Round-Optimal Password-Based Group Key Exchange Protocols in the Standard Model
Password-based group key exchange protocols allow group users who share only a short, low entropy password to agree on a cryptographically strong session key. One fundamental complexity measure of such protocols is its round complexity. In this paper, we
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Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China {xujing,huxuexian,zfzhang}@tca.iscas.ac.cn 2 State Key Laboratory of Mathematical Engineering and Advanced Computing, Information Engineering University, Zhengzhou 450002, China
Abstract. Password-based group key exchange protocols allow group users who share only a short, low entropy password to agree on a cryptographically strong session key. One fundamental complexity measure of such protocols is its round complexity. In this paper, we present the first one-round password-based group key exchange protocol in the common random string model. Furthermore, we propose a completely new approach to remove the need for the common random string and then construct a two-round password-based group key exchange protocol that does not require any setup assumption. This is - to the best of our knowledge - the first password-based group key exchange protocol without trusted setup. Using indistinguishability obfuscation as main tool, both protocols are provably secure in the standard model. Keywords: Group key exchange protocol · Password based authentication · Round complexity · Indistinguishability obfuscation
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Introduction
Password-based authenticated key exchange (PAKE) protocols [1] allow users who share only a short, low-entropy password to agree on a cryptographically strong session key. PAKE protocols are fascinating from a theoretical perspective, as they can be viewed as a means of “bootstrapping” a common cryptographic key from the (essentially) minimal setup assumption of a short, shared secret. PAKE protocols are also important in practice, since passwords are perhaps the most common and widely-used means of authentication. In this paper, we consider PAKE protocols in the group setting where the number of users involved in the computation of a common session key can be large. This work was supported by the National Grand Fundamental Research (973) Program of China under Grant 2013CB338003, China Postdoctoral Science Foundation under Grant 2014M552524, and the National Natural Science Foundation of China (NSFC) under Grants 61170279, U1536205 and 61170278. c Springer International Publishing Switzerland 2015 T. Malkin et al. (Eds.): ACNS 2015, LNCS 9092, pp. 42–61, 2015. DOI: 10.1007/978-3-319-28166-7 3
Round-Optimal Password-Based Group Key Exchange Protocols
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The difficulty in designing password-based protocols is to prevent off-line dictionary attacks whereby an eavesdropping adversary exhaustively enumerates passwords, attempting to match the correct password to the eavesdropped session. However, the adversary can always correctly determine the correct password via an on-line dictionary attack in which the adversary tries to impersonate one of the parties using each possible password. Although an on-line dictionary attack is not avoidable, the damage it may cause can be mitigated by other means such as limiting the number of failed login attempts. Roughly, a secure password-ba
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