We design communication efficient two-party and multi-party protocols for the longest common subsequence (LCS) and related problems. Our protocols achieve privacy with respect to passive adversaries, under reasonable cryptographic assumptions. We benefit from the somewhat surprising interplay of an efficient block-retrieval PIR (Gentry-Ramzan, ICALP 2005) with the classic “four Russians” algorithmic design. This result is the first improvement to the communication complexity for this application over generic results (such as Yao’s garbled circuit protocol) and, as such, is interesting as a contribution to the theory of communication efficiency for secure two-party and multiparty applications.
We design communication efficient two-party and multi-party protocols for the longest common subsequence (LCS) and related problems. Our protocols achieve privacy with respect to passive adversaries, under reasonable cryptographic assumptions. We benefit from the somewhat surprising interplay of an efficient block-retrieval PIR (Gentry-Ramzan, ICALP 2005) with the classic “four Russians” algorithmic design. This result is the first improvement to the communication complexity for this application over generic results (such as Yao’s garbled circuit protocol) and, as such, is interesting as a contribution to the theory of communication efficiency for secure two-party and multiparty applications.
We develop a new multi-party generalization of Naor-Nissim indirect indexing, making it possible for many participants to simulate a RAM machine with only poly-logarithmic blow-up. Underlying our approach is a new multi-party variant of oblivious transfer which may be of independent interest. Our most efficient instantiation (built from length-flexible additively homomorphic public key encryption) improves the communication complexity of secure multi-party computation for a number of problems in the literature. We explore, in depth, some of these applications, including private distributed constraint satisfaction problems, private stable bipartite matching, and private longest common subsequence.
In the case of the private bipartite stable matching (stable marriage) problem, we follow-up the work of Golle (Financial Crypto 2006) who motivates the application and introduces a novel framework for the solving the problem. We show that the communication complexity of Golle’s main protocol is substantially greater than what was claimed, in part due to surprising pathological behavior of Golle’s variant of the Gale-Shapley stable matching algorithm. We develop new secure protocols in Golle’s basic framework with greatly reduced communication complexity.
In the case of the longest common subsequence problem, we design communication efficient two-party and multi-party protocols for several variants of this and related problems. Our protocols achieve the first improvement to the communication complexity for this application over generic results (such as Yao’s garbled circuit protocol). As such, this result is interesting as a contribution to the theory of communication efficiency for secure two-party and multi-party applications. We benefit from the felicitous interplay of an efficient block-retrieval PIR (Gentry-Ramzan, ICALP 2005) with the classic “four Russians” algorithmic design. We believe this technique will be useful for privately implementing a variety of “efficiently encodable” dynamic programming applications.
Abstract. Secure multi-party computation has been considered by the cryptographic community for a number of years. Until recently it has been a purely theoretical area, with few implementations with which to test various ideas. This has led to a number of optimisations being proposed which are quite restricted in their application. In this paper we describe an implementation of the two-party case, using Yao’s garbled circuits, and present various algorithmic protocol improvements. These optimisations are analysed both theoretically and empirically, using experiments of various adversarial situations. Our experimental data is provided for reasonably large circuits, including one which performs an AES encryption, a problem which we discuss in the context of various possible applications. 1
In this thesis we design and implement three approaches to provide efficient Secure Two- Party Computation (2PC) protocols that are secure in presence of malicious adversaries. The field of secure two-party computation enables two mutually distrusting parties, each with their own private input, to run a computation of an arbitrary program. At the end of the computation, nothing about their private input is leaked except for what can be learned from the output of the computation. The seminal work of Yao in 1986 provided the first proof that such a computation is feasible using the so called garbled circuits and given an Oblivious Transfer protocol. In this thesis, we follow Yao’s garbled circuit approach and focus on efficient protocols that are secure against malicious adversaries. We examine three different categories of optimization. In each category, we present a 2PC protocol, prove its security, and implement it as a proof of concept to demonstrate its running time in practice. Non-interactive Secure Computation: In this category, we offer the first implementation of a malicious 2PC protocol that reduces the required rounds of interaction between the two parties to only two rounds (i.e., each party sends only one message to the other party). Mixed Secure Two-Party Computation: In the second category we target big and complex programs and break them into subprograms. Then, we compute each subprogram using the most efficient 2PC protocol that is suitable for it. Finally, we securely connect these subprograms together. The goal is to reduce the overhead of the garbled circuits significantly, which results in a more efficient overall 2PC protocol for programs with specific properties. Secure Computation for Random Access Machine Programs: In the third category, we target programs that require random access to the memory (as opposed to a sequential access). We present the first efficient maliciously-secure protocol for computing such programs.
The Private Information Retrieval protocol(PIR) is an important secure multi-party computation protocol.In PIR,a user can perform a query from a database without revealing his private information;meanwhile the privacy of the database will be protected,too.This paper proposes a new scheme in which we apply cryptographic technology on the auxiliary random servers protocol to solve the problem of PIR.This scheme is efficient in computational complexity and doesn't increase the cost of communication.It is very practical and can retrieve a block of bits.Detailed analysis of security,computational complexity and communicational complexity to the scheme is also given in this paper.
We focus on three different types of multi-party cryptographic protocols. The first is in the area of unconditionally secure signature schemes, the goal of which is to provide users the ability to electronically sign documents without the reliance on computational assumptions needed in traditional digital signatures. The second is on cooperative protocols in which users help each other maintain privacy while querying a database, called user-private information retrieval protocols. The third is concerned with the generalized Russian cards problem, in which two card players wish to communicate their hands to each other via public announcements without the third player learning the card deal. The latter two problems have close ties to the field of combinatorial designs, and properly fit within the field of combinatorial cryptography. All of these problems have a common thread, in that they are grounded in the information-theoretically secure or unconditionally secure setting.
Secure two-party computation allows two parties to evaluate a function on their private inputs while keeping all information private except what can be inferred from the outputs. A major building block and the foundation for many efficient secure computation protocols is oblivious transfer (OT). In an OT protocol a sender inputs two messages (x_{0}, x_{1}) while a receiver with choice bit c wants to receive message x_{c}.The OT protocol execution guarantees that the sender learns no information about c and the receiver learns no information about x_{1−c}. This thesis focuses on the efficient generation of OTs and their use in secure computation. In particular, we show how to compute OTs more efficiently, improve generic secure computation protocols which can be used to securely evaluate any functionality, and develop highly efficient special-purpose protocols for private set intersection (PSI). We outline our contributions in more detail next. More Efficient OT Extensions. The most efficient OT protocols are based on public-key cryptography and require a constant number of exponentiations per OT. However, for many practical applications where millions to billions of OTs need to be computed, these exponentiations become prohibitively slow. To enable these applications, OT extension protocols [Bea96, IKNP03] can be used, which extend a small number of public-key-based OTs to an arbitrarily large number using cheap symmetric-key cryptography only. We improve the computation and communication efficiency of OT extension protocols and show how to achieve security against malicious adversaries, which can arbitrarily deviate from the protocol, at low overhead. Our resulting protocols can compute several million of OTs per second and we show that, in contrast to previous belief, the local computation overhead for computing OTs is so low that the main bottleneck is the network bandwidth. Parts of these results are published in: • G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More Efficient Oblivious Transfer and Extensions for Faster Secure Computation. In 20th ACM Conference on Computer and Communications Security (CCS’13). • G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More Efficient Oblivious Transfer Extensions with Security for Malicious Adversaries. In 34th Advances in Cryptology – EUROCRYPT’15. • G. Asharov, Y. Lindell, T. Schneider, M. Zohner. More Efficient Oblivious Transfer Extensions. To appear in Journal of Cryptology. Online at http://eprint.iacr.org/2016/602. Communication-Efficient Generic Secure Two-Party Computation. Generic secure two-party computation techniques allow to evaluate a function, represented as a circuit of linear (XOR) and non-linear (AND) gates. One of the most prominent generic secure two-party computation protocols is Yao’s garbled circuits [Yao86], for which many optimizations have been proposed. Shortly after Yao’s protocol, the generic secure protocol by Goldreich-Micali-Wigderson (GMW) [GMW87] was introduced. The GMW protocol requires a large number of OTs and was believed to be less efficient for secure two-party computation than Yao’s protocol [HL10, CHK+12]. We improve the efficiency of the GMW protocol and show that it can outperform Yao’s garbled circuits protocol in settings with low bandwidth. Furthermore, we utilize the flexibility of OT and outline special-purpose constructions that can be used within the GMW protocol and which improve its efficiency even further. Parts of these results are published in: • T. Schneider, M. Zohner. GMW vs. Yao? Efficient Secure Two-Party Computation with Low Depth Circuits. In 17th International Conference on Financial Cryptography and Data Security (FC’13). • D. Demmler, T. Schneider, M. Zohner. ABY - A Framework for Efficient Mixed-Protocol Secure Two-Party Computation. In 22th Network and Distributed System Security Symposium (NDSS’15). • G. Dessouky, F. Koushanfar, A.-R. Sadeghi, T. Schneider, S. Zeitouni, M. Zohner. Pushing the Communication Barrier in Secure Computation using Lookup Tables. In 24th Network and Distributed System Security Symposium (NDSS’17). Faster Private Set Intersection (PSI). PSI allows two parties to compute the intersection of their private sets without revealing any element that is not in the intersection. PSI is a well-studied problem in secure computation and many special-purpose protocols have been proposed. However, existing PSI protocols are several orders of magnitude slower than an insecure naive hashing solution that is used in practice. In addition, many protocols were compared in a biased fashion, which makes it difficult to identify the most promising solution for a particular scenario. We systematize the progress made on PSI protocols by reviewing, optimizing, and comparing existing PSI protocols. We then introduce a novel PSI protocol that is based on our efficiency improvements in OT extension protocols and which outperforms existing protocols by up to two orders of magnitude. Parts of these results are published in: • B. Pinkas, T. Schneider, M. Zohner. Faster Private Set Intersection Based on OT Extension. In 23th USENIX Security Symposium (USENIX Security’14). • B. Pinkas, T. Schneider, G. Segev, M. Zohner. Phasing: Private Set Intersection using Permutation-based Hashing. In 24th USENIX Security Symposium (USENIX Security’15). • B. Pinkas, T. Schneider, M. Zohner. Scalable Private Set Intersection Based on OT Extension. Journal paper. In submission. Online at http://iacr.eprint.org/2016/930.