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OALib

Tightly-Secure Authenticated Key Exchange without NAXOS’ Approach Based on Decision Linear Problem

Mojahed Mohamed, Xiaofen Wang, Xiaosong Zhang

Published Jan 1, 2016• 3 citations
Publisher

Abstract

Design Secure Authenticated Key Exchange (AKE) protocol without NAXOS approach is remaining as an open problem.NAXOS approach [4] is used to hide the ephemeral secret key from an adversary even if the adversary in somehow may obtain the ephemeral secret key.Using NAXOS approach will cause two main drawbacks: (i) leaking of the static secret key which will be utilized in computing the exponent of the ephemeral public key; (ii) maximization of using random oracle when applying to the exponent of the ephemeral public key and session key derivation.In this paper, we present another AKE-secure without NAXOS approach based on decision linear assumption in the random oracle model.We fasten our security using games sequences tool which gives tight security for our protocol.

DOI
10.4236/oalib.1103033

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Security models for two-party authenticated key exchange (AKE) protocols have developed over time to prove the security of AKE protocols even when the adversary learns certain secret values. In this work, we address more granular leakage: partial leakage of long-term secrets of protocol principals, even after the session key is established. We introduce a generic key exchange security model, which can be instantiated allowing bounded or continuous leakage, even when the adversary learns certain ephemeral secrets or session keys. Our model is the strongest known partial-leakage-based security model for key exchange protocols. We propose a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the proposed model, by introducing a new concept: the leakage-resilient NAXOS trick. We identify a special property for public-key cryptosystems: pair generation indistinguishability, and show how to obtain the leakage-resilient NAXOS trick from a pair generation indistinguishable leakage-resilient public-key cryptosystem.

ACM Asia Conference on Computer and Communications Security (ASIA CCS)•May 30, 2014•44 citations
Design Secure Authenticated Key Exchange (AKE) protocol without NAXOS approach is remaining as an open problem.NAXOS approach [4] is used to hide the ephemeral secret key from an adversary even if the adversary in somehow may obtain the ephemeral secret key.Using NAXOS approach will cause two main drawbacks: (i) leaking of the static secret key which will be utilized in computing the exponent of the ephemeral public key; (ii) maximization of using random oracle when applying to the exponent of the ephemeral public key and session key derivation.In this paper, we present another AKE-secure without NAXOS approach based on decision linear assumption in the random oracle model.We fasten our security using games sequences tool which gives tight security for our protocol.
Authenticated key exchange protocols are a fundamental cryptography building block for establishing a secret shared key among participating parties over an open network model. Mohamed et al. proposed a tightly-secure authenticated key exchange without NAXOS approach based on decision linear problem in order to solve an open problem for designing an authenticated key exchange protocol without using NAXOS trick. Mohamed et al.'s protocol has tight security proof in the eCK model under the random oracle problem and its security claims verified by using the games sequence tool. However, we show that Mohamed et al.'s protocol cannot withstand the key compromise impersonation attacks and man in the middle attacks. Furthermore, Mohamed et al.'s protocol cannot provide an implicit entity authentication property since it is a basic security property for an authenticated key exchange protocol. Therefore, the protocol is not secure in the eCK model.
LaMacchia, Lauter and Mityagin [19] proposed a novel security definition for authenticate key exchange (AKE) that gives an adversary the power to obtain ephemeral information regarding a target test session. To demonstrate feasibility of secure protocols in the new definition, henceforth called eCK, the authors described a protocol called NAXOS. NAXOS combines an ephemeral private key x with a static private key a to generate an ephemeral public key X (more precisely in what we call the NAXOS' approach X=gH(x,a)). Thus no one is able to query the discrete logarithm of X without knowing both the ephemeral and static private keys. This idea is crucial in the security argument to guard against leaked ephemeral secrets belonging to the test session. Another important assumption is the gap assumption that allows the protocol to remain secure even in the presence of malicious insiders. Both ideas have been successfully used in creating various protocols secure in the eCK model. In this paper, we construct two eCK-secure protocols without the above mentioned ideas. KFU1 is secure under the GDH assumption without using the NAXOS' approach. KFU2 builds upon KFU1 and drops the gap requirement, thus it is secure under the CDH assumption. Efficiency and security of the proposed protocols are comparable to the well-known HMQV [15] protocol. Furthermore, unlike HMQV and NAXOS the use of the random oracle in KFU1 and KFU2 is restricted to the key derivation function making them more suitable for practical applications.
Two-party key exchange protocol is a mechanism in which two parties communicate with each other over an insecure channel and output the same session key.A key exchange protocol that is secure against an active adversary who can control and modify the exchanged messages is called authenticated key exchange (AKE) protocol.LaMacchia, Lauter and Mityagin presented a strong security definition for public key infrastructure (PKI) based two-pass protocol, which we call the extended Canetti-Krawczyk (eCK) security model, and some researchers have provided eCK-secure AKE protocols in recent years.However, almost all protocols are provably secure in the random oracle model or rely on a special implementation technique so-called the NAXOS trick.In this paper, we present a PKI-based two-pass AKE protocol that is secure in the eCK security model.The security of the proposed protocol is proven without random oracles (under three assumptions), and does not rely on implementation techniques such as the NAXOS trick.
Security models for two-party authenticated key exchange (AKE) protocols have developed over time to prove the security of AKE protocols even when the adversary learns certain secret values. In this work, we address more granular leakage: partial leakage of long-term secrets of protocol principals, even after the session key is established. We introduce a generic key exchange security model, which can be instantiated allowing bounded or continuous leakage, even when the adversary learns certain ephemeral secrets or session keys. Our model is the strongest known partial-leakage-based security model for key exchange protocols. We propose a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the proposed model, by introducing a new concept: the leakage-resilient NAXOS trick. We identify a special property for public-key cryptosystems: pair generation indistinguishability, and show how to obtain the leakage-resilient NAXOS trick from a pair generation indistinguishable leakage-resilient public-key cryptosystem.
Abstract Since the introduction of extended Canetti–Krawczyk (eCK) security model for two‐party key exchange, many protocols have been proposed to provide eCK security. However, most of those protocols are provably secure in the random oracle model or rely on special design technique, which is well known as the NAXOS trick. In contrast to previous schemes, we present an eCK secure protocol in the standard model, without NAXOS trick and without knowledge of secret key assumption for public key registration. The security proof of our scheme is based on standard pairing assumption, collision‐resistant hash functions, Bilinear Decision Diffie–Hellman and Decision Linear Diffie–Hellman assumptions, and pseudo‐random functions with pairwise independent random source. Although our proposed protocol is based on bilinear groups, it does not require any pairing operation during key exchange procedure. Copyright © 2014 John Wiley & Sons, Ltd.
Security models for two-party authenticated key exchange (AKE) protocols have developed over time to prove the security of AKE protocols even when the adversary learns certain secret values. In this work, we address more granular leakage: partial leakage of long-term secrets of protocol principals, even after the session key is established. We introduce a generic key exchange security model, which can be instantiated allowing bounded or continuous leakage, even when the adversary learns certain ephemeral secrets or session keys. Our model is the strongest known partial-leakage-based security model for key exchange protocols. We propose a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the proposed model, by introducing a new concept: the leakage-resilient NAXOS trick. We identify a special property for public-key cryptosystems: pair generation indistinguishability, and show how to obtain the leakage-resilient NAXOS trick from a pair generation indistinguishable leakage-resilient public-key cryptosystem.