Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps

{\em Verifiable computation} (VC) allows a computationally weak client to outsource the evaluation of a function on many inputs to a powerful but untrusted server. The client invests a large amount of off-line computation and gives an encoding of its function to the server. The server returns both an evaluation of the function on the client's input and a proof such that the client can verify the evaluation using substantially less effort than doing the evaluation on its own. We consider how to privately outsource computations using {\em privacy preserving} VC schemes whose executions reveal no information on the client's input or function to the server. We construct VC schemes with {\em input privacy} for univariate polynomial evaluation and matrix multiplication and then extend them such that the {\em function privacy} is also achieved. Our tool is the recently developed {mutilinear maps}. The proposed VC schemes can be used in outsourcing {private information retrieval (PIR)}.Comment: 23 pages, A preliminary version appears in the 12th International Conference on Cryptology and Network Security (CANS 2013

Quantum Cryptography Beyond Quantum Key Distribution

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two- and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries---including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference

Reuse It Or Lose It: More Efficient Secure Computation Through Reuse of Encrypted Values

Two-party secure function evaluation (SFE) has become significantly more feasible, even on resource-constrained devices, because of advances in server-aided computation systems. However, there are still bottlenecks, particularly in the input validation stage of a computation. Moreover, SFE research has not yet devoted sufficient attention to the important problem of retaining state after a computation has been performed so that expensive processing does not have to be repeated if a similar computation is done again. This paper presents PartialGC, an SFE system that allows the reuse of encrypted values generated during a garbled-circuit computation. We show that using PartialGC can reduce computation time by as much as 96% and bandwidth by as much as 98% in comparison with previous outsourcing schemes for secure computation. We demonstrate the feasibility of our approach with two sets of experiments, one in which the garbled circuit is evaluated on a mobile device and one in which it is evaluated on a server. We also use PartialGC to build a privacy-preserving "friend finder" application for Android. The reuse of previous inputs to allow stateful evaluation represents a new way of looking at SFE and further reduces computational barriers.Comment: 20 pages, shorter conference version published in Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, Pages 582-596, ACM New York, NY, US

Entangled cloud storage

Entangled cloud storage (Aspnes et al., ESORICS 2004) enables a set of clients to “entangle” their files into a single clew to be stored by a (potentially malicious) cloud provider. The entanglement makes it impossible to modify or delete significant part of the clew without affecting all files encoded in the clew. A clew keeps the files in it private but still lets each client recover his own data by interacting with the cloud provider; no cooperation from other clients is needed. At the same time, the cloud provider is discouraged from altering or overwriting any significant part of the clew as this will imply that none of the clients can recover their files. We put forward the first simulation-based security definition for entangled cloud storage, in the framework of universal composability (Canetti, 2001). We then construct a protocol satisfying our security definition, relying on an entangled encoding scheme based on privacy-preserving polynomial interpolation; entangled encodings were originally proposed by Aspnes et al. as useful tools for the purpose of data entanglement. As a contribution of independent interest we revisit the security notions for entangled encodings, putting forward stronger definitions than previous work (that for instance did not consider collusion between clients and the cloud provider). Protocols for entangled cloud storage find application in the cloud setting, where clients store their files on a remote server and need to be ensured that the cloud provider will not modify or delete their data illegitimately. Current solutions, e.g., based on Provable Data Possession and Proof of Retrievability, require the server to be challenged regularly to provide evidence that the clients’ files are stored at a given time. Entangled cloud storage provides an alternative approach where any single client operates implicitly on behalf of all others, i.e., as long as one client's files are intact, the entire remote database continues to be safe and unblemishe