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.

Functional encryption for threshold functions (or fuzzy IBE) from lattices

Cryptosystems based on the hardness of lattice problems have recently acquired much importance due to their average-case to worst-case equivalence, their conjectured resistance to quantum cryptanalysis, their ease of implementation and increasing practicality, and, lately, their promising potential as a platform for constructing advanced functionalities. In this work, we construct “Fuzzy” Identity Based Encryption from the hardness of the Learning With Errors (LWE) problem. We note that for our parameters, the underlying lattice problems (such as gapSVP or SIVP) are assumed to be hard to approximate within supexponential factors for adversaries running in subexponential time. We give CPA and CCA secure variants of our construction, for small and large universes of attributes. All our constructions are secure against selective-identity attacks in the standard model. Our construction is made possible by observing certain special properties that secret sharing schemes need to satisfy in order to be useful for Fuzzy IBE. We also discuss some obstacles towards realizing lattice-based attribute-based encryption (ABE).

Bitter to better - how to make bitcoin a better currency

Bitcoin is a distributed digital currency which has attracted a substantial number of users. We perform an in-depth investigation to understand what made Bitcoin so successful, while decades of research on cryptographic e-cash has not lead to a large-scale deployment. We ask also how Bitcoin could become a good candidate for a long-lived stable currency. In doing so, we identify several issues and attacks of Bitcoin, and propose suitable techniques to address them.

Kamouflage : loss-resistant password management

We introduce Kamouflage: a new architecture for building theft-resistant password managers. An attacker who steals a laptop or cell phone with a Kamouflage-based password manager is forced to carry out a considerable amount of online work before obtaining any user credentials. We implemented our proposal as a replacement for the built-in Firefox password manager, and provide performance measurements and the results from experiments with large real-world password sets to evaluate the feasibility and effectiveness of our approach. Kamouflage is well suited to become a standard architecture for password managers on mobile devices.

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.

Shrinking the keys of discrete-log-type lossy trapdoor functions

To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(λ 2) group elements for a reduction from the decisional Diffie-Hellman assumption (where λ is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(λ) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption. Our first construction achieves this result at the expense of a long common reference string of Θ(λ 2) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(λ), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction. The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.

Efficient lattice (H)IBE in the standard model

We construct an efficient identity based encryption system based on the standard learning with errors (LWE) problem. Our security proof holds in the standard model. The key step in the construction is a family of lattices for which there are two distinct trapdoors for finding short vectors. One trapdoor enables the real system to generate short vectors in all lattices in the family. The other trapdoor enables the simulator to generate short vectors for all lattices in the family except for one. We extend this basic technique to an adaptively-secure IBE and a Hierarchical IBE.

Preventing pollution attacks in multi-source network coding

Network coding is a method for achieving channel capacity in networks. The key idea is to allow network routers to linearly mix packets as they traverse the network so that recipients receive linear combinations of packets. Network coded systems are vulnerable to pollution attacks where a single malicious node floods the network with bad packets and prevents the receiver from decoding correctly. Cryptographic defenses to these problems are based on homomorphic signatures and MACs. These proposals, however, cannot handle mixing of packets from multiple sources, which is needed to achieve the full benefits of network coding. In this paper we address integrity of multi-source mixing. We propose a security model for this setting and provide a generic construction.

Lattice mixing and vanishing trapdoors : a framework for fully secure short signatures and more

We propose a framework for adaptive security from hard random lattices in the standard model. Our approach borrows from the recent Agrawal-Boneh-Boyen families of lattices, which can admit reliable and punctured trapdoors, respectively used in reality and in simulation. We extend this idea to make the simulation trapdoors cancel not for a specific forgery but on a non-negligible subset of the possible challenges. Conceptually, we build a compactly representable, large family of input-dependent “mixture” lattices, set up with trapdoors that “vanish” for a secret subset which we hope the forger will target. Technically, we tweak the lattice structure to achieve “naturally nice” distributions for arbitrary choices of subset size. The framework is very general. Here we obtain fully secure signatures, and also IBE, that are compact, simple, and elegant.

Strong cryptography from weak secrets

Distributed-password public-key cryptography (DPwPKC) allows the members of a group of people, each one holding a small secret password only, to help a leader to perform the private operation, associated to a public-key cryptosystem. Abdalla et al. recently defined this tool [1], with a practical construction. Unfortunately, the latter applied to the ElGamal decryption only, and relied on the DDH assumption, excluding any recent pairing-based cryptosystems. In this paper, we extend their techniques to support, and exploit, pairing-based properties: we take advantage of pairing-friendly groups to obtain efficient (simulation-sound) zero-knowledge proofs, whose security relies on the Decisional Linear assumption. As a consequence, we provide efficient protocols, secure in the standard model, for ElGamal decryption as in [1], but also for Linear decryption, as well as extraction of several identity-based cryptosystems [6,4]. Furthermore, we strenghten their security model by suppressing the useless testPwd queries in the functionality.

HPAKE : Password authentication secure against cross-site user impersonation

We propose a new kind of asymmetric mutual authentication from passwords with stronger privacy against malicious servers, lest they be tempted to engage in “cross-site user impersonation” to each other. It enables a person to authenticate (with) arbitrarily many independent servers, over adversarial channels, using a memorable and reusable single short password. Beside the usual PAKE security guarantees, our framework goes to lengths to secure the password against brute-force cracking from privileged server information.

Distributed public-key cryptography from weak secrets

We introduce the notion of distributed password-based public-key cryptography, where a virtual high-entropy private key is implicitly defined as a concatenation of low-entropy passwords held in separate locations. The users can jointly perform private-key operations by exchanging messages over an arbitrary channel, based on their respective passwords, without ever sharing their passwords or reconstituting the key. Focusing on the case of ElGamal encryption as an example, we start by formally defining ideal functionalities for distributed public-key generation and virtual private-key computation in the UC model. We then construct efficient protocols that securely realize them in either the RO model (for efficiency) or the CRS model (for elegance). We conclude by showing that our distributed protocols generalize to a broad class of “discrete-log”-based public-key cryptosystems, which notably includes identity-based encryption. This opens the door to a powerful extension of IBE with a virtual PKG made of a group of people, each one memorizing a small portion of the master key.

Hidden credential retrieval from a reusable password

We revisit the venerable question of access credentials management, which concerns the techniques that we, humans with limited memory, must employ to safeguard our various access keys and tokens in a connected world. Although many existing solutions can be employed to protect a long secret using a short password, those solutions typically require certain assumptions on the distribution of the secret and/or the password, and are helpful against only a subset of the possible attackers. After briefly reviewing a variety of approaches, we propose a user-centric comprehensive model to capture the possible threats posed by online and offline attackers, from the outside and the inside, against the security of both the plaintext and the password. We then propose a few very simple protocols, adapted from the Ford-Kaliski server-assisted password generator and the Boldyreva unique blind signature in particular, that provide the best protection against all kinds of threats, for all distributions of secrets. We also quantify the concrete security of our approach in terms of online and offline password guesses made by outsiders and insiders, in the random-oracle model. The main contribution of this paper lies not in the technical novelty of the proposed solution, but in the identification of the problem and its model. Our results have an immediate and practical application for the real world: they show how to implement single-sign-on stateless roaming authentication for the internet, in a ad-hoc user-driven fashion that requires no change to protocols or infrastructure.

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.

The uber-assumption family

We offer an exposition of Boneh, Boyen, and Goh’s “uber-assumption” family for analyzing the validity and strength of pairing assumptions in the generic-group model, and augment the original BBG framework with a few simple but useful extensions.