## CryptoDB

### Niv Gilboa

#### Affiliation: Ben-Gurion University

#### Publications

**Year**

**Venue**

**Title**

2019

CRYPTO

Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs
📺
Abstract

We introduce and study the notion of fully linear probabilistically checkable proof systems. In such a proof system, the verifier can make a small number of linear queries that apply jointly to the input and a proof vector.Our new type of proof system is motivated by applications in which the input statement is not fully available to any single verifier, but can still be efficiently accessed via linear queries. This situation arises in scenarios where the input is partitioned or secret-shared between two or more parties, or alternatively is encoded using an additively homomorphic encryption or commitment scheme. This setting appears in the context of secure messaging platforms, verifiable outsourced computation, PIR writing, private computation of aggregate statistics, and secure multiparty computation (MPC). In all these applications, there is a need for fully linear proof systems with short proofs.While several efficient constructions of fully linear proof systems are implicit in the interactive proofs literature, many questions about their complexity are open. We present several new constructions of fully linear zero-knowledge proof systems with sublinear proof size for “simple” or “structured” languages. For example, in the non-interactive setting of fully linear PCPs, we show how to prove that an input vector $$x\in {\mathbb {F}}^n$$, for a finite field $${\mathbb {F}}$$, satisfies a single degree-2 equation with a proof of size $$O(\sqrt{n})$$ and $$O(\sqrt{n})$$ linear queries, which we show to be optimal. More generally, for languages that can be recognized by systems of constant-degree equations, we can reduce the proof size to $$O(\log n)$$ at the cost of $$O(\log n)$$ rounds of interaction.We use our new proof systems to construct new short zero-knowledge proofs on distributed and secret-shared data. These proofs can be used to improve the performance of the example systems mentioned above.Finally, we observe that zero-knowledge proofs on distributed data provide a general-purpose tool for protecting MPC protocols against malicious parties. Applying our short fully linear PCPs to “natural” MPC protocols in the honest-majority setting, we can achieve unconditional protection against malicious parties with sublinear additive communication cost. We use this to improve the communication complexity of recent honest-majority MPC protocols. For instance, using any pseudorandom generator, we obtain a 3-party protocol for Boolean circuits in which the amortized communication cost is only one bit per AND gate per party (compared to 10 bits in the best previous protocol), matching the best known protocols for semi-honest parties.

2019

CRYPTO

Efficient Pseudorandom Correlation Generators: Silent OT Extension and More
📺
Abstract

Secure multiparty computation (MPC) often relies on correlated randomness for better efficiency and simplicity. This is particularly useful for MPC with no honest majority, where input-independent correlated randomness enables a lightweight “non-cryptographic” online phase once the inputs are known. However, since the amount of randomness typically scales with the circuit size of the function being computed, securely generating correlated randomness forms an efficiency bottleneck, involving a large amount of communication and storage.A natural tool for addressing the above limitations is a pseudorandom correlation generator (PCG). A PCG allows two or more parties to securely generate long sources of useful correlated randomness via a local expansion of correlated short seeds and no interaction. PCGs enable MPC with silent preprocessing, where a small amount of interaction used for securely sampling the seeds is followed by silent local generation of correlated pseudorandomness.A concretely efficient PCG for Vector-OLE correlations was recently obtained by Boyle et al. (CCS 2018) based on variants of the learning parity with noise (LPN) assumption over large fields. In this work, we initiate a systematic study of PCGs and present concretely efficient constructions for several types of useful MPC correlations. We obtain the following main contributions:PCG foundations. We give a general security definition for PCGs. Our definition suffices for any MPC protocol satisfying a stronger security requirement that is met by existing protocols. We prove that a stronger security requirement is indeed necessary, and justify our PCG definition by ruling out a stronger and more natural definition.Silent OT extension. We present the first concretely efficient PCG for oblivious transfer correlations. Its security is based on a variant of the binary LPN assumption and any correlation-robust hash function. We expect it to provide a faster alternative to the IKNP OT extension protocol (Crypto 2003) when communication is the bottleneck. We present several applications, including protocols for non-interactive zero-knowledge with bounded-reusable preprocessing from binary LPN, and concretely efficient related-key oblivious pseudorandom functions.PCGs for simple 2-party correlations. We obtain PCGs for several other types of useful 2-party correlations, including (authenticated) one-time truth-tables and Beaver triples. While the latter PCGs are slower than our PCG for OT, they are still practically feasible. These PCGs are based on a host of assumptions and techniques, including specialized homomorphic secret sharing schemes and pseudorandom generators tailored to their structure.Multiparty correlations. We obtain PCGs for multiparty correlations that can be used to make the (input-dependent) online communication of MPC protocols scale linearly with the number of parties, instead of quadratically.

2019

TCC

Secure Computation with Preprocessing via Function Secret Sharing
Abstract

We propose a simple and powerful new approach for secure computation with input-independent preprocessing, building on the general tool of function secret sharing (FSS) and its efficient instantiations. Using this approach, we can make efficient use of correlated randomness to compute any type of gate, as long as a function class naturally corresponding to this gate admits an efficient FSS scheme. Our approach can be viewed as a generalization of the “TinyTable” protocol of Damgård et al. (Crypto 2017), where our generalized variant uses FSS to achieve exponential efficiency improvement for useful types of gates.By instantiating this general approach with efficient PRG-based FSS schemes of Boyle et al. (Eurocrypt 2015, CCS 2016), we can implement useful nonlinear gates for equality tests, integer comparison, bit-decomposition and more with optimal online communication and with a relatively small amount of correlated randomness. We also provide a unified and simplified view of several existing protocols in the preprocessing model via the FSS framework.Our positive results provide a useful tool for secure computation tasks that involve secure integer comparisons or conversions between arithmetic and binary representations. These arise in the contexts of approximating real-valued functions, machine-learning classification, and more. Finally, we study the necessity of the FSS machinery that we employ, in the simple context of secure string equality testing. First, we show that any “online-optimal” secure equality protocol implies an FSS scheme for point functions, which in turn implies one-way functions. Then, we show that information-theoretic secure equality protocols with relaxed optimality requirements would follow from the existence of big families of “matching vectors.” This suggests that proving strong lower bounds on the efficiency of such protocols would be difficult.

1998

EPRINT

Private Information Retrieval by Keywords
Abstract

Private information retrieval (PIR) schemes enable a user to
access one or more servers that hold copies of
a database and {\em privately} retrieve parts of the $n$
bits of data stored in the database. This means that the queries
give each individual
database no partial information (in the information theoretic or computational
sense) on the identity of the item retrieved by the user.
All known PIR schemes assume that the user knows the {\em physical address}
of the sought item. This is usually not the case when accessing a public
database that is not managed by the user. Such databases are typically
presented with keywords, which are then internally translated (at the
database end) to physical addresses, using an appropriate search
structure (for example, a hash table or a binary tree). In this note we
describe a simple, modular way to privately access data by keywords.
It combines {\em any} conventional search structure with {\em any}
underlying PIR scheme (including single server schemes). The transformation
requires no modification in the way that the search structure is maintained.
Therefore the same database will support both private and regular (non
private) searches.

#### Program Committees

- Eurocrypt 2017

#### Coauthors

- Dan Boneh (1)
- Elette Boyle (6)
- Benny Chor (1)
- Henry Corrigan-Gibbs (1)
- Geoffroy Couteau (1)
- Shlomi Dolev (1)
- Yuval Ishai (8)
- Lisa Kohl (1)
- Ximing Li (1)
- Moni Naor (1)
- Peter Scholl (1)