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Certificateless non-interactive key exchange protocol without pairings

Yun Wei, Fushan Wei, Chuangui Ma

Published Aug 1, 2014• 2 citations
OpenAlex

Abstract

Non-interactive key exchange (NIKE) allows two parties to establish a shared key without communications. In ID-based non-interactive key exchange (ID-NIKE) protocols, private key generator (PKG) knows user's private key, so it can calculate the shared key between two participants, and most constructions of ID-NIKE need expensive pairing operation. To overcome these disadvantages, a security model of certificateless non-interactive key exchange (CL-NIKE) is proposed in this paper. And a scheme without pairings is also given. The proposed protocol is proved secure in the Random Oracle Model (ROM) based on the gap Diffie-Hellman (GDH) and computational Diffie-Hellman (CDH) problem. In the new protocol, key generation center (KGC) only knows user's partial key and is not able to calculate the shared key. Moreover, the new protocol is more efficient than the existing ID-NIKE schemes because it is pairing-free.

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•Jan 1, 2015•0 citations
Non-interactive key exchange (NIKE) allows two parties to establish a shared key without communications. In ID-based non-interactive key exchange (ID-NIKE) protocols, private key generator (PKG) knows user's private key, so it can calculate the shared key between two participants, and most constructions of ID-NIKE need expensive pairing operation. To overcome these disadvantages, a security model of certificateless non-interactive key exchange (CL-NIKE) is proposed in this paper. And a scheme without pairings is also given. The proposed protocol is proved secure in the Random Oracle Model (ROM) based on the gap Diffie-Hellman (GDH) and computational Diffie-Hellman (CDH) problem. In the new protocol, key generation center (KGC) only knows user's partial key and is not able to calculate the shared key. Moreover, the new protocol is more efficient than the existing ID-NIKE schemes because it is pairing-free.
Designing efficient key agreement protocols is a fundamental cryptographic problem. In this paper, we first define a security model for key agreement in certificateless cryptography that is an extension of earlier models. We note that the existing pairing free protocols are not secure in our model. We design an efficient pairing-free, single round protocol that is secure in our model based on the hardness assumption of the Computational Diffie Hellman (CDH) problem. We also observe that previously existing pairing-free protocols were secure based on much stronger assumptions such as the hardness of the Gap Diffie Hellman problem. We use a restriction of our scheme to design an efficient pairing-free single round identity based key agreement protocol that is secure in the id-CK+ model based on the hardness assumption of the CDH problem. Additionally, both our schemes satisfy several other security properties such as forward secrecy, resistance to reflection attacks etc.
A pairing-free certificateless two party key agreement scheme(CL-KA) is proposed.This work is able demonstrates all existing CL-KA schemes(except for Lippold's scheme) are insecure in the eCK model.The scheme is secure in the eCK model as long as each party has at least one uncompromised secret.The scheme has proven to be secure in the random oracle model(ROM),assuming that the computational Diffie-Hellman assumption hold even if the key generation centre(KGC) learns the ephemeral secrets of both parties,or reveal secret values/replace public keys,but not both.The scheme eliminates pairing computation.It achieves efficiency in computational cost when compared with all the other known certificateless key agreement schemes.The scheme is more suitable for the restricted bandwidth of the communication environment,such as ad hoc networks,wireless sensors,and so on.
Non-interactive key exchange (NIKE) enables two or multiple parties (just knowing the public system parameters and each other's public key) to derive a (group) session key without the need for interaction. Recently, NIKE in multi-party settings has been attached importance. However, we note that most existing multi-party NIKE protocols, underlying costly cryptographic techniques (i.e., multilinear maps and indistinguishability obfuscation), lead to high computational costs once employed in practice. Therefore, it is a challenging task to achieve multi-party NIKE protocols by using more practical cryptographic primitives. In this paper, we propose a secure and efficient NIKE protocol for secure communications in dynamic groups, whose construction only bases on bilinear maps. This protocol allows multiple parties to negotiate asymmetric group keys (a public group encryption key and each party's decryption key) without any interaction among one another. Additionally, the protocol supports updating of group keys in an efficient and non-interactive way once any party outside a group or any group member joins or leaves the group. Further, any party called a sender (even outside a group) intending to connect with some or all of group members called receivers in a group, just needs to generate a ciphertext with constant size under the public group encryption key, and only the group member who is the real receiver can decrypt the ciphertext to obtain the session key. We prove our protocol captures the correctness and indistinguishability of session key under k-Bilinear Diffie-Hellman exponent (k-BDHE) assumption. Efficiency evaluation shows the efficiency of our protocol.
The space Delay Tolerant Network(DTN) has characteristic such as high delay and frequent disconnectivity.Aiming at this problem,this paper designs a non-interactive key exchange protocol,and it is proven secure in the random oracle model.The proposed protocol enables two parties to agree on a symmetric shared key without requiring any interaction.The protocol eliminates the dependency on certificate used in Public Key Infrastructure(PKI) and avoids the key escrow problem in ID-based Public Key Cryptography(ID-PKC).Analysis result shows that the proposed protocol does not utilize the expensive pairing computation and achieves higher efficiency compared with other Non-interactive Key Exchange(NIKE) protocols, and thus proves to be suitable for the space environment with restricted computing and few power resource.
In certificateless cryptography, a user secret key is derived from two partial secrets: one is the identity-based secret key (corresponding to the user identity) generated by a Key Generation Center (KGC), and the other is the user self-generated secret key (corresponding to a user self-generated and uncertified public key). Two types of adversaries are considered for certificateless cryptography: a Type-I adversary who can replace the user self-generated public key (in transmission or in a public directory), and a Type-II adversary who is an honest-but-curious KGC. In this paper, we present a formal study on certificateless key exchange (CLKE). We show that the conventional definition of Type-I and Type-II security may not be suitable for certificateless key exchange when considering the notion of forward secrecy which is important for key exchange protocols. We then present a new security model in which a single adversary (instead of Type-I and Type-II adversaries) is considered. We also construct a strongly secure certificateless key exchange protocol without expensive pairing operations. As far as we know, our proposed protocol is the first proven secure CLKE protocol without pairing.
Non-interactive key exchange (NIKE) is a fundamental notion in Cryptography.This notion was introduced by Diffie and Hellman in 1976. They proposed thewell-known 2-party NIKE protocol and left open the generic question of whetherNIKE could be realized in the multiparty setting. NIKE has since then been anactive area of research with an ultimate goal of obtaining best possible security inthe multiparty setting. Although this has evaded researchers for many decades,advancements have been made through relaxations in multiple directions such asrestricting to 3-parties, static/semi-static model (where the adversary needs tocommit to the set of parties he wishes to be challenged upon ahead of time),random-oracle model, allowing initial setup, etc.This dissertation provides a solution to the open question: it provides a multipartyNIKE protocol that is adaptively secure with no setup and in the standardmodel.The solution employs novel techniques of using indistinguishability obfuscation,which are interesting in their own right and which seem promising in findingwider applications in other settings. One such technique pertains overcoming thesomewhat inherent drawback of non-adaptivity of the puncturing technique introduced by Sahai and Waters [STOC'14].