We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result – that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable. Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable. Lattice-based cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a public-key ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits. Unfortunately, our initial scheme is not quite bootstrappable – i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a server-aided cryptosystem.

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Abstract. Predicate encryption is a new paradigm generalizing, among other things, identity-based encryption. In a predicate encryption scheme, secret keys correspond to predicates and ciphertexts are associated with attributes; the secret key SKf corresponding to a predicate f can be used to decrypt a ciphertext associated with attribute I if and only if f(I) = 1. Constructions of such schemes are currently known for relatively few classes of predicates. We construct such a scheme for predicates corresponding to the evaluation of inner products over ZN (for some large integer N). This, in turn, enables constructions in which predicates correspond to the evaluation of disjunctions, polynomials, CNF/DNF formulae, or threshold predicates (among others). Besides serving as a significant step forward in the theory of predicate encryption, our results lead to a number of applications that are interesting in their own right. 1

In this paper, we present two fully secure functional encryption schemes. Our first result is a fully secure attribute-based encryption (ABE) scheme. Previous constructions of ABE were only proven to be selectively secure. We achieve full security by adapting the dual system encryption methodology recently introduced by Waters and previously leveraged to obtain fully secure IBE and HIBE systems. The primary challenge in applying dual system encryption to ABE is the richer structure of keys and ciphertexts. In an IBE or HIBE system, keys and ciphertexts are both associated with the same type of simple object: identities. In an ABE system, keys and ciphertexts are associated with more complex objects: attributes and access formulas. We use a novel information-theoretic argument to adapt the dual system encryption methodology to the more complicated structure of ABE systems. We construct our system in composite order bilinear groups, where the order is a product of three primes. We prove the security of our system from three static assumptions. Our ABE scheme supports arbitrary monotone access formulas. Our second result is a fully secure (attribute-hiding) predicate encryption (PE) scheme

Non-interactive zero-knowledge proofs and non-interactive witness-indistinguishable proofs have played a significant role in the theory of cryptography. However, lack of efficiency has prevented them from being used in practice. One of the roots of this inefficiency is that non-interactive zero-knowledge proofs have been constructed for general NP-complete languages such as Circuit Satisfiability, causing an expensive blowup in the size of the statement when reducing it to a circuit. The contribution of this paper is a general methodology for constructing very simple and efficient non-interactive zero-knowledge proofs and non-interactive witness-indistinguishable proofs that work directly for groups with a bilinear map, without needing a reduction to Circuit Satisfiability. Groups with bilinear maps have enjoyed tremendous success in the field of cryptography in recent years and have been used to construct a plethora of protocols. This paper provides non-interactive witnessindistinguishable proofs and non-interactive zero-knowledge proofs that can be used in connection with these protocols. Our goal is to spread the use of non-interactive cryptographic proofs from mainly theoretical purposes to the large class of practical cryptographic protocols based on bilinear groups.

We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of “short vector problems ” on arbitrary lattices. Our construction improves on previous works in two aspects: 1. We show that “somewhat homomorphic” encryption can be based on LWE, using a new relinearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. 2. We deviate from the “squashing paradigm” used in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the ciphertexts and reduces the decryption complexity of our scheme, without introducing additional assumptions. Our scheme has very short ciphertexts and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is k · polylog(k) + log |DB | bits per single-bit query (here, k is a security parameter).

Secure two-party computation allows two untrusting parties to jointly compute an arbitrary function on their respective private inputs while revealing no information beyond the outcome. Existing cryptographic compilers can automatically generate secure computation protocols from high-level specifications, but are often limited in their use and efficiency of generated protocols as they are based on either garbled circuits or (additively) homomorphic encryption only. In this paper we present TASTY, a novel tool for automating, i.e., describing, generating, executing, benchmarking, and comparing, efficient secure two-party computation protocols. TASTY is a new compiler that can generate protocols based on homomorphic encryption and efficient garbled circuits as well as combinations of both, which often yields the most efficient protocols available today. The user provides a high-level description of the computations to be performed on encrypted data in a domain-specific language. This is automatically transformed into a protocol. TASTY provides most recent techniques and optimizations for practical secure two-party computation with low online latency. Moreover, it allows to efficiently evaluate circuits generated by the well-known Fairplay compiler. We use TASTY to compare protocols for secure multiplication based on homomorphic encryption with those based on garbled circuits and highly efficient Karatsuba multiplication. Further, we show how TASTY improves the online latency for securely evaluating the AES functionality by an order of magnitude compared to previous software implementations. TASTY allows to automatically generate efficient secure protocols for many privacy-preserving applications where we consider the use cases for private set intersection and face recognition protocols.

Non-interactive zero-knowledge proofs play an essential role in many cryptographic protocols. We suggest several NIZK proof systems based on prime order groups with a bilinear map. We obtain linear size proofs for relations among group elements without going through an expensive reduction to an NP-complete language such as Circuit Satisfiability. Security of all our constructions is based on the decisional linear assumption. The NIZK proof system is quite general and has many applications such as digital signatures, verifiable encryption and group signatures. We focus on the latter and get the first group signature scheme satisfying the strong security definition of Bellare, Shi and Zhang [7] in the standard model without random oracles where each group signature consists only of a constant number of group elements. We also suggest a simulation-sound NIZK proof of knowledge, which is much more efficient than previous constructions in the literature. Caveat: The constants are large, and therefore our schemes are not practical. Nonetheless, we find it very interesting for the first time to have NIZK proofs and group signatures that except for a constant factor are optimal without using the random oracle model to argue security.

Abstract. The prospect of outsourcing an increasing amount of data storage and management to cloud services raises many new privacy concerns for individuals and businesses alike. The privacy concerns can be satisfactorily addressed if users encrypt the data they send to the cloud. If the encryption scheme is homomorphic, the cloud can still perform meaningful computations on the data, even though it is encrypted. In fact, we now know a number of constructions of fully homomorphic encryption schemes that allow arbitrary computation on encrypted data. In the last two years, solutions for fully homomorphic encryption have been proposed and improved upon, but it is hard to ignore the elephant in the room, namely efficiency – can homomorphic encryption ever be efficient enough to be practical? Certainly, it seems that all known fully homomorphic encryption schemes have a long way to go before they can be used in practice. Given this state of affairs, our contribution is two-fold. First, we exhibit a number of real-world applications, in the medical, financial, and the advertising domains, which require only that the encryption scheme is “somewhat ” homomorphic. Somewhat homomorphic encryption schemes, which support a limited number of homomorphic operations, can be much faster, and more compact than fully homomorphic encryption schemes. Secondly, we show a proof-of-concept implementation of the recent somewhat homomorphic encryption scheme of Brakerski and Vaikuntanathan, whose security relies on the “ring learning with errors ” (Ring LWE) problem. The system is very efficient, and has reasonably short ciphertexts. Our unoptimized implementation in magma enjoys comparable efficiency to even optimized pairing-based schemes with the same level of security and homomorphic capacity. We also show a number of application-specific optimizations to the encryption scheme, most notably the ability to convert between different message encodings in a ciphertext.

We construct a fully secure HIBE scheme with short ciphertexts. The previous construction of Boneh, Boyen, and Goh was only proven to be secure in the selective model, under a non-static assumption which depended on the depth of the hierarchy. To obtain full security, we apply the dual system encryption concept recently introduced by Waters. A straightforward application of this technique is insufficient to achieve short ciphertexts, since the original instantiation of the technique includes tags that do not compress. To overcome this challenge, we design a new method for realizing dual system encryption. We provide a system in composite order groups (of three primes) and prove the security of our scheme under three static assumptions.