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
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
Abstract. We study an adaptive variant of oblivious transfer in which a sender has N messages, of which a receiver can adaptively choose to re-ceive k one-after-the-other, in such a way that (a) the sender learns noth-ing about the receiver’s selections, and (b) the receiver only learns about the k requested messages. We propose two practical protocols for this primitive that achieve a stronger security notion than previous schemes with comparable efficiency. In particular, by requiring full simulatabil-ity for both sender and receiver security, our notion prohibits a subtle selective-failure attack not addressed by the security notions achieved by previous practical schemes. Our first protocol is a very efficient generic construction from unique blind signatures in the random oracle model. The second construction does not assume random oracles, but achieves remarkable efficiency with only a constant number of group elements sent during each transfer. This second construction uses novel techniques for building efficient simulat-able protocols. 1
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.
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.
1 IntroductionOblivious Transfer (OT) protocols allow one party, the sender, to transmit part of its inputs to another party, the chooser, in a manner that protects both of them: the sender is assured that the chooser does not receive more information than it is entitled, while the chooser is assured that the sender does not learn which part of the inputs it received. OT is used as a key component in many applications of cryptography. Its computational requirements are quite demanding and they are likely to be the bottleneck in many applications that invoke it.1.1 Contributions.This paper presents several significant improvements to oblivious transfer (OT) protocols of strings, and in particular: (i) Improving the efficiency of applications which many invocations of oblivious transfer. (ii) Providing the first two-round OT protocol whose security analysis does not invoke the random oracle model.
Oblivious Transfer (OT) is a fundamental building block for secure computation, in which a sender holds two messages and a receiver learns exactly one of them, without revealing which one was chosen and without learning the other. While generic constructions for Universally Composable (UC) OT exist, instantiating them from post-quantum assumptions remains challenging, particularly under adaptive corruption. In this work, we present the first adaptively UC-secure OT protocol based on Group Actions, specifically assuming weakly pseudorandom Effective Group Actions (EGA) like CSIDH. We adhere to the framework of [BC15], which derives an adaptively UC-secure OT protocol from SPHF-friendly extractable and equivocable ( ⋿ 2 ) commitment schemes. The central challenge in instantiating this construction from group actions is the lack of SPHF-friendly IND-CCA encryption. Classical CCA transformations such as Fujisaki-Okamoto destroy the algebraic structure required for building SPHFs over ciphertexts, while known group action-based schemes offer no native mechanism to prove ciphertext validity. To overcome this obstacle, we construct from group actions an IND-CCA encryption scheme with enough algebraic structure to efficiently recognize valid ciphertexts. Our contributions are threefold: (1) a verifiable chameleon hash function with perfect soundness in the standard model, (2) an SPHF-friendly, publicly verifiable IND-CCA encryption scheme in the random oracle model, and (3) we combine these to build an SPHF-friendly ⋿ 2 commitment scheme and derive a fully adaptively secure OT protocol in the UC framework. This is the first construction of its kind under group action assumptions, enabling post-quantum secure OT with adaptive security guarantees. These building blocks may also be of independent interest e.g., to obtain digital signatures, non-malleable commitment schemes, or verifiable encryption.
Abstract: Oblivious transfer is an important cryptographic protocol in various security applications. For example, in on-line transactions, a k-out-of-n oblivious transfer scheme allows a buyer to privately choose k out of n digital goods from a merchant without learning information about other n−k goods. In this paper, we propose several efficient two-round k-out-of-n oblivious transfer schemes, in which the receiver R sends O(k) messages to the sender S, andS sends O(n) messages back to R. The schemes provide unconditional security for either sender or receiver. The computational security for the other side is based on the Decisional Diffie-Hellman (DDH) or Chosen-Target Computational Diffie-Hellman (CT-CDH) problems. Our schemes have the nice property of universal parameters, that is, each pair of R and S need not hold any secret before performing the protocol. The system parameters can be used by all senders and receivers without any trapdoor specification. In some cases, our OT k n schemes are the most efficient ones in terms of the communication cost, either in rounds or the number of messages. Moreover, one of our schemes is extended to an adaptive oblivious transfer scheme. In that scheme, S sends O(n) messages to R in one round in the commitment phase. For each query of R, onlyO(1) messages are exchanged and O(1) operations are performed. The preliminary version of this paper was published at PKC ’05 [Chu and Tzeng 2005].