Bilinear Entropy Expansion from the Decisional Linear Assumption

We develop a technique inspired by pseudorandom functions that allows us to increase the entropy available for proving the security of dual system encryption schemes under the Decisional Linear Assumption. We show an application of the tool to Attribute-Based Encryption by presenting a Key-Policy ABE scheme that is fully-secure under DLIN with short public parameters

Attribute-Based Encryption Optimized for Cloud Computing

Abstract. In this work, we aim to make attribute-based encryption (ABE) more suitable for access control to data stored in the cloud. For this purpose, we concentrate on giving to the encryptor full control over the access rights, providing feasible key management even in case of multiple independent authorities, and enabling viable user revocation, which is essential in practice. Our main result is an extension of the decentralized CP-ABE scheme of Lewko and Waters [LW11] with identity-based user revocation. Our revocation system is made feasible by removing the computational burden of a revocation event from the cloud service provider, at the expense of some permanent, yet acceptable overhead of the encryption and decryption algorithms run by the users. Thus, the computation overhead is distributed over a potentially large number of users, instead of putting it on a single party (e.g., a proxy server), which would easily lead to a performance bottleneck. Besides describing our scheme, we also give a formal proof of its security in the generic bilinear group and random oracle models.

Special Libraries, June 1921

Volume 12, Issue 6https://scholarworks.sjsu.edu/sla_sl_1921/1005/thumbnail.jp

Unbounded Dynamic Predicate Compositions in Attribute-Based Encryption

We present several transformations that combine a set of attribute-based encryption (ABE) schemes for simpler predicates into a new ABE scheme for more expressive composed predicates. Previous proposals for predicate compositions of this kind, the most recent one being that of Ambrona et.al. at Crypto\u2717, can be considered static (or partially dynamic), meaning that the policy (or its structure) that specifies a composition must be fixed at the setup. Contrastingly, our transformations are dynamic and unbounded: they allow a user to specify an arbitrary and unbounded-size composition policy right into his/her own key or ciphertext. We propose transformations for three classes of composition policies, namely, the classes of any monotone span programs, any branching programs, and any deterministic finite automata. These generalized policies are defined over arbitrary predicates, hence admitting modular compositions. One application from modularity is a new kind of ABE for which policies can be ``nested\u27\u27 over ciphertext and key policies. As another application, we achieve the first fully secure completely unbounded key-policy ABE for non-monotone span programs, in a modular and clean manner, under the q-ratio assumption. Our transformations work inside a generic framework for ABE called symbolic pair encoding, proposed by Agrawal and Chase at Eurocrypt\u2717. At the core of our transformations, we observe and exploit an unbounded nature of the symbolic property so as to achieve unbounded-size policy compositions

Déjà Q all over again: Tighter and broader reductions of q-type assumptions

In this paper, we demonstrate that various cryptographic constructions—including ones for broadcast, attribute-based, and hierarchical identity-based encryption—can rely for security on only the static subgroup hiding assumption when instantiated in composite-order bilinear groups, as opposed to the dynamic q-type assumptions on which their security previously was based. This specific goal is accomplished by more generally extending the recent Déjà Q framework (Chase and Meiklejohn, Eurocrypt 2014) in two main directions. First, by teasing out common properties of existing reductions, we expand the q-type assumptions that can be covered by the framework; i.e., we demonstrate broader classes of assumptions that can be reduced to subgroup hiding. Second, while the original framework applied only to asymmetric composite-order bilinear groups, we provide a reduction to subgroup hiding that works in symmetric (as well as asymmetric) composite-order groups. As a bonus, our new reduction achieves a tightness of log(q) rather than q

Generic Transformations of Predicate Encodings: Constructions and Applications

Predicate encodings (Wee, TCC 2014; Chen, Gay, Wee, EUROCRYPT 2015), are symmetric primitives that can be used for building predicate encryption schemes. We give an algebraic characterization of the notion of privacy from predicate encodings, and explore several of its consequences. Specifically, we propose more efficient predicate encodings for boolean formulae and arithmetic span programs, and generic optimizations of predicate encodings. We define new constructions to build boolean combination of predicate encodings. We formalize the relationship between predicate encodings and pair encodings (Attrapadung, EUROCRYPT 2014), another primitive that can be transformed generically into predicate encryption schemes, and compare our constructions for boolean combinations of pair encodings with existing similar constructions from pair encodings. Finally, we demonstrate that our results carry to tag-based encodings (Kim, Susilo, Guo, and Au, SCN 2016)

Fully Key-Homomorphic Encryption, Arithmetic Circuit ABE and Compact Garbled Circuits

We construct the first (key-policy) attribute-based encryption (ABE) system with short secret keys: the size of keys in our system depends only on the depth of the policy circuit, not its size. Our constructions extend naturally to arithmetic circuits with arbitrary fan-in gates thereby further reducing the circuit depth. Building on this ABE system we obtain the first reusable circuit garbling scheme that produces garbled circuits whose size is the same as the original circuit plus an additive poly(λ,d) bits, where λ is the security parameter and d is the circuit depth. All previous constructions incurred a multiplicative poly(λ) blowup. We construct our ABE using a new mechanism we call fully key-homomorphic encryption, a public-key system that lets anyone translate a ciphertext encrypted under a public-key x into a ciphertext encrypted under the public-key (f(x),f) of the same plaintext, for any efficiently computable f. We show that this mechanism gives an ABE with short keys. Security of our construction relies on the subexponential hardness of the learning with errors problem. We also present a second (key-policy) ABE, using multilinear maps, with short ciphertexts: an encryption to an attribute vector x is the size of x plus poly(λ,d) additional bits. This gives a reusable circuit garbling scheme where the garbled input is short.United States. Defense Advanced Research Projects Agency (Grant FA8750-11-2-0225)Alfred P. Sloan Foundation (Sloan Research Fellowship

Tightly Secure Hierarchical Identity-Based Encryption

We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation

Leakage-Resilient Key Exchange and Two-Seed Extractors

Can Alice and Bob agree on a uniformly random secret key without having any truly secret randomness to begin with? Here we consider a setting where Eve can get partial leakage on the internal state of both Alice and Bob individually before the protocol starts. They then run a protocol using their states without any additional randomness and need to agree on a shared key that looks uniform to Eve, even after observing the leakage and the protocol transcript. We focus on non-interactive (one round) key exchange (NIKE), where Alice and Bob send one message each without waiting for one another. We first consider this problem in the symmetric-key setting, where the states of Alice and Bob include a shared secret as well as individual uniform randomness. However, since Eve gets leakage on these states, Alice and Bob need to perform privacy amplification to derive a fresh secret key from them. Prior solutions require Alice and Bob to sample fresh uniform randomness during the protocol, while in our setting all of their randomness was already part of their individual states a priori and was therefore subject to leakage. We show an information-theoretic solution to this problem using a novel primitive that we call a two-seed extractor, which we in turn construct by drawing a connection to communication-complexity lower-bounds in the number-on-forehead (NOF) model. We then turn to studying this problem in the public-key setting, where the states of Alice and Bob consist of independent uniform randomness. Unfortunately, we give a black-box separation showing that leakage-resilient NIKE in this setting cannot be proven secure via a black-box reduction under any game-based assumption when the leakage is super-logarithmic. This includes virtually all assumptions used in cryptography, and even very strong assumptions such as indistinguishability obfuscation (iO). Nevertheless, we also provide positive results that get around the above separation: - We show that every key exchange protocol (e.g., Diffie-Hellman) is secure when the leakage amount is logarithmic, or potentially even greater if we assume sub-exponential security without leakage. - We notice that the black-box separation does not extend to schemes in the common reference string (CRS) model, or to schemes with preprocessing, where Alice and Bob can individually pre-process their random coins to derive their secret state prior to leakage. We give a solution in the CRS model with preprocessing using bilinear maps. We also give solutions in just the CRS model alone (without preprocessing) or just with preprocessing (without a CRS), using iO and lossy functions