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Key Agreement in the Standard Model

Georg Lippold, Juan Gonz

Published Jan 1, 2010• 1 citation
OpenAlex

Abstract

We show how to construct a certicateless key agreement protocol from the certicateless key encapsulation mechanism introduced by Lippold et al. (2009a) in ICISC 2009 using the Boyd et al. (2008) protocol from ACISP 2008. We introduce the CanettiKrawczyk (CK) model for certicateless cryptography, give security notions for Type I and Type II adversaries in the CK model, and highlight the dierences to the existing e 2 CK model discussed by Lippold et al. (2009b). The resulting CK model is more relaxed thus giving more power to the adversary than the original CK model.

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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jan 1, 2016•6 citations
We show how to construct a certicateless key agreement protocol from the certicateless key encapsulation mechanism introduced by Lippold et al. (2009a) in ICISC 2009 using the Boyd et al. (2008) protocol from ACISP 2008. We introduce the CanettiKrawczyk (CK) model for certicateless cryptography, give security notions for Type I and Type II adversaries in the CK model, and highlight the dierences to the existing e 2 CK model discussed by Lippold et al. (2009b). The resulting CK model is more relaxed thus giving more power to the adversary than the original CK model.
We show how to construct a certificateless key agreement protocol from the certificateless key encapsulation mechanism introduced by \\cite{lippold-ICISC_2009} in ICISC 2009 using the \\cite{DBLP:conf/acisp/BoydCNP08} protocol from ACISP 2008. We introduce the Canetti-Krawczyk (CK) model for certificateless cryptography, give security notions for Type I and Type II adversaries in the CK model, and highlight the differences to the existing e2^22CK model discussed by \\cite{DBLP:conf/pairing/LippoldBN09}. The resulting CK model is more relaxed thus giving more power to the adversary than the original CK model.
Certificateless cryptography aims at combining the advantages of identity based and public key cryptography in order to avoid the key escrow problem inherent in the identity based cryptography and cumbersome certificate management in the traditional public key infrastructure. The provably secure certificateless key agreement protocol is proposed by Lippold et al. in 2009, but their protocol suffers from computation burden. Owing to the above-mentioned situations, a new certificateless two party key agreement protocol (CL-KA) is proposed and the security attributes are analyzed in the extended Canetti-Krawzcyk(eCK) security model. Our protocol only requires each entity to compute two pairings, up to now, it turns out to be the most efficient one of all the previously known security CL-KA schemes.
The contributions of this thesis fall into three areas of certificateless cryptography. The first area is encryption, where we propose new constructions for both identity-based and certificateless cryptography. We construct an n-out-of- n group encryption scheme for identity-based cryptography that does not require any special means to generate the keys of the trusted authorities that are participating. We also introduce a new security definition for chosen ciphertext secure multi-key encryption. We prove that our construction is secure as long as at least one authority is uncompromised, and show that the existing constructions for chosen ciphertext security from identity-based encryption also hold in the group encryption case. We then consider certificateless encryption as the special case of 2-out-of-2 group encryption and give constructions for highly efficient certificateless schemes in the standard model. Among these is the first construction of a lattice-based certificateless encryption scheme. Our next contribution is a highly efficient certificateless key encapsulation mechanism (KEM), that we prove secure in the standard model. We introduce a new way of proving the security of certificateless schemes based that are based on identity-based schemes. We leave the identity-based part of the proof intact, and just extend it to cover the part that is introduced by the certificateless scheme. We show that our construction is more efficient than any instanciation of generic constructions for certificateless key encapsulation in the standard model. The third area where the thesis contributes to the advancement of certificateless cryptography is key agreement. Swanson showed that many certificateless key agreement schemes are insecure if considered in a reasonable security model. We propose the first provably secure certificateless key agreement schemes in the strongest model for certificateless key agreement. We extend Swanson's definition for certificateless key agreement and give more power to the adversary. Our new schemes are secure as long as each party has at least one uncompromised secret. Our first construction is in the random oracle model and gives the adversary slightly more capabilities than our second construction in the standard model. Interestingly, our standard model construction is as efficient as the random oracle model construction.
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.
Two new authenticated key agreement protocols in the certificateless setting are presented in this paper. Both are proved secure in the extended Canetti-Krawczyk model, under the BDH assumption. The first one is more efficient than the Lippold et al.'s (LBG) protocol, and is proved secure in the same security model. The second protocol is proved secure under the Swanson et al.'s security model, a weaker model. As far as we know, our second proposed protocol is the first one proved secure in the Swanson et al.'s security model. If no pre-computations are done, the first protocol is about 26% faster than LBG, and the second protocol is about 49% faster than LBG, and about 31% faster than the first one. If pre-computations of some operations are done, our two protocols remain faster.