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

DATS - data containers for web applications

Data containers enable users to control access to their data while untrusted applications compute on it. However, they require replicating an application inside each container - compromising functionality, programmability, and performance. We propose DATS - a system to run web applications that retains application usability and efficiency through a mix of hardware capability enhanced containers and the introduction of two new primitives modeled after the popular model-view-controller (MVC) pattern. (1) DATS introduces a templating language to create views that compose data across data containers. (2) DATS uses authenticated storage and confinement to enable an untrusted storage service, such as memcached and deduplication, to operate on plain-text data across containers. These two primitives act as robust declassifiers that allow DATS to enforce non-interference across containers, taking large applications out of the trusted computing base (TCB). We showcase eight different web applications including Gitlab and a Slack-like chat, significantly improve the worst-case overheads due to application replication, and demonstrate usable performance for common-case usage

Authenticated LSM Trees with Minimal Trust

In the age of user-generated contents, the workloads imposed on information-security infrastructures become increasingly write-intensive. How- ever, existing security protocols, specifically authenticated data structures (ADSs), are historically designed based on update-in-place data structures and incur overhead when serving write-intensive workloads. In this work, we present LPAD (Log-structured Persistent Authenticated Directory), a new ADS protocol designed uniquely based on the log-structured merge trees (LSM trees) which recently gained popularity in the design of modern storage systems. On the write path, LPAD supports streaming, non-interactive updates with constant proof from trusted data owners. On the read path, LPAD supports point queries over the dynamic dataset with polynomial proof. The key to enable this efficiency is a verifiable reorganization operation, called verifiable merge, in LPAD. Verifiable merge is secured by the execution in an enclave of trusted execution environments (TEE). To minimize the trusted computing base (TCB), LPAD places the code related to verifiable merge in enclave, and nothing else. Our implementation of LPAD on Google LevelDB codebase and on Intel SGX shows that the TCB is reduced by 20 times: The enclave size of LPAD is one thousand code lines out of more than twenty thousands code lines of a vanilla LevelDB. Under the YCSB workloads, LPAD improves the performance by an order of magnitude compared with that of existing update-in-place ADSs

Aggregatable Subvector Commitments for Stateless Cryptocurrencies

An aggregatable subvector commitment (aSVC) scheme is a vector commitment (VC) scheme that can aggregate multiple proofs into a single, small subvector proof. In this paper, we formalize aSVCs and give a construction from constant-sized polynomial commitments. Our construction is unique in that it has linear-sized public parameters, it can compute all constant-sized proofs in quasilinear time, it updates proofs in constant time and it can aggregate multiple proofs into a constant-sized subvector proof. Furthermore, our concrete proof sizes are small due to our use of pairing-friendly groups. We use our aSVC to obtain a payments-only stateless cryptocurrency with very low communication and computation overheads. Specifically, our constant-sized, aggregatable proofs reduce each block’s proof overhead to a single group element, which is optimal. Furthermore, our subvector proofs speed up block verification and our smaller public parameters further reduce block size

Stateful Multi-Client Verifiable Computation

This paper develops a cryptographic protocol for outsourcing arbitrary stateful computation among multiple clients to an untrusted server, while guaranteeing integrity of the data. The clients communicate only with the server and store only a short authenticator to ensure that the server does not cheat. Our contribution is two-fold. First, we extend the recent hash&prove scheme of Fiore et al. (CCS 2016) to stateful computations that support arbitrary updates by the untrusted server, in a way that can be verified by the clients. We use this scheme to generically instantiate authenticated data types. Second, we describe a protocol for multi-client verifiable computation based on an authenticated data type, and prove that it achieves a computational version of fork linearizability. This is the strongest guarantee that can be achieved in the setting where clients do not communicate directly; it ensures correctness and consistency of outputs seen by the clients individually

Boosting Verifiable Computation on Encrypted Data

International audienceWe consider the setting in which an untrusted server stores a collection of data and is asked to compute a function over it. In this scenario, we aim for solutions where the untrusted server does not learn information about the data and is prevented from cheating. This problem is addressed by verifiable and private delegation of computation, proposed by Gennaro, Gentry and Parno (CRYPTO'10), a notion that is close to both the active areas of homomorphic encryption and verifiable computation (VC). However, in spite of the efficiency advances in the respective areas, VC protocols that guarantee privacy of the inputs are still expensive. The only exception is a protocol by Fiore, Gennaro and Pastro (CCS'14) that supports arithmetic circuits of degree at most 2. In this paper we propose new efficient protocols for VC on encrypted data that improve over the state of the art solution of Fiore et al. in multiple aspects. First, we can support computations of degree higher than 2. Second, we achieve public delegatability and public verifiability whereas Fiore et al. need the same secret key to encode inputs and verify outputs. Third, we achieve a new property that guarantees that verifiers can be convinced about the correctness of the outputs without learning information on the inputs. The key tool to obtain our new protocols is a new SNARK that can efficiently handle computations over a quotient polynomial ring, such as the one used by Ring-LWE somewhat homomorphic encryption schemes. This SNARK in turn relies on a new commit-and-prove SNARK for proving evaluations on the same point of several committed polynomials. We propose a construction of this scheme under an extractability assumption over bilinear groups in the random oracle model

Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updateable Structured Reference Strings

Ever since their introduction, zero-knowledge proofs have become an important tool for addressing privacy and scalability concerns in a variety of applications. In many systems each client downloads and verifies every new proof, and so proofs must be small and cheap to verify. The most practical schemes require either a trusted setup, as in (pre-processing) zk-SNARKs, or verification complexity that scales linearly with the complexity of the relation, as in Bulletproofs. The structured reference strings required by most zk-SNARK schemes can be constructed with multi-party computation protocols, but the resulting parameters are specific to an individual relation. Groth et al. discovered a zk-SNARK protocol with a universal structured reference string that is also updatable, but the string scales quadratically in the size of the supported relations. Here we describe a zero-knowledge SNARK, Sonic, which supports a universal and continually updatable structured reference string that scales linearly in size. We also describe a generally useful technique in which untrusted "helpers" can compute advice that allows batches of proofs to be verified more efficiently. Sonic proofs are constant size, and in the "helped" batch verification context the marginal cost of verification is comparable with the most efficient SNARKs in the literature

New Code-Based Privacy-Preserving Cryptographic Constructions

Code-based cryptography has a long history but did suffer from periods of slow development. The field has recently attracted a lot of attention as one of the major branches of post-quantum cryptography. However, its subfield of privacy-preserving cryptographic constructions is still rather underdeveloped, e.g., important building blocks such as zero-knowledge range proofs and set membership proofs, and even proofs of knowledge of a hash preimage, have not been known under code-based assumptions. Moreover, almost no substantial technical development has been introduced in the last several years. This work introduces several new code-based privacy-preserving cryptographic constructions that considerably advance the state-of-the-art in code-based cryptography. Specifically, we present $3$ major contributions, each of which potentially yields various other applications. Our first contribution is a code-based statistically hiding and computationally binding commitment scheme with companion zero-knowledge (ZK) argument of knowledge of a valid opening that can be easily extended to prove that the committed bits satisfy other relations. Our second contribution is the first code-based zero-knowledge range argument for committed values, with communication cost logarithmic in the size of the range. A special feature of our range argument is that, while previous works on range proofs/arguments (in all branches of cryptography) only address ranges of non-negative integers, our protocol can handle signed fractional numbers, and hence, can potentially find a larger scope of applications. Our third contribution is the first code-based Merkle-tree accumulator supported by ZK argument of membership, which has been known to enable various interesting applications. In particular, it allows us to obtain the first code-based ring signatures and group signatures with logarithmic signature sizes