Hila Zarosim

Fair and Efficient Secure Multiparty Computation with Reputation Systems

A reputation system for a set of entities is essentially a list of scores that provides a measure of the reliability of each entity in the set. The score given to an entity can be interpreted (and in the reputation system literature it often is [12]) as the probability that an entity will behave honestly. In this paper, we ask whether or not it is possible to utilize reputation systems for carrying out secure multiparty computation. We provide formal definitions of secure computation in this setting, and carry out a theoretical study of feasibility. We present almost tight results showing when it is and is not possible to achieve fair secure computation in our model. We suggest applications for our model in settings where some information about the honesty of other parties is given. This can be preferable to the current situation where either an honest majority is arbitrarily assumed, or a protocol that is secure for a dishonest majority is used and the efficiency and security guarantees (including fairness) of an honest majority are not obtained.

On the feasibility of extending oblivious transfer

Oblivious transfer is one of the most basic and important building blocks in cryptography. As such, understanding its cost is of prime importance. Beaver (STOC 1996) showed that it is possible to obtain poly(n) oblivious transfers given only n actual oblivious transfer calls and using one-way functions, where n is the security parameter. In addition, he showed that it is impossible to extend oblivious transfer information theoretically. The notion of extending oblivious transfer is important theoretically (to understand the complexity of computing this primitive) and practically (since oblivious transfers can be expensive and thus extending them using only one-way functions is very attractive). Despite its importance, very little is known about the feasibility of extending oblivious transfer, beyond the fact that it is impossible information theoretically. Specifically, it is not known whether or not one-way functions are actually necessary for extending oblivious transfer, whether or not it is possible to extend oblivious transfers with adaptive security, and whether or not it is possible to extend oblivious transfers when starting with O(logn) oblivious transfers. In this paper, we address these questions and provide almost complete answers to all of them. We show that the existence of any oblivious transfer extension protocol with security for static semi-honest adversaries implies one-way functions, that an oblivious transfer extension protocol with adaptive security implies oblivious transfer with static security, and that the existence of an oblivious transfer extension protocol from only O(logn) oblivious transfers implies oblivious transfer itself.

Adaptive Zero-Knowledge Proofs and Adaptively Secure Oblivious Transfer

In the setting of secure computation, a set of parties wish to securely compute some function of their inputs, in the presence of an adversary. The adversary in question may be static (meaning that it controls a predetermined subset of the parties) or adaptive (meaning that it can choose to corrupt parties during the protocol execution and based on what it sees). In this paper, we study two fundamental questions relating to the basic zero-knowledge and oblivious transfer protocol problems: Adaptive zero-knowledge proofs: We ask whether it is possible to construct adaptive zero-knowledge proofs (with unconditional soundness) for all of

The Feasibility of Outsourced Database Search in the Plain Model

\mathcal{NP}

Limits on the Usefulness of Random Oracles

. Beaver (STOC [1996]) showed that known zero-knowledge proofs are not adaptively secure, and in addition showed how to construct zero-knowledge arguments (with computational soundness).Adaptively secure oblivious transfer: All known protocols for adaptively secure oblivious transfer rely on seemingly stronger hardness assumptions than for the case of static adversaries. We ask whether this is inherent, and in particular, whether it is possible to construct adaptively secure oblivious transfer from enhanced trapdoor permutations alone. We provide surprising answers to the above questions, showing that achieving adaptive security is sometimes harder than achieving static security, and sometimes not. First, we show that assuming the existence of one-way functions only, there exist adaptive zero-knowledge proofs for all languages in

Completeness for Symmetric Two-Party Functionalities: Revisited

\mathcal{NP}

On the Feasibility of Extending Oblivious Transfer

. In order to prove this, we overcome the problem that all adaptive zero-knowledge protocols known until now used equivocal commitments (which would enable an all-powerful prover to cheat). Second, we prove a black-box separation between adaptively secure oblivious transfer and enhanced trapdoor permutations. As a corollary, we derive a black-box separation between adaptively and statically secure oblivious transfer. This is the first black-box separation to relate to adaptive security and thus the first evidence that it is indeed harder to achieve security in the presence of adaptive adversaries than in the presence of static adversaries.

Limits on the usefulness of random oracles

The problem of securely outsourcing computation to an untrusted server gained momentum with the recent penetration of cloud computing services. The ultimate goal in this setting is to design efficient protocols that minimize the computational overhead of the clients and instead rely on the extended resources of the server. In this paper, we focus on the outsourced database search problem which is highly motivated in the context of delegatable computing since it offers storage alternatives for massive databases, that may contain confidential data. This functionality is described in two phases: 1 setup phase and 2 query phase. The main goal is to minimize the parties workload in the query phase so that it is proportional to the query size and its corresponding response. We study whether a trusted setup or a random oracle are necessary for protocols with minimal interaction that meet the optimal communication and computation bounds in the query phase. We answer this question positively and demonstrate a lower bound on the communication or the computational overhead in this phase.

Completeness for symmetric two-party functionalities - revisited

In their seminal work, Impagliazzo and Rudich (STOC’89) showed that no key-agreement protocol exists in the random-oracle model, yielding that key agreement cannot be black-box reduced to one-way functions. In this work, we generalize their result, showing that, to a large extent, no-private-input, semi-honest, two-party functionalities that can be securely implemented in the random oracle model can be securely implemented information theoretically (where parties are assumed to be all powerful, and no oracle is given). Using a recent information-theoretic impossibility result by McGregor et al. (FOCS’10), our result yields that certain functionalities (e.g. inner product) cannot be computed both in an accurately and in a differentially private manner in the random oracle model, implying that protocols for computing these functionalities cannot be black-box reduced to the existence of one-way functions.

Completeness for Symmetric Two-Party Functionalities - Revisited.

Understanding the minimal assumptions required for carrying out cryptographic tasks is one of the fundamental goals of theoretic cryptography. A rich body of work has been dedicated to understanding the complexity of cryptographic tasks in the context of (semi-honest) secure two-party computation. Much of this work has focused on the characterization of trivial and complete functionalities (resp., functionalities that can be securely implemented unconditionally, and functionalities that can be used to securely compute all functionalities). Most previous works define reductions via an ideal implementation of the functionality; i.e., f reduces to g if one can implement f using a black-box (or oracle) that computes the function g and returns the output to both parties. Such a reduction models the computation of f as an atomic operation. However, in the real world, protocols proceed in rounds, and the output is not learned by the parties simultaneously. In this paper, we show that this distinction is significant. Specifically, we show that there exist symmetric functionalities (where both parties receive the same outcome) that are neither trivial nor complete under “black-box reductions,” and yet the existence of a constant-round protocol for securely computing such a functionality implies infinitely often oblivious transfer (meaning that it is secure for infinitely many values of the security parameter). In light of the above, we propose an alternative definitional infrastructure for studying the triviality and completeness of functionalities.