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An adaptive k-out-of-N Priced Oblivious Transfer (POT) scheme is a two-party protocol between a vendor and a buyer. The vendor sells a set of messages m 1 ,. .. , m N with prices p 1 ,. .. , p N. In each transfer phase i = 1,. .. , k, the buyer chooses a selection value σ i ∈ {1,. .. , N } and interacts with the vendor to buy message m σi in such a way that the vendor does not learn σ i and the buyer does not get any information about the other messages. We present a POT scheme secure under pairing-related assumptions in the standard model. Our scheme is universally composable and thus, unlike previous results, preserves security when it is executed with multiple protocol instances that run concurrently in an adversarially controlled way. Furthermore, after an initialization phase of complexity O(N), each transfer phase is optimal in terms of rounds of communication and it has constant computational and communication cost. To achieve these properties, we design the first efficient non-interactive proof of knowledge that a value lies in a given interval we are aware of.

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Abstract. Searchable encryption schemes provide an important mechanism to cryptographically protect data while keeping it available to be searched and accessed. In a common approach for their construction, the encrypting entity chooses one or several keywords that describe the content of each encrypted record of data. To perform a search, a user obtains a trapdoor for a keyword of her interest and uses this trapdoor to find all the data described by this keyword.We present a searchable encryption scheme that allows users to privately search by keywords on encrypted data in a public key setting and decrypt the search results. To this end, we define and implement two primitives: public key encryption with oblivious keyword search (PEOKS) and committed blind anonymous identity-based encryption (IBE). PEOKS is an extension of public key encryption with keyword search (PEKS) in which users can obtain trapdoors from the secret key holder without revealing the keywords. Furthermore, we define committed blind trapdoor extraction, which facilitates the definition of authorisation policies to describe which trapdoor a particular user can request. We construct a PEOKS scheme by using our other primitive, which we believe to be the first blind and anonymous IBE scheme.We apply our PEOKS scheme to build a public key encrypted database that permits authorised private searches, i.e., neither the keywords nor the search results are revealed.

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