Oblivious Transfer (OT) is a fundamental cryptographic primitive and a core building block for many multiparty cryptographic protocols. While existing OT extension techniques achieve excellent asymptotic efficiency for very large batches, their performance degrades when the total number of OTs is only moderate, since the cost of generating the required base OTs is no longer effectively amortized. In this work, we close this gap by presenting OT constructions that achieve square-root communication complexity for batched OT generation. Concretely, our most efficient protocol generates ell random OTs using O(lambda sqrt(ell)) bits of communication, where lambda is the security parameter. Our constructions are inspired by recent advances in homomorphic secret sharing and techniques for distributed discrete logarithm computation, and explore complementary points in the design space. The first construction is based on the Damgård-Jurik cryptosystem and standard assumptions, at the cost of a one-time trusted setup. The second eliminates the need for trusted setup, relying instead on a power-DDH assumption over prime-order groups. For 128-bit security, our schemes require approximately 2.6 KiB and 1.25 KiB of communication, respectively, to generate 128 random OTs, including the hash key in the power-DDH construction. Our best construction outperforms existing OT extension techniques for batch sizes of up to 32,768 OTs.
Oblivious Transfer (OT) is a fundamental cryptographic primitive and a core building block for many multiparty cryptographic protocols. While existing OT extension techniques achieve excellent asymptotic efficiency for very large batches, their performance degrades when the total number of OTs is only moderate, since the cost of generating the required base OTs is no longer effectively amortized. In this work, we close this gap by presenting OT constructions that achieve square-root communication complexity for batched OT generation. Concretely, our most efficient protocol generates ell random OTs using O(lambda sqrt(ell)) bits of communication, where lambda is the security parameter. Our constructions are inspired by recent advances in homomorphic secret sharing and techniques for distributed discrete logarithm computation, and explore complementary points in the design space. The first construction is based on the Damgård-Jurik cryptosystem and standard assumptions, at the cost of a one-time trusted setup. The second eliminates the need for trusted setup, relying instead on a power-DDH assumption over prime-order groups. For 128-bit security, our schemes require approximately 2.6 KiB and 1.25 KiB of communication, respectively, to generate 128 random OTs, including the hash key in the power-DDH construction. Our best construction outperforms existing OT extension techniques for batch sizes of up to 32,768 OTs.
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 primitive enabling privacy-preserving computation and constitutes a core building block for secure multi-party computation while supporting a wide range of security-sensitive applications: private information retrieval, zero-knowledge proofs, and password-authenticated key exchange, to cite a few. While recent advances in OT extension have significantly reduced amortised costs, their reliance on batches of random base OTs and substantial pre-computation phases limits their practicality in scenarios where the number of transfers is modest or where communication latency and client-side computation are critical constraints. In such settings, efficient base OT protocols remain both relevant and necessary. In this work, we introduce I-(OT)2, a novel base 1-out-of-2 OT protocol grounded in the quadratic residuosity problem, specifically designed to minimise receiver-side computation and interaction. Our construction is particularly appealing on client--server architectures in which the receiver operates on low-power hardware, such as Internet of Things (IoT) devices. Through a lightweight offline pre-computation phase, I-(OT)2 shifts the on-transfer computational burden almost entirely to the Sender, while reducing online communication to only six messages and four digests exchanged. We provide a detailed description of the protocol, accompanied by a formal proof of its security. Moreover, to demonstrate the viability of I-(OT)2, we also present an open-source proof-of-concept implementation (in C language) evaluated on real IoT hardware. Results are staggering: for 128-bit security using a 3072-bit RSA modulus, the receiver incurs an average online cost per OT as low as 2.80 μs on desktop platforms and 39.90 μs on IoT devices, more than 10× faster than the well known SimplestOT.
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 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.
In an adaptive oblivious transfer (OT) protocol, a sender commits to a database of messages and then repeatedly interacts with a receiver in such a way that the receiver obtains one message per interaction of his choice (and nothing more) while the sender learns nothing about any of the choices. Recently, there has been significant effort to design practical adaptive OT schemes and to use these protocols as a building block for larger database applications. To be well suited for these applications, the underlying OT protocol should: (1) support an efficient initialization phase where one commitment can support an arbitrary number of receivers who are guaranteed of having the same view of the database, (2) execute transfers in time independent of the size of the database, and (3) satisfy a strong notion of security under a simple assumption in the standard model. We present the first adaptive OT protocol simultaneously satisfying these requirements. The sole complexity assumption required is that given (g, g a, g b, g c, Q), where g generates a bilinear group of prime order p and a, b, c are selected randomly from Zp, it is hard to decide if Q = g abc. All prior protocols in the standard model either do not meet our efficiency requirements or
Oblivious Transfer (OT), a fundamental primitive in cryptography and a cornerstone of Secure Multi-Party Computation (SMPC), is widely applied in privacy-preserving domains. Constructing efficient and secure OT protocols remains an active research area. To address the limitations of existing OT protocols, such as high time complexity and poor scalability, this paper proposes a secure and efficient k-out-of-n oblivious transfer protocol based on the Paillier homomorphic encryption algorithm . The protocol employs a system of multivariate equations to enable the receiver to select k messages from n messages held by the sender. By integrating multi-threaded parallel processing, the computational speed of ciphertext matrix-vector operations is significantly improved. Additionally, plaintext-ciphertext computation replaces traditional encryption methods to optimize the Paillier algorithm’s efficiency for batch data encryption. Experimental results demonstrate that, compared to recent k-out-of-n OT schemes: when n exceeds 30,000 with k=1, the protocol achieves a 200% performance improvement; when n=512 and k=256, it outperforms existing protocols by approximately 100% in overall efficiency.