We present unconditionally perfectly secure protocols in the semi-honest setting for several functionalities: (1) private elementwise equality; (2) private bitwise integer comparison; and (3) bit-decomposition. These protocols are built upon a new concept called Shared Oblivious Transfer (Shared OT). Shared OT extends the one-out-of-N String OT by replacing strings with integers modulo M and allowing additive secret-sharing of all inputs and outputs. These extensions can be implemented by simple local computations without incurring additional OT invocations. We believe our Shared OT may be of independent interest. Our protocols demonstrate the best round, communication, and computational complexities compared to all other protocols secure in a similar setting. Moreover, all of our protocols involve either 2 or 3 rounds.
We present unconditionally perfectly secure protocols in the semi-honest setting for several functionalities: (1) private elementwise equality; (2) private bitwise integer comparison; and (3) bit-decomposition. These protocols are built upon a new concept called Shared Oblivious Transfer (Shared OT). Shared OT extends the one-out-of-N String OT by replacing strings with integers modulo M and allowing additive secret-sharing of all inputs and outputs. These extensions can be implemented by simple local computations without incurring additional OT invocations. We believe our Shared OT may be of independent interest. Our protocols demonstrate the best round, communication, and computational complexities compared to all other protocols secure in a similar setting. Moreover, all of our protocols involve either 2 or 3 rounds.
Oblivious transfer (OT) protocol is an essential tool in cryptography that provides a wide range of applications such as secure multi-party computation, private information retrieval, private set intersection, contract signing, and privacy-preserving location-based services. The OT protocol has different variants such as one-out-of-2, one-out-of- n , k -out-of- n , and OT extension. In the OT (one-out-of-2, one-out-of- n , and OT extension) protocol, the sender has a set of messages, whereas the receiver has a key. The receiver sends that key to the sender in a secure way; the sender cannot get any information about the received key. The sender encrypts every message by operating on every message using the received key and sends all the encrypted messages to the receiver. The receiver is able to extract only the required message using his key. However, in the k -out-of- n OT protocol, the receiver sends a set of k keys to the sender, and in replay, the sender sends all the encrypted messages. The receiver uses his keys and extracts the required messages, but it cannot gain any information about the messages that it has not requested. Generally, the OT protocol requires high communication and computation cost if we transfer millions of oblivious messages. The OT extension protocol provides a solution for this, where the receiver transfers a set of keys to the sender by executing a few numbers of OT protocols. Then, the sender encrypts all the messages using cheap symmetric key cryptography with the help of a received set of keys and transfers millions of oblivious messages to the receiver. In this work, we present different variants of OT protocols such as one-out-of-2, one-out-of- n , k -out-of- n , and OT extension. Furthermore, we cover various aspects of theoretical security guarantees such as semi-honest and malicious adversaries, universally composable, used techniques, computation, and communication efficiency aspects. From the analysis, we found that the semi-honest adversary-based OT protocols required low communication and computation costs as compared to malicious adversary-based OT protocols.
Oblivious Transfer (OT) is a fundamental cryptographic protocol with applications in secure Multi-Party Computation, Federated Learning, and Private Set Intersection. With the advent of quantum computing, it is crucial to develop unconditionally secure core primitives like OT to ensure their continued security in the post-quantum era. Despite over four decades since OT's introduction, the literature has predominantly relied on computational assumptions, except in cases using unconventional methods like noisy channels or a fully trusted party. Introducing "Supersonic OT", a highly efficient and unconditionally secure OT scheme that avoids public-key-based primitives, we offer an alternative to traditional approaches. Supersonic OT enables a receiver to obtain a response of size O(1). Its simple (yet non-trivial) design facilitates easy security analysis and implementation. The protocol employs a basic secret-sharing scheme, controlled swaps, the one-time pad, and a third-party helper who may be corrupted by a semi-honest adversary. Our implementation and runtime analysis indicate that a single instance of Supersonic OT completes in 0.35 milliseconds, making it up to 2000 times faster than the state-of-the-art base OT.
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.
We propose constant-round protocols for interval tests, equality tests, and comparisons where shared secret inputs are not given bitwise. In [9]. Damgard et al. presented a novel protocol called the bit-decomposition, which can convert a polynomial sharing of an element in prime field p into sharings of bits. Though, by using the bit-decomposition protocol, those protocols can be constructed with constant round complexities theoretically, it involves expensive computation, leading to relatively high round and communication complexities. In this paper, we construct more efficient protocols for those protocols without relying on the bit-decomposition protocol. In the interval test protocol, checking whether a shared secret exists in the known interval is reduced to checking whether a bitwise-shared random secret exists in the appropriate interval. In the comparison protocol, comparing two shared secrets is reduced to comparing the two secrets via p/2 indirectly where p is an odd prime for an underlying linear secret sharing scheme. In the equality test protocol, checking whether two shared secrets are equal is reduced to checking whether the difference of the two secrets is zero and furthermore checking whether the difference is a zero is reduced to checking quadratice residuosity of a random secret in a probabilistic way.
We propose a new secure equality testing (SET) protocol, namely SET-OT, for two-party setting by using a recently introduced Private Set Membership Protocol (PSM) based on Oblivious Transfer (OT) as a building block. We designed our equality test in such a way that the test result will not be revealed in clear text, which is desired in several cryptographic protocols. The advantage of using OT is that with the help of OT Extension (OTE) protocols, the cost of asymmetric operations per OT operations reduces when the number of OT executions increases. This makes our protocol competitive especially for the cases where the number of equality tests to be invoked is high. When the number of equality test increases, the time complexity of SET-OT converges to one asymmetric key decryption operation, this operation is the dominant part in terms of computational cost. SET-OT has a better performance in terms of the communication rounds and data transmission cost than state-of-the-art solutions: three communication rounds and 2.9 KB of data transmission are the communication costs of performing equality testing protocol for 20-bit string pairs. In addition to our complexity analysis, we also present test results to validate our claim on performance.
We provide new two-round multiparty secure computation (MPC) protocols in the dishonest majority setting assuming the minimal assumption that two-round oblivious transfer (OT) exists. If the assumed two-round OT protocol is secure against semi-honest adversaries (in the plain model) then so is our two-round MPC protocol. Similarly, if the assumed two-round OT protocol is secure against malicious adversaries (in the common random/reference string model) then so is our two-round MPC protocol. Previously, two-round MPC protocols were only known under relatively stronger computational assumptions.