No abstract

No abstract

Abstract. We address the problem in which a client stores a large amount of data with an untrusted server in such a way that, at any moment, the client can ask the server to compute a function on some portion of its outsourced data. In this scenario, the client must be able to efficiently verify the correctness of the result despite no longer knowing the inputs of the delegated computation, it must be able to keep adding elements to its remote storage, and it does not have to fix in advance (i.e., at data outsourcing time) the functions that it will delegate. Even more ambitiously, clients should be able to verify in time independent of the input-size -a very appealing property for computations over huge amounts of data.In this work we propose novel cryptographic techniques that solve the above problem for the class of computations of quadratic polynomials over a large number of variables. This class covers a wide range of significant arithmetic computations -notably, many important statistics. To confirm the efficiency of our solution, we show encouraging performance results, e.g., correctness proofs have size below 1 kB and are verifiable by clients in less than 10 milliseconds.

Abstract. We put forward the study of a new primitive that we call Vector Commitment (VC, for short). Informally, VCs allow to commit to an ordered sequence of q values (m1, . . . , mq) in such a way that one can later open the commitment at specific positions (e.g., prove that mi is the i-th committed message). For security, Vector Commitments are required to satisfy a notion that we call position binding which states that an adversary should not be able to open a commitment to two different values at the same position. Moreover, what makes our primitive interesting is that we require VCs to be concise, i.e. the size of the commitment string and of its openings has to be independent of the vector length. We show two realizations of VCs based on standard and well established assumptions, such as RSA, and Computational Diffie-Hellman (in bilinear groups). Next, we turn our attention to applications and we show that Vector Commitments are useful in a variety of contexts, as they allow for compact and efficient solutions which significantly improve previous works either in terms of efficiency of the resulting solutions, or in terms of "quality" of the underlying assumption, or both. These applications include: Verifiable Databases with Efficient Updates, Updatable Zero-Knowledge Databases, and Universal Dynamic Accumulators.

Abstract. Homomorphic message authenticators allow the holder of a (public) evaluation key to perform computations over previously authenticated data, in such a way that the produced tag σ can be used to certify the authenticity of the computation. More precisely, a user knowing the secret key sk used to authenticate the original data, can verify that σ authenticates the correct output of the computation. This primitive has been recently formalized by Gennaro and Wichs, who also showed how to realize it from fully homomorphic encryption. In this paper, we show new constructions of this primitive that, while supporting a smaller set of functionalities (i.e., polynomially-bounded arithmetic circuits as opposite to boolean ones), are much more efficient and easy to implement. Moreover, our schemes can tolerate any number of (malicious) verification queries. Our first construction relies on the sole assumption that one way functions exist, allows for arbitrary composition (i.e., outputs of previously authenticated computations can be used as inputs for new ones) but has the drawback that the size of the produced tags grows with the degree of the circuit. Our second solution, relying on the D-DiffieHellman Inversion assumption, offers somewhat orthogonal features as it allows for very short tags (one single group element!) but poses some restrictions on the composition side.