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International Journal of Computer Mathematics Computer Systems Theory

Efficient single round attribute-based authenticated key exchange protocol

Suvradip Chakraborty, Y. Sreenivasa Rao, Chandrasekharan Pandu Rangan

Published Jan 14, 2021• 3 citations

Abstract

Attribute-Based Authenticated Key Exchange (ABAKE) protocols allow two or more users to establish a shared key and achieve mutual authentication over an insecure network, while providing fine-grained access control over transmitted data. The existing ABAKE protocols are very inefficient, requiring a large number (polynomial in the size of the access policies) of pairing and exponentiation operations. This presents a major hindrance in the real-world deployment of these protocols. In this work, we present a construction of ABAKE protocol where the number of pairing operations is constant (to be precise only 7) and the number of exponentiation operations is linear to the number of clauses in the disjunctive normal form representing the general access policies. To this end, we construct an Attribute-Based Signcryption (ABSC) scheme with constant number of pairings, and use it as the main building block in our ABAKE construction. This also gives the first construction of ABSC schemes with constant number of pairings for general purpose access policies in the standard model. Another important and desirable feature of our ABAKE construction is that it is round-optimal, i.e. it is a single round protocol. We analyse the security of our ABAKE construction in the Attribute-Based extended Canetti-Krawzyck (ABeCK) model, and prove its security assuming the hardness of a variant of the Bilinear Diffie-Hellman Exponent problem in the random oracle model.

DOI: 10.1080/23799927.2021.1873192

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Attribute-Based Authenticated Key Exchange (ABAKE) protocols allow two or more users to establish a shared key and achieve mutual authentication over an insecure network, while providing fine-grained access control over transmitted data. The existing ABAKE protocols are very inefficient, requiring a large number (polynomial in the size of the access policies) of pairing and exponentiation operations. This presents a major hindrance in the real-world deployment of these protocols. In this work, we present a construction of ABAKE protocol where the number of pairing operations is constant (to be precise only 7) and the number of exponentiation operations is linear to the number of clauses in the disjunctive normal form representing the general access policies. To this end, we construct an Attribute-Based Signcryption (ABSC) scheme with constant number of pairings, and use it as the main building block in our ABAKE construction. This also gives the first construction of ABSC schemes with constant number of pairings for general purpose access policies in the standard model. Another important and desirable feature of our ABAKE construction is that it is round-optimal, i.e. it is a single round protocol. We analyse the security of our ABAKE construction in the Attribute-Based extended Canetti-Krawzyck (ABeCK) model, and prove its security assuming the hardness of a variant of the Bilinear Diffie-Hellman Exponent problem in the random oracle model.

Available Attribute-Based Authenticated Key Exchange(ABAKE) protocols are all designed in the single Attribute Authority(AA) environment.However,secure communication is in demand between parties from different Attribute Authorities(AAs).Based on Waters' attribute-based encryption scheme,an ABAKE protocol is proposed in multiple AAs environment and the security of the proposed protocol is reduced to Gap Bilinear Diffie-Hellman(GBDH) and Computational Diffie-Hellman(CDH) assumptions in the Attribute-Based extended Canetti-Krawczyk(ABeCK) model.Moreover,the scheme,which transmits attribute authentication policy represented by linear secret sharing scheme via Boolean formulas,can express flexible policies and decrease communication cost drastically.

In this paper, we propose a generic construction of one-round attribute-based (implicitly) authenticated key exchange (ABAKE). The construction is based on a chosen-ciphertext (CCA) secure attribute-based KEM and the decisional Diffie-Hellman (DDH) assumption. If an underlying attribute-based KEM scheme allows expressive access controls and is secure in the standard model (StdM), an instantiated ABAKE scheme also achieves them. Our scheme enjoys the best of both worlds: efficiency and security. The number of rounds is one (optimal) while the known secure scheme in the StdM is not one-round protocol. Our scheme is comparable in communication complexity with the most efficient known scheme that is not proved in the StdM. Also, our scheme is proved to satisfy security against advanced attacks like key compromise impersonation.

Attribute-based authenticated key agreement(ABAKA) protocol is used to establish session key among parties in the communication environment in which the identity information of individual is protected.Attribute-based extended Canetti-Krawczyk(ABe CK) model is a model with more security applying to the security proof of ABAKE protocol.This paper presents gap computational parallel bilinear Diffie-Hellman exponent(GCPBDHE) assumption based on gap computational Diffie-Hellman(GCDH) assumption.Based on Waters scheme,it establishes an ABAKA protocol,and proves its security in ABe CK model under GCPBDHE and CDH assumptions.Compared with the existing ABAKE protocols,the new protocol is more efficient in communication cost.

Attribute-based authenticated key exchange (AB-AKE) is a useful primitive that allows a group of users to establish a shared secret key and at the same time enables fine-grained access control. A straightforward approach to design an AB-AKE protocol is to extend a key exchange protocol using an attribute-based authentication technique. However, insider security is a challenge security issue for AB-AKE in the multi-party setting and cannot be solved using the straightforward approach. In addtion, many existing key exchange protocols for the multi-party setting (e.g., the well-known Burmester-Desmedt protocol) require multiple broadcast rounds to complete the protocol. In this paper, we propose a novel one-round attribute-based key exchange (OAKE) protocol in the multi-party setting. We define the formal security models, including session key security, insider security and user privacy, for OAKE, and prove the security of the proposed protocol under some standard assumptions in the random oracle model.

One-round group authenticated key exchange (GAKE) protocols typically provide implicit authentication and appealing bandwidth efficiency. As a special case of GAKE – the pairing-based one-round tripartite authenticated key exchange (3AKE), recently gains much attention of research community due to its strong security. Several pairing-based one-round 3AKE protocols have recently been proposed to achieve provable security in the g-eCK model. In contrast to earlier GAKE models, the g-eCK model particularly formulates the security properties regarding resilience to the leakage of various combinations of long-term key and ephemeral session state, and provision of weak perfect forward secrecy in a single model. However, the g-eCK security proofs of previous protocols are only given under the random oracle model. In this work, we give a new construction for pairing-based one-round 3AKE protocol which is provably secure in the g-eCK model without random oracles. Security of proposed protocol is reduced to the hardness of Cube Bilinear Decisional Diffie-Hellman (CBDDH) problem for symmetric pairing. We also extend the proposed 3AKE scheme to a GAKE scheme with more than three group members, based on multilinear maps. We prove g-eCK security of our GAKE scheme in the standard model under the natural multilinear generalization of the CBDDH assumption.

A two-party authenticated key exchange (AKE) protocol allows each of the two parties to share a common secret key over insecure channels, even in the presence of active adversaries who can actively control and modify the exchanged messages. To capture the malicious behaviors of the adversaries, there have been many efforts to define security models. Amongst them, the extended Canetti–Krawczyk (eCK) security model is considered one of the strongest security models and has been widely adopted. In this paper, we present a simple construction of a pairing-based eCK-secure AKE protocol in the standard model. Our protocol can be instantiated with a suitable signature scheme (i.e., an existentially unforgeable signature scheme against adaptive chosen message attacks). The underlying assumptions of our construction are the decisional bilinear Diffie–Hellman assumption and the existence of a pseudorandom function. Note that the previous eCK-secure protocol constructions either relied on random oracles for their security or used somewhat strong assumptions, such as the existence of strong-pseudorandom functions, target collision-resistant functions, etc., while our protocol construction uses fewer and more-standard assumptions in the standard model. Furthermore, preserving the same security argument, our protocol can be instantiated with any appropriate signature scheme that comes in the future with better efficiency.