a trivial task. This work has several contributions. We first correct some flaws in the definition of the ideal signature functionality of Canetti, 2001, and subsequent formulations. Next we provide a minimal formalization of “ideal certification authorities ” and show how authenticated communication can be obtained using ideal signatures and an ideal certification authority. This is done while guaranteeing full modularity (i.e., each component is analyzed as stand-alone), and in an unconditional and errorless way. This opens the door to symbolic and automated analysis of protocols for these tasks, in a way that is both modular and cryptographically sound.
Recently some efforts were made towards capturing the security requirements from digital signature schemes as an ideal functionality within a composable security framework. This modeling of digital signatures potentially has some significant analytical advantages (such as enabling component-wise analysis of complex systems that use signature schemes, as well as symbolic and automatable analysis of such systems). However, it turns out that formulating ideal functionalities that capture the properties expected from signature schemes in a way that is both sound and enjoys the above advantages is not a trivial task. This work has several contributions. We first correct some flaws in the definition of the ideal signature functionality of Canetti, 2001, and subsequent formulations. Next we provide a minimal formalization of "ideal certification authorities" and show how authenticated communication can be obtained using ideal signatures and an ideal certification authority. This is done while guaranteeing full modularity (i.e., each component is analyzed as stand-alone), and in an unconditional and errorless way. This opens the door to symbolic and automated analysis of protocols for these tasks, in a way that is both modular and cryptographically sound.
Recently some efforts were made towards capturing the security requirements from digital signature schemes as an ideal functionality within a composable security framework. This modeling of digital signatures potentially has some significant analytical advantages (such as enabling component-wise analysis of complex systems that use signature schemes, as well as symbolic and automatable analysis of such systems). However, it turns out that formulating ideal functionalities that capture the properties expected from signature schemes in a way that is both sound and enjoys the above advantages is not a trivial task. This work has several contributions. We first correct some flaws in the definition of the ideal signature functionality of Canetti, 2001, and subsequent formulations. Next we provide a minimal formalization of “ideal certification authorities” and show how authenticated communication can be obtained using ideal signatures and an ideal certification authority. This is done while guaranteeing full modularity (i.e., each component is analyzed as stand-alone), and in an unconditional and errorless way. This opens the door to symbolic and automated analysis of protocols for these tasks, in a way that is both modular and cryptographically sound. ∗An extended abstract of this work appears in the proceedings of the 17th Computer Security Foundations Workshop (CSFW). This is a slightly corrected version. The first version of this paper, which dates November 18 2003, contained by mistake the date November 16, 2004 on its title page. †IBM T.J. Watson Research Center. Email: canetti@watson.ibm.com.
Protocols for authenticated key exchange (AKE) allow parties within an insecure network to establish a common session key which can then be used to secure their future communication. It is fair to say that group AKE is currently less well understood than the case of two-party AKE; in particular, attacks by malicious insiders --- a concern specific to the group setting --- have so far been considered only in a relatively "ad-hoc" fashion. The main contribution of this work is to address this deficiency by providing a formal, comprehensive model and definition of security for group AKE which automatically encompasses insider attacks. We do so by defining an appropriate ideal functionality for group AKE within the universal composability (UC) framework. As a side benefit, any protocol secure with respect to our definition is secure even when run concurrently with other protocols, and the key generated by any such protocol may be used securely in any subsequent application.In addition to proposing this definition, we show that the resulting notion of security is strictly stronger than the one proposed by Bresson, et al. (termed "AKE-security"), and that our definition implies all previously-suggested notions of security against insider attacks. We also show a simple technique for converting any AKE-secure protocol into one secure with respect to our definition.