Short signature without random oracles and the SDH assumption in bilinear groups

We describe a short signature scheme that is strongly existentially unforgeable under an adaptive chosen message attack in the standard security model. Our construction works in groups equipped with an efficient bilinear map, or, more generally, an algorithm for the Decision Diffie-Hellman problem. The security of our scheme depends on a new intractability assumption we call Strong Diffie-Hellman (SDH), by analogy to the Strong RSA assumption with which it shares many properties. Signature generation in our system is fast and the resulting signatures are as short as DSA signatures for comparable security. We give a tight reduction proving that our scheme is secure in any group in which the SDH assumption holds, without relying on the random oracle model.

Secure universal designated verifier signature without random oracles

In Asiacrypt 2003, the concept of universal designated verifier signature (UDVS) was introduced by Steinfeld, Bull, Wang and Pieprzyk. In the new paradigm, any signature holder (not necessarily the signer) can designate the publicly verifiable signature to any desired designated verifier (using the verifier’s public key), such that only the designated verifier can believe that the signature holder does have a valid publicly verifiable signature, and hence, believes that the signer has signed the message. Any other third party cannot believe this fact because this verifier can use his secret key to create a valid UDVS which is designated to himself. In ACNS 2005, Zhang, Furukawa and Imai proposed the first UDVS scheme without random oracles. In this paper, we give a security analysis to the scheme of Zhang et al. and propose a novel UDVS scheme without random oracles based on Waters’ signature scheme, and prove that our scheme is secure under the Gap Bilinear Diffie Hellman assumption

Password Based Server Aided Key Exchange

We propose a new password-based 3-party protocol with a formal security proof in the standard model. Under reasonable assumptions we show that our new protocol is more efficient than the recent protocol of Abdalla and Pointcheval (FC 2005), proven in the random oracle model. We also observe some limitations in the model due to Abdalla, Fouque and Pointcheval (PKC 2005) for proving security of such protocols.

Universally composable contributory group key exchange

We treat the security of group key exchange (GKE) in the universal composability (UC) framework. Analyzing GKE protocols in the UC framework naturally addresses attacks by malicious insiders. We define an ideal functionality for GKE that captures contributiveness in addition to other desired security goals. We show that an efficient two-round protocol securely realizes the proposed functionality in the random oracle model. As a result, we obtain the most efficient UC-secure contributory GKE protocol known.

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 one-round key exchange in the standard model

We consider one-round key exchange protocols secure in the standard model. The security analysis uses the powerful security model of Canetti and Krawczyk and a natural extension of it to the ID-based setting. It is shown how KEMs can be used in a generic way to obtain two different protocol designs with progressively stronger security guarantees. A detailed analysis of the performance of the protocols is included; surprisingly, when instantiated with specific KEM constructions, the resulting protocols are competitive with the best previous schemes that have proofs only in the random oracle model.

Efficient one-round key exchange in the efficient one-round key exchange in the standard model

We consider one-round key exchange protocols secure in the standard model. The security analysis uses the powerful security model of Canetti and Krawczyk and a natural extension of it to the ID-based setting. It is shown how KEMs can be used in a generic way to obtain two different protocol designs with progressively stronger security guarantees. A detailed analysis of the performance of the protocols is included; surprisingly, when instantiated with specific KEM constructions, the resulting protocols are competitive with the best previous schemes that have proofs only in the random oracle model.

Efficient one-round key exchange in the standard model

We consider one-round key exchange protocols secure in the standard model. The security analysis uses the powerful security model of Canetti and Krawczyk and a natural extension of it to the ID-based setting. It is shown how KEMs can be used in a generic way to obtain two different protocol designs with progressively stronger security guarantees. A detailed analysis of the performance of the protocols is included; surprisingly, when instantiated with specific KEM constructions, the resulting protocols are competitive with the best previous schemes that have proofs only in the random oracle model.

Attribute-based authenticated key exchange

We introduce the concept of attribute-based authenticated key exchange (AB-AKE) within the framework of ciphertext policy attribute-based systems. A notion of AKE-security for AB-AKE is presented based on the security models for group key exchange protocols and also taking into account the security requirements generally considered in the ciphertext policy attribute-based setting. We also extend the paradigm of hybrid encryption to the ciphertext policy attribute-based encryption schemes. A new primitive called encapsulation policy attribute-based key encapsulation mechanism (EP-AB-KEM) is introduced and a notion of chosen ciphertext security is de�ned for EP-AB-KEMs. We propose an EP-AB-KEM from an existing attribute-based encryption scheme and show that it achieves chosen ciphertext security in the generic group and random oracle models. We present a generic one-round AB-AKE protocol that satis�es our AKE-security notion. The protocol is generically constructed from any EP-AB-KEM that satis�es chosen ciphertext security. Instantiating the generic AB-AKE protocol with our EP-AB-KEM will result in a concrete one-round AB-AKE protocol also secure in the generic group and random oracle models.

Design and analysis of group key exchange protocols

A group key exchange (GKE) protocol allows a set of parties to agree upon a common secret session key over a public network. In this thesis, we focus on designing efficient GKE protocols using public key techniques and appropriately revising security models for GKE protocols. For the purpose of modelling and analysing the security of GKE protocols we apply the widely accepted computational complexity approach. The contributions of the thesis to the area of GKE protocols are manifold. We propose the first GKE protocol that requires only one round of communication and is proven secure in the standard model. Our protocol is generically constructed from a key encapsulation mechanism (KEM). We also suggest an efficient KEM from the literature, which satisfies the underlying security notion, to instantiate the generic protocol. We then concentrate on enhancing the security of one-round GKE protocols. A new model of security for forward secure GKE protocols is introduced and a generic one-round GKE protocol with forward security is then presented. The security of this protocol is also proven in the standard model. We also propose an efficient forward secure encryption scheme that can be used to instantiate the generic GKE protocol. Our next contributions are to the security models of GKE protocols. We observe that the analysis of GKE protocols has not been as extensive as that of two-party key exchange protocols. Particularly, the security attribute of key compromise impersonation (KCI) resilience has so far been ignored for GKE protocols. We model the security of GKE protocols addressing KCI attacks by both outsider and insider adversaries. We then show that a few existing protocols are not secure against KCI attacks. A new proof of security for an existing GKE protocol is given under the revised model assuming random oracles. Subsequently, we treat the security of GKE protocols in the universal composability (UC) framework. We present a new UC ideal functionality for GKE protocols capturing the security attribute of contributiveness. An existing protocol with minor revisions is then shown to realize our functionality in the random oracle model. Finally, we explore the possibility of constructing GKE protocols in the attribute-based setting. We introduce the concept of attribute-based group key exchange (AB-GKE). A security model for AB-GKE and a one-round AB-GKE protocol satisfying our security notion are presented. The protocol is generically constructed from a new cryptographic primitive called encapsulation policy attribute-based KEM (EP-AB-KEM), which we introduce in this thesis. We also present a new EP-AB-KEM with a proof of security assuming generic groups and random oracles. The EP-AB-KEM can be used to instantiate our generic AB-GKE protocol.

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.

Towards a provably secure DoS-Resilient key exchange protocol with perfect forward secrecy

Just Fast Keying (JFK) is a simple, efficient and secure key exchange protocol proposed by Aiello et al. (ACM TISSEC, 2004). JFK is well known for its novel design features, notably its resistance to denial-of-service (DoS) attacks. Using Meadows’ cost-based framework, we identify a new DoS vulnerability in JFK. The JFK protocol is claimed secure in the Canetti-Krawczyk model under the Decisional Diffie-Hellman (DDH) assumption. We show that security of the JFK protocol, when reusing ephemeral Diffie-Hellman keys, appears to require the Gap Diffie-Hellman (GDH) assumption in the random oracle model. We propose a new variant of JFK that avoids the identified DoS vulnerability and provides perfect forward secrecy even under the DDH assumption, achieving the full security promised by the JFK protocol.

Practical client puzzles in the standard model

Client puzzles are cryptographic problems that are neither easy nor hard to solve. Most puzzles are based on either number theoretic or hash inversions problems. Hash-based puzzles are very efficient but so far have been shown secure only in the random oracle model; number theoretic puzzles, while secure in the standard model, tend to be inefficient. In this paper, we solve the problem of constucting cryptographic puzzles that are secure int he standard model and are very efficient. We present an efficient number theoretic puzzle that satisfies the puzzle security definition of Chen et al. (ASIACRYPT 2009). To prove the security of our puzzle, we introduce a new variant of the interval discrete logarithm assumption which may be of independent interest, and show this new problem to be hard under reasonable assumptions. Our experimental results show that, for 512-bit modulus, the solution verification time of our proposed puzzle can be up to 50x and 89x faster than the Karame-Capkum puzzle and the Rivest et al.'s time-lock puzzle respectively. In particular, the solution verification tiem of our puzzle is only 1.4x slower than that of Chen et al.'s efficient hash based puzzle.

Computationally sound automated proofs of cryptographic schemes

Proving security of cryptographic schemes, which normally are short algorithms, has been known to be time-consuming and easy to get wrong. Using computers to analyse their security can help to solve the problem. This thesis focuses on methods of using computers to verify security of such schemes in cryptographic models. The contributions of this thesis to automated security proofs of cryptographic schemes can be divided into two groups: indirect and direct techniques. Regarding indirect ones, we propose a technique to verify the security of public-key-based key exchange protocols. Security of such protocols has been able to be proved automatically using an existing tool, but in a noncryptographic model. We show that under some conditions, security in that non-cryptographic model implies security in a common cryptographic one, the Bellare-Rogaway model [11]. The implication enables one to use that existing tool, which was designed to work with a different type of model, in order to achieve security proofs of public-key-based key exchange protocols in a cryptographic model. For direct techniques, we have two contributions. The first is a tool to verify Diffie-Hellmanbased key exchange protocols. In that work, we design a simple programming language for specifying Diffie-Hellman-based key exchange algorithms. The language has a semantics based on a cryptographic model, the Bellare-Rogaway model [11]. From the semantics, we build a Hoare-style logic which allows us to reason about the security of a key exchange algorithm, specified as a pair of initiator and responder programs. The other contribution to the direct technique line is on automated proofs for computational indistinguishability. Unlike the two other contributions, this one does not treat a fixed class of protocols. We construct a generic formalism which allows one to model the security problem of a variety of classes of cryptographic schemes as the indistinguishability between two pieces of information. We also design and implement an algorithm for solving indistinguishability problems. Compared to the two other works, this one covers significantly more types of schemes, but consequently, it can verify only weaker forms of security.