Vanishree et.al proposed a novel unconditionally oblivious polynomial evaluation protocol and they claimed that can fulfill both sender and receiver’s security. Here, this protocol is cryptanalyzed. We find that it has a fatal fault which cannot implement the receiver’s security at all and show the detail analyzing process. Keywords oblivious polynomial evaluation, oblivious transfer, multi-party computation
Vanishree et.al proposed a novel unconditionally oblivious polynomial evaluation protocol and they claimed that can fulfill both sender and receiver’s security. Here, this protocol is cryptanalyzed. We find that it has a fatal fault which cannot implement the receiver’s security at all and show the detail analyzing process. Keywords oblivious polynomial evaluation, oblivious transfer, multi-party computation
Abstract—Oblivious polynomial evaluation is a protocol involving two parties, a sender whose input is a polynomial P, and a receiver whose input is a value x. At the end of the protocol, the receiver learns P (x) and nothing more about P, while the sender remains oblivious of both x and P (x). It is used as a primitive in many applications including protocols for private comparison of data, for mutually authenticated key exchange based on (possibly weak) passwords, and for anonymous coupons. In this paper, we describe a novel unconditionally secure oblivious polynomial evaluation protocol. Keywords—Multi-Party Computation, Oblivious Transfer, Oblivious Polynomial Evaluation.
Oblivious polynomial evaluation is a protocol involving two parties: a sender whose input is a polynomial and a receiver whose input is a value a .Most of existing Oblivious Polynomial Evaluation protocols were built based on some cryptographically intractable problems which made them a higher computation complexity.By using some random and hiding secure information in them, this paper presents an unconditionally secure oblivious polynomial evaluation protocol.It does not rely on any cryptographic assumption and involves only simple computation.Further, our protocol does not include any third party and is more practice.
Historically, cryptography was created and used to deliver messages between people in such a way that only the intended receiver would be able to read them. The two persons communicating trusted each other, but not the rest of the world - for instance, not the message bearer. But what happens if we assume instead that even the receiver of a message may not be trusted by the sender, while both still have an interest in communicating? This problem is addressed by secure multi-party computation, that studies communication and shared computation between mutually distrusting parties. In a world where most of the communication happens over the Internet, and where an ever-increasing amount of computation is outsourced, for example to the cloud, multi-party computation is a subject of crucial importance. However, unconditionally secure multi-party protocols have never found practical application: the lack of realistic noisy channel models, that are required to achieve security against computationally unbounded adversaries, prevents implementation over real-world, standard communication protocols.\n\nIn this thesis, we study the properties and characteristics of noisy channels, and we introduce new models based on real-world error sources that have never been studied in this context, such as delays. On the contrary, previous works mostly focused on theoretical noisy channels that have little in common with the reality of network communication. We show that the models we propose are suitable for multi-party computation by building on each of them a protocol for oblivious transfer, a fundamental cryptographic primitive that implies any secure computation. Thanks to the realism of our noisy channels, we are able to provide the first working implementation of unconditionally secure oblivious transfer over both wired and wireless networks and different Internet protocols, which we test thoroughly in an extensive set of experiments. Our constructions are not only more realistic, but also more flexible, as they allow larger ranges of error probabilities. This will eventually open the way for the widespread use of unconditionally secure multi-party computation.
In this article, the authors cryptanalyze a k-out-of-n oblivious transfer protocol proposed in [12 Jain , A. , and C. Hari . 2010 . A New Efficient Protocol for k-out-of-n Oblivious Transfer , Cryptologia , 34 ( 4 ): 282 – 290 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]]. Their protocol is one of the most efficient k-out-of-n oblivious transfer protocols and is directly built from a 1-out-of-n oblivious transfer protocol. However, their analysis shows that the proposed k-out-of-n oblivious transfer protocol is insecure, though the primitive 1-out-of-n oblivious transfer protocol is secure. The weakness is that with high probability the receiver in their protocol can get all n secret messages encrypted by the sender. Finally, they fix the serious flaw and introduce an improved k-out-of-n oblivious transfer protocol without increasing any cost.
Abstract. Oblivious polynomial evaluation (OPE) consists of a two-party protocol where a sender inputs a polynomial p(x), and a receiver inputs a single value x0. At the end of the protocol, the sender learns nothing and the receiver learns p(x0). This paper deals with the problem of oblivious polynomial evaluation under an information-theoretic perspective, which is based on recent definitions of Unconditional Security developed by Crépeau et al. [11]. In this paper, we propose an information-theoretic model for oblivious polynomial evaluation relying on pre-distributed data, and prove very general lower bounds on the size of the pre-distributed data, as well as the size of the communications in any protocol. It is demonstrated that these bounds are tight by obtaining a round-optimal OPE protocol, which meets the lower bounds simultaneously. We present a natural generalization to OPE called oblivious linear functional evaluation.
We introduce a new approach to actively secure two-party computation based on so-called oblivious linear function evaluation (OLE), a natural generalisation of oblivious transfer (OT) and a special case of the notion of oblivious polynomial evaluation introduced by Naor and Pinkas at STOC 1999. OLE works over a finite field F. In an OLE the sender inputs two field elements a ƒ F and b ƒ F, and the receiver inputs a field element x ∈ F and learns only ƒx) = ax + b. Our protocol can evaluate an arithmetic circuit over a finite field F given black-box access to OLE for F. The protocol is unconditionally secure and consumes only a constant number of OLEs per multiplication gate. An OLE over a field F of size O(2κ) be implemented with communication O(κ). This gives a protocol with communication complexity O(C κ) for large enough fields, where C is an arithmetic circuit computing the desired function.