At Crypto 2003 Ishai et al. gave a protocol which given a small number of (possibly extremely inefficient) oblivious transfers implements an essentially unbounded number of oblivious transfers for an additional overhead, per oblivious transfer, of computing and sending only two hash values. This highly efficient protocol is however only passive secure. To get active security, except with probability 2 −m, the protocol had to suffer an additional overhead of a factor 1 + m. We introduce a new approach to adding robustness. For practical security parameters this approach allows to add robustness while suffering only a small constant overhead over the passive secure protocol. As an example we can generate one million oblivious transfers with security 2 −42 with an amortized cost of just 9 hash values per oblivious transfer.
At Crypto 2003 Ishai et al. gave a protocol which given a small number of (possibly extremely inefficient) oblivious transfers implements an essentially unbounded number of oblivious transfers for an additional overhead, per oblivious transfer, of computing and sending only two hash values. This highly efficient protocol is however only passive secure. To get active security, except with probability 2 −m, the protocol had to suffer an additional overhead of a factor 1 + m. We introduce a new approach to adding robustness. For practical security parameters this approach allows to add robustness while suffering only a small constant overhead over the passive secure protocol. As an example we can generate one million oblivious transfers with security 2 −42 with an amortized cost of just 9 hash values per oblivious transfer.
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
Abstract. On top of the passively secure extension protocol of [IKNP03] we build a new construction secure against active adversaries. We can replace the invocation of the hash function that is used to check the receiver is well-behaved with the XOR of bit strings. This is pos-sible by applying a cut-and-choose technique on the length of the bit strings that the receiver sends in the reversed OT. We also improve on the number of seeds required for the extension, both asymptotically and practically. Moreover, the protocol used to test receiver’s behaviour en-joys unconditional security. 1
Abstract. We consider the problem of extending oblivious transfers: Given a small number of oblivious transfers “for free, ” can one implement a large number of oblivious transfers? Beaver has shown how to extend oblivious transfers given a one-way function. However, this protocol is inefficient in practice, in part due to its non-black-box use of the underlying one-way function. We give efficient protocols for extending oblivious transfers in the random oracle model. We also put forward a new cryptographic primitive which can be used to instantiate the random oracle in our constructions. Our methods suggest particularly fast heuristics for oblivious transfer that may be useful in a wide range of applications. 1
Oblivious transfer is one of the most basic and important building blocks in cryptography. As such, understanding its cost is of prime importance. Beaver (STOC 1996) showed that it is possible to obtain poly(n) oblivious transfers given only n actual oblivious transfer calls and using one-way functions, where n is the security parameter. In addition, he showed that it is impossible to extend oblivious transfer information theoretically. The notion of extending oblivious transfer is important theoretically (to understand the complexity of computing this primitive) and practically (since oblivious transfers can be expensive and thus extending them using only one-way functions is very attractive). Despite its importance, very little is known about the feasibility of extending oblivious transfer, beyond the fact that it is impossible information theoretically. Specifically, it is not known whether or not one-way functions are actually necessary for extending oblivious transfer, whether or not it is possible to extend oblivious transfers with adaptive security, and whether or not it is possible to extend oblivious transfers when starting with just a few. In this paper, we address these questions and provide almost complete answers to all of them. We show that the existence of any oblivious transfer extension protocol with security for static semihonest adversaries implies one-way functions, that an oblivious transfer extension protocol with adaptive security implies oblivious transfer with static security, and that the existence of an oblivious transfer extension protocol from only O(log n) oblivious transfers implies oblivious transfer itself.
Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We provide the first oblivious transfer protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust the setup (and some setup is needed for UC security). Trust in computational assumptions: only one of the parties needs to trust a computational assumption. Round complexity: it uses only two rounds. Communication complexity: it communicates O(1) group elements to transfer one out of two group elements. The Big-O notation hides 32, meaning that the communication is probably not optimal, but is essentially optimal in that the overhead is at least constant. Our construction is based on pairings, and we assume the presence of a key registration authority.
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.