Oblivious Transfer has played a crucial role in the design of secure multi party computation. Nevertheless, there are not many practical solutions that achieve simulation based security and at the same time instantiable based on different assumptions. In this work, we consider a simulation based security notion that we call endemic security. We show how to construct highly efficient oblivious transfer in the random oracle model that achieves endemic security under a wide range of assumptions, among them DDH, CDH, LWE and coding based assumptions. We construct a secure oblivious transfer based on DDH that takes only a single communication round which allows significant performance gains. We also instantiate our oblivious transfer with the Crystals.Kyber key agreement. Our implementation shows that both instantiations can be computed in under one millisecond. Further, we revisit, correct and improve existing oblivious transfer extension techniques. We provide an implementation of an oblivious transfer extension protocol in the ideal cipher model that is actively secure, processing up to 23 million OTs per second and up to 10 times faster than previous secure implementations. We also show that our framework can compute endemically secure OT extension and the base OTs in just two rounds.
Oblivious Transfer has played a crucial role in the design of secure multi party computation. Nevertheless, there are not many practical solutions that achieve simulation based security and at the same time instantiable based on different assumptions. In this work, we consider a simulation based security notion that we call endemic security. We show how to construct highly efficient oblivious transfer in the random oracle model that achieves endemic security under a wide range of assumptions, among them DDH, CDH, LWE and coding based assumptions. We construct a secure oblivious transfer based on DDH that takes only a single communication round which allows significant performance gains. We also instantiate our oblivious transfer with the Crystals.Kyber key agreement. Our implementation shows that both instantiations can be computed in under one millisecond. Further, we revisit, correct and improve existing oblivious transfer extension techniques. We provide an implementation of an oblivious transfer extension protocol in the ideal cipher model that is actively secure, processing up to 23 million OTs per second and up to 10 times faster than previous secure implementations. We also show that our framework can compute endemically secure OT extension and the base OTs in just two rounds.
Oblivious transfer (OT) is one of the most fundamental primitives in cryptography and is widely used in protocols for secure two-party and multi-party computation. As secure com-putation becomes more practical, the need for practical large scale oblivious transfer protocols is becoming more evident. Oblivious transfer extensions are protocols that enable a relatively small number of “base-OTs ” to be utilized to compute a very large number of OTs at low cost. In the semi-honest setting, Ishai et al. (CRYPTO 2003) presented an OT extension protocol for which the cost of each OT (beyond the base-OTs) is just a few hash function operations. In the malicious setting, Nielsen et al. (CRYPTO 2012) presented an efficient OT extension protocol for the setting of active adversaries, that is secure in the random oracle model. In this work, we present an OT extension protocol for the setting of malicious adversaries that is more efficient and uses less communication than previous works. In addition, our protocol can be proven secure in both the random oracle model, and in the standard model with a type of correlation robustness. Given the importance of OT in many secure computation protocols, increasing the efficiency of OT extensions is another important step forward to making secure
Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM.
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.
Oblivious Transfer (OT) is the fundamental building block of cryptographic protocols. In this paper we describe the simplest and most efficient protocol for 1-out-of- n OT to date, which is obtained by tweaking the Diffie-Hellman key-exchange protocol. The protocol achieves UC-security against active and adaptive corruptions in the random oracle model. Due to its simplicity, the protocol is extremely efficient and it allows to perform m 1-out-of- n OTs using only: Computation: (n+1)m+2 exponentiations ( mn for the receiver, mn+2 for the sender) and Communication: 32(m+1) bytes (for the group elements), and 2 mn ciphertexts. We also report on an implementation of the protocol using elliptic curves, and on a number of mechanisms we employ to ensure that our software is secure against active attacks too. Experimental results show that our protocol (thanks to both algorithmic and implementation optimizations) is at least one order of magnitude faster than previous work. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Abstract. Adaptive oblivious transfer (adaptive OT) schemes have wide applications such as oblivious database searches, secure multiparty computation and etc. It is a two-party protocol which simulates an ideal world such that the sender sends M1, · · · , Mn to the trusted third party (TTP) first, and then the receiver receives Mσi from TTP adaptively for i = 1, 2, · · · k. In the standard model, however, the fully simulatable schemes known so far had to rely on dynamic assumptions such as q-strong DH assumption, q-PDDH assumption and q-hidden LRSW assumption. This paper shows two fully simulatable adaptive OT schemes which do not rely on dynamic assumptions in the standard model. Our first scheme holds under the DDH assumption and our second scheme holds under the Paillier’s decisional Nth residuosity assumption, respectively.