We consider the problem of securely generating useful instances of two-party correlations, such as many independent copies of a random oblivious transfer (OT) correlation, using a small amount of communication. This problem is motivated by the goal of secure computation with silent preprocessing, where a low-communication input-independent setup, followed by local ("silent") computation, enables a lightweight "non-cryptographic" online phase once the inputs are known. Recent works of Boyle et al. (CCS 2018, Crypto 2019) achieve this goal with good concrete efficiency for useful kinds of two-party correlations, including OT correlations, under different variants of the Learning Parity with Noise (LPN) assumption, and using a small number of "base" oblivious transfers. The protocols of Boyle et al. have several limitations. First, they require a large number of communication rounds. Second, they are only secure against semi-honest parties. Finally, their concrete efficiency estimates are not backed by an actual implementation. In this work we address these limitations, making three main contributions:-Eliminating interaction. Under the same assumption, we obtain the first concretely efficient 2-round protocols for generating useful correlations, including OT correlations, in the semihonest security model. This implies the first efficient 2-round OT extension protocol of any kind and, more generally, protocols for non-interactive secure computation (NISC) that are concretely efficient and have the silent preprocessing feature.-Malicious security. We provide security against malicious parties (in the random oracle model) without additional interaction and with only a modest concrete overhead; prior to our work, no similar protocols were known with any number of rounds.-Implementation. Finally, we implemented, optimized, and benchmarked our 2-round OT extension protocol, demonstrating that it offers a more attractive alternative to the OT extension protocol of Ishai et al. (Crypto 2003) in many realistic settings.
We consider the problem of securely generating useful instances of two-party correlations, such as many independent copies of a random oblivious transfer (OT) correlation, using a small amount of communication. This problem is motivated by the goal of secure computation with silent preprocessing, where a low-communication input-independent setup, followed by local ("silent") computation, enables a lightweight "non-cryptographic" online phase once the inputs are known. Recent works of Boyle et al. (CCS 2018, Crypto 2019) achieve this goal with good concrete efficiency for useful kinds of two-party correlations, including OT correlations, under different variants of the Learning Parity with Noise (LPN) assumption, and using a small number of "base" oblivious transfers. The protocols of Boyle et al. have several limitations. First, they require a large number of communication rounds. Second, they are only secure against semi-honest parties. Finally, their concrete efficiency estimates are not backed by an actual implementation. In this work we address these limitations, making three main contributions:-Eliminating interaction. Under the same assumption, we obtain the first concretely efficient 2-round protocols for generating useful correlations, including OT correlations, in the semihonest security model. This implies the first efficient 2-round OT extension protocol of any kind and, more generally, protocols for non-interactive secure computation (NISC) that are concretely efficient and have the silent preprocessing feature.-Malicious security. We provide security against malicious parties (in the random oracle model) without additional interaction and with only a modest concrete overhead; prior to our work, no similar protocols were known with any number of rounds.-Implementation. Finally, we implemented, optimized, and benchmarked our 2-round OT extension protocol, demonstrating that it offers a more attractive alternative to the OT extension protocol of Ishai et al. (Crypto 2003) in many realistic settings.
We consider the problem of securely generating useful instances of two-party correlations, such as many independent copies of a random oblivious transfer (OT) correlation, using a small amount of communication. This problem is motivated by the goal of secure computation with silent preprocessing, where a low-communication input-independent setup, followed by local ("silent") computation, enables a lightweight "non-cryptographic" online phase once the inputs are known. Recent works of Boyle et al. (CCS 2018, Crypto 2019) achieve this goal with good concrete efficiency for useful kinds of two-party correlations, including OT correlations, under different variants of the Learning Parity with Noise (LPN) assumption, and using a small number of "base'' oblivious transfers. The protocols of Boyle et al. have several limitations. First, they require a large number of communication rounds. Second, they are only secure against semi-honest parties. Finally, their concrete efficiency estimates are not backed by an actual implementation. In this work we address these limitations, making three main contributions: Eliminating interaction. Under the same assumption, we obtain the first concretely efficient 2-round protocols for generating useful correlations, including OT correlations, in the semi-honest security model. This implies the first efficient 2-round OT extension protocol of any kind and, more generally, protocols for non-interactive secure computation (NISC) that are concretely efficient and have the silent preprocessing feature. Malicious security. We provide security against malicious parties without additional interaction and with only a modest overhead; prior to our work, no similar protocols were known with any number of rounds. Implementation. Finally, we implemented, optimized, and benchmarked our 2-round OT extension protocol, demonstrating that it offers a more attractive alternative to the OT extension protocol of Ishai et al. (Crypto 2003) in many realistic settings.
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
We construct the first constant-round protocols for secure quantum computation in the two-party (2PQC) and multi-party (MPQC) settings with security against malicious adversaries. Our protocols are in the common random string (CRS) model. - Assuming two-message oblivious transfer (OT), we obtain (i) three-message 2PQC, and (ii) five-round MPQC with only three rounds of online (input-dependent) communication; such OT is known from quantum-hard Learning with Errors (QLWE). - Assuming sub-exponential hardness of QLWE, we obtain (i) three-round 2PQC with two online rounds and (ii) four-round MPQC with two online rounds. - When only one (out of two) parties receives output, we achieve minimal interaction (two messages) from two-message OT; classically, such protocols are known as non-interactive secure computation (NISC), and our result constitutes the first maliciously-secure quantum NISC. Additionally assuming reusable malicious designated-verifier NIZK arguments for NP (MDV-NIZKs), we give the first MDV-NIZK for QMA that only requires one copy of the quantum witness. Finally, we perform a preliminary investigation into two-round secure quantum computation where each party must obtain output. On the negative side, we identify a broad class of simulation strategies that suffice for classical two-round secure computation that are unlikely to work in the quantum setting. Next, as a proof-of-concept, we show that two-round secure quantum computation exists with respect to a quantum oracle.
Correlated oblivious transfer (COT) is a crucial building block for secure multi-party computation (MPC) and can be generated efficiently via OT extension. Recent works based on the pseudorandom correlation generator (PCG) paradigm presented a new way to generate random COT correlations using only communication sublinear to the output length. However, due to their high computational complexity, these protocols are only faster than the classical IKNP-style OT extension under restricted network bandwidth. In this paper, we propose new COT protocols in the PCG paradigm that achieve unprecedented performance. \em With 50 Mbps network bandwidth, our maliciously secure protocol can produce one COT correlation in 22 nanoseconds. More specifically, our results are summarized as follows: \beginenumerate \item We propose a semi-honest COT protocol with sublinear communication and linear computation. This protocol assumes primal-LPN and is built upon a recent VOLE protocol with semi-honest security by Schoppmann et al. (CCS 2019). We are able to apply various optimizations to reduce its communication cost by roughly 15×, not counting a one-time setup cost that diminishes as we generate more COT correlations. \item We strengthen our COT protocol to malicious security with no loss of efficiency. Among all optimizations, our new protocol features a new checking technique that ensures correctness and consistency essentially for free. In particular, our maliciously secure protocol is only \em 1−3 nanoseconds slower for each COT. \item We implemented our protocols, and the code will be publicly available at EMP toolkit. We observe at least 9× improvement in running time compared to the state-of-the-art protocol by Boyle et al. (CCS 2019) in both semi-honest and malicious settings under any network faster than 50 Mbps. \endenumerate With this new record of efficiency for generating COT correlations, we anticipate new protocol designs and optimizations will flourish on top of our protocol.
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.