Efficient selective identity-based encryption without random oracles

We construct two efficient Identity-Based Encryption (IBE) systems that admit selective-identity security reductions without random oracles in groups equipped with a bilinear map. Selective-identity secure IBE is a slightly weaker security model than the standard security model for IBE. In this model the adversary must commit ahead of time to the identity that it intends to attack, whereas in an adaptive-identity attack the adversary is allowed to choose this identity adaptively. Our first system—BB1—is based on the well studied decisional bilinear Diffie–Hellman assumption, and extends naturally to systems with hierarchical identities, or HIBE. Our second system—BB2—is based on a stronger assumption which we call the Bilinear Diffie–Hellman Inversion assumption and provides another approach to building IBE systems. Our first system, BB1, is very versatile and well suited for practical applications: the basic hierarchical construction can be efficiently secured against chosen-ciphertext attacks, and further extended to support efficient non-interactive threshold decryption, among others, all without using random oracles. Both systems, BB1 and BB2, can be modified generically to provide “full” IBE security (i.e., against adaptive-identity attacks), either using random oracles, or in the standard model at the expense of a non-polynomial but easy-to-compensate security reduction.

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.

From Selective-ID to Full-ID IBS without Random Oracles

Since its induction, the selective-identity (sID) model for identity-based cryptosystems and its relationship with various other notions of security has been extensively studied. As a result, it is a general consensus that the sID model is much weaker than the full-identity (ID) model. In this paper, we study the sID model for the particular case of identity-based signatures (IBS). The main focus is on the problem of constructing an ID-secure IBS given an sID-secure IBS without using random oracles-the so-called standard model-and with reasonable security degradation. We accomplish this by devising a generic construction which uses as black-box: i) a chameleon hash function and ii) a weakly-secure public-key signature. We argue that the resulting IBS is ID-secure but with a tightness gap of O(q(s)), where q(s) is the upper bound on the number of signature queries that the adversary is allowed to make. To the best of our knowledge, this is the first attempt at such a generic construction.

Modeling key compromise impersonation attacks on group key exchange protocols

A key exchange protocol allows a set of parties to agree upon a secret session key over a public network. Two-party key exchange (2PKE) protocols have been rigorously analyzed under various models considering different adversarial actions. However, the analysis of group key exchange (GKE) protocols has not been as extensive as that of 2PKE protocols. Particularly, the security attribute of key compromise impersonation (KCI) resilience has so far been ignored for the case of GKE protocols. We first 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 even against outsider KCI attacks. The attacks on these protocols demonstrate the necessity of considering KCI resilience for GKE protocols. Finally, we give a new proof of security for an existing GKE protocol under the revised model assuming random oracles.

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.

Automated proof for formal indistinguishability and its applications

Bana et al. proposed the relation formal indistinguishability (FIR), i.e. an equivalence between two terms built from an abstract algebra. Later Ene et al. extended it to cover active adversaries and random oracles. This notion enables a framework to verify computational indistinguishability while still offering the simplicity and formality of symbolic methods. We are in the process of making an automated tool for checking FIR between two terms. First, we extend the work by Ene et al. further, by covering ordered sorts and simplifying the way to cope with random oracles. Second, we investigate the possibility of combining algebras together, since it makes the tool scalable and able to cover a wide class of cryptographic schemes. Specially, we show that the combined algebra is still computationally sound, as long as each algebra is sound. Third, we design some proving strategies and implement the tool. Basically, the strategies allow us to find a sequence of intermediate terms, which are formally indistinguishable, between two given terms. FIR between the two given terms is then guaranteed by the transitivity of FIR. Finally, we show applications of the work, e.g. on key exchanges and encryption schemes. In the future, the tool should be extended easily to cover many schemes. This work continues previous research of ours on use of compilers to aid in automated proofs for key exchange.

Modeling key compromise impersonation attacks on group key exchange protocols

Two-party key exchange (2PKE) protocols have been rigorously analyzed under various models considering different adversarial actions. However, the analysis of group key exchange (GKE) protocols has not been as extensive as that of 2PKE protocols. Particularly, an important security attribute called key compromise impersonation (KCI) resilience has been completely ignored for the case of GKE protocols. Informally, a protocol is said to provide KCI resilience if the compromise of the long-term secret key of a protocol participant A does not allow the adversary to impersonate an honest participant B to A. In this paper, we argue that KCI resilience for GKE protocols is at least as important as it is for 2PKE protocols. Our first contribution is revised definitions of security for GKE protocols considering KCI attacks by both outsider and insider adversaries. We also give a new proof of security for an existing two-round GKE protocol under the revised security definitions assuming random oracles. We then show how to achieve insider KCIR in a generic way using a known compiler in the literature. As one may expect, this additional security assurance comes at the cost of an extra round of communication. Finally, we show that a few existing protocols are not secure against outsider KCI attacks. The attacks on these protocols illustrate the necessity of considering KCI resilience for GKE protocols.

Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE

We present a technique for delegating a short lattice basis that has the advantage of keeping the lattice dimension unchanged upon delegation. Building on this result, we construct two new hierarchical identity-based encryption (HIBE) schemes, with and without random oracles. The resulting systems are very different from earlier lattice-based HIBEs and in some cases result in shorter ciphertexts and private keys. We prove security from classic lattice hardness assumptions.

Parallel authentication and public-key encryption

A parallel authentication and public-key encryption is introduced and exemplified on joint encryption and signing which compares favorably with sequential Encrypt-then-Sign (ɛtS) or Sign-then-Encrypt (Stɛ) schemes as far as both efficiency and security are concerned. A security model for signcryption, and thus joint encryption and signing, has been recently defined which considers possible attacks and security goals. Such a scheme is considered secure if the encryption part guarantees indistinguishability and the signature part prevents existential forgeries, for outsider but also insider adversaries. We propose two schemes of parallel signcryption, which are efficient alternative to Commit-then-Sign-and- Encrypt (Ct&G3&S). They are both provably secure in the random oracle model. The first one, called generic parallel encrypt and sign, is secure if the encryption scheme is semantically secure against chosen-ciphertext attacks and the signature scheme prevents existential forgeries against random-message attacks. The second scheme, called optimal parallel encrypt. and sign, applies random oracles similar to the OAEP technique in order to achieve security using encryption and signature components with very weak security requirements — encryption is expected to be one-way under chosen-plaintext attacks while signature needs to be secure against universal forgeries under random-plaintext attack, that is actually the case for both the plain-RSA encryption and signature under the usual RSA assumption. Both proposals are generic in the sense that any suitable encryption and signature schemes (i.e. which simply achieve required security) can be used. Furthermore they allow both parallel encryption and signing, as well as parallel decryption and verification. Properties of parallel encrypt and sign schemes are considered and a new security standard for parallel signcryption is proposed.

A Closer Look at Multiple Forking: Leveraging (In)Dependence for a Tighter Bound

Boldyreva, Palacio and Warinschi introduced a multiple forking game as an extension of general forking. The notion of (multiple) forking is a useful abstraction from the actual simulation of cryptographic scheme to the adversary in a security reduction, and is achieved through the intermediary of a so-called wrapper algorithm. Multiple forking has turned out to be a useful tool in the security argument of several cryptographic protocols. However, a reduction employing multiple forking incurs a significant degradation of , where denotes the upper bound on the underlying random oracle calls and , the number of forkings. In this work we take a closer look at the reasons for the degradation with a tighter security bound in mind. We nail down the exact set of conditions for success in the multiple forking game. A careful analysis of the cryptographic schemes and corresponding security reduction employing multiple forking leads to the formulation of `dependence' and `independence' conditions pertaining to the output of the wrapper in different rounds. Based on the (in)dependence conditions we propose a general framework of multiple forking and a General Multiple Forking Lemma. Leveraging (in)dependence to the full allows us to improve the degradation factor in the multiple forking game by a factor of . By implication, the cost of a single forking involving two random oracles (augmented forking) matches that involving a single random oracle (elementary forking). Finally, we study the effect of these observations on the concrete security of existing schemes employing multiple forking. We conclude that by careful design of the protocol (and the wrapper in the security reduction) it is possible to harness our observations to the full extent.

Cryptographic Tamper Evidence

We propose a new notion of cryptographic tamper evidence. A tamper-evident signature scheme provides an additional procedure Div which detects tampering: given two signatures, Div can determine whether one of them was generated by the forger. Surprisingly, this is possible even after the adversary has inconspicuously learned (exposed) some-or even all-the secrets in the system. In this case, it might be impossible to tell which signature is generated by the legitimate signer and which by the forger. But at least the fact of the tampering will be made evident. We define several variants of tamper-evidence, differing in their power to detect tampering. In all of these, we assume an equally powerful adversary: she adaptively controls all the inputs to the legitimate signer (i.e., all messages to be signed and their timing), and observes all his outputs; she can also adaptively expose all the secrets at arbitrary times. We provide tamper-evident schemes for all the variants and prove their optimality. Achieving the strongest tamper evidence turns out to be provably expensive. However, we define a somewhat weaker, but still practical, variant: α-synchronous tamper-evidence (α-te) and provide α-te schemes with logarithmic cost. Our α-te schemes use a combinatorial construction of α-separating sets, which might be of independent interest. We stress that our mechanisms are purely cryptographic: the tamper-detection algorithm Div is stateless and takes no inputs except the two signatures (in particular, it keeps no logs), we use no infrastructure (or other ways to conceal additional secrets), and we use no hardware properties (except those implied by the standard cryptographic assumptions, such as random number generators). Our constructions are based on arbitrary ordinary signature schemes and do not require random oracles.