Strongly Secure Certificateless Key Agreement

We introduce a formal model for certificateless authenticated key exchange (CL-AKE) protocols. Contrary to what might be expected, we show that the natural combination of an ID-based AKE protocol with a public key based AKE protocol cannot provide strong security. We provide the first one-round CL-AKE scheme proven secure in the random oracle model. We introduce two variants of the Diffie-Hellman trapdoor the introduced by \cite{DBLP:conf/eurocrypt/CashKS08}. The proposed key agreement scheme is secure as long as each party has at least one uncompromised secret. Thus, our scheme is secure even if the key generation centre learns the ephemeral secrets of both parties.

Efficient certificateless KEM in the standard model

We give a direct construction of a certificateless key encapsulation mechanism (KEM) in the standard model that is more efficient than the generic constructions proposed before by Huang and Wong \cite{DBLP:conf/acisp/HuangW07}. We use a direct construction from Kiltz and Galindo's KEM scheme \cite{DBLP:conf/acisp/KiltzG06} to obtain a certificateless KEM in the standard model; our construction is roughly twice as efficient as the generic construction. We also address the security flaw discovered by Selvi et al. \cite{cryptoeprint:2009:462}.

Certificateless key agreement in the standard 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 e$^2$CK 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.

Encryption schemes and key exchange protocols in the certificateless setting

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.

Lattice-based certificateless public-key encryption in the standard model

The notion of certificateless public-key encryption (CL-PKE) was introduced by Al-Riyami and Paterson in 2003 that avoids the drawbacks of both traditional PKI-based public-key encryption (i.e., establishing public-key infrastructure) and identity-based encryption (i.e., key escrow). So CL-PKE like identity-based encryption is certificate-free, and unlike identity-based encryption is key escrow-free. In this paper, we introduce simple and efficient CCA-secure CL-PKE based on (hierarchical) identity-based encryption. Our construction has both theoretical and practical interests. First, our generic transformation gives a new way of constructing CCA-secure CL-PKE. Second, instantiating our transformation using lattice-based primitives results in a more efficient CCA-secure CL-PKE than its counterpart introduced by Dent in 2008.