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.

Further observations on certificateless public key encryption

Certificateless public key encryption can be classified into two types, namely, CLE and CLE † , both of which were introduced by Al-Riyami and Paterson in Asiacrypt 2003. Most works about certificateless public key encryption belong to CLE, where the partial secret key is uniquely determined by an entity’s identity. In CLE † , an entity’s partial secret key is not only determined by the identity information but also by his/her (partial) public key. Such techniques can enhance the resilience of certificateless public key encryption against a cheating KGC. In this paper, we first formalize the security definitions of CLE † . After that, we demonstrate the gap between the security model of CLE † and CLE, by showing the insecurity of a CLE † scheme proposed by Lai and Kou in PKC 2007. We give an attack that can successfully break the indistinguishability of their CLE † scheme, although their scheme can be proved secure in the security model of CLE. Therefore, it does not suffice to consider the security of CLE † in the security model of CLE. Finally, we show how to secure Lai-Kou’s scheme by providing a new scheme with the security proof in the model of CLE †

Certificate-based signatures: New definitions and a generic construction from certificateless signatures

Certificate-based encryption was introduced in Eurocrypt’03 to solve the certificate management problem in public key encryption. Recently, this idea has been extended to certificate-based signatures. To date, several new schemes and security models of certificate-based signatures have been proposed. In this paper, we first introduce a new security model of certificate-based signatures. Our model is not only more elaborated when compared with the existing ones, but also defines several new types of adversaries in certificate-based signatures. We then investigate the relationship between certificate-based signatures and certificateless signatures, by proposing a generic construction of certificate-based signatures from certificateless signatures. Our generic construction is secure (in the random oracle model) under the security model defined in this paper, assuming the underlying certificateless signatures satisfying certain security notions.

A concrete certificateless signature scheme without pairings

Certificateless public key cryptography was introduced to avoid the inherent key escrow problem in identity-based cryptography, and eliminate the use of certificates in traditional PKI. Most cryptographic schemes in certificateless cryptography are built from bilinear mappings on elliptic curves which need costly operations. Despite the investigation of certificateless public key encryption without pairings, certificateless signature without pairings received much less attention than what it deserves. In this paper, we present a concrete pairing-free certificateless signature scheme for the first time. Our scheme is more computationally efficient than others built from pairings. The new scheme is provably secure in the random oracle model assuming the hardness of discrete logarithm problem.

Efficient and short certificateless signatures secure against realistic adversaries

The notion of certificateless cryptography is aimed to eliminate the use of certificates in traditional public key cryptography and also to solve the key-escrow problem in identity-based cryptography. Many kinds of security models have been designed for certificateless cryptography and many new schemes have been introduced based on the correspondence of the security models. In generally speaking, a stronger security model can ensure a certificateless cryptosystem with a higher security level, but a realistic model can lead to a more efficient scheme. In this paper, we focus on the efficiency of a certificateless signature (CLS) scheme and introduce an efficient CLS scheme with short signature size. On one hand, the security of the scheme is based on a realistic model. In this model, an adversary is not allowed to get any valid signature under false public keys. On the other hand, our scheme is as efficient as BLS short signature scheme in both communication and computation and, therefore, turns out to be more efficient than other CLS schemes proposed so far. We provide a rigorous security proof of our scheme in the random oracle model. The security of our scheme is based on the k-CAA hard problem and a new discovered hard problem, namely the modified k-CAA problem. Our scheme can be applied to systems where signatures are typed in by human or systems with low-bandwidth channels and/or low-computation power.

Certificateless ignatures: New schemes and security models

We present a study of security in certificateless signatures. We divide potential adversaries according to their attack power, and for the first time, three new kinds of adversaries are introduced into certificateless signatures. They are Normal Adversary, Strong Adversary and Super Adversary (ordered by their attack power). Combined with the known Type I Adversary and Type II Adversary in certificateless cryptography, we then define the security of certificateless signatures in different attack scenarios. Our new security models, together with others in the literature, provide a clear definition of the security in certificateless signatures. Two concrete schemes with different security levels are also proposed in this paper. The first scheme, which is proven secure (in the random oracle model) against Normal Type I and Super Type II adversaries, has the shortest signature length among all known certificateless signature schemes. The second scheme is secure (in the random oracle model) against Super Type I and Type II adversaries. Compared with another scheme that has a similar security level, our second scheme requires less operational cost but a little longer signature length. Two server-aided verification protocols are also proposed to reduce the verification cost on the verifier.