Abstract.We study the problem of searching on data that is encrypted using a public key system. Consider user Bob who sends email to user Alice encrypted under Alice's public key. An email gateway wants to test whether the email contains the keyword "urgent" so that it could route the email accordingly. Alice, on the other hand does not wish to give the gateway the ability to decrypt all her messages. We define and construct a mechanism that enables Alice to provide a key to the gateway that enables the gateway to test whether the word "urgent" is a keyword in the email without learning anything else about the email. We refer to this mechanism as Public Key Encryption with keyword Search. As another example, consider a mail server that stores various messages publicly encrypted for Alice by others. Using our mechanism Alice can send the mail server a key that will enable the server to identify all messages containing some specific keyword, but learn nothing else. We define the concept of public key encryption with keyword search and give several constructions.

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Abstract.A Single-Database Private Information Retrieval (PIR) is a protocol that allows a user to privately retrieve from a database an entry with as small as possible communication complexity. We call a PIR protocol non-trivial if its total communication is strictly less than the size of the database. Non-trivial PIR is an important cryptographic primitive with many applications. Thus, understanding which assumptions are necessary for implementing such a primitive is an important task, although (so far) not a well-understood one. In this paper we show that any non-trivial PIR implies Oblivious Transfer, a far better understood primitive. Our result not only significantly clarifies our understanding of any non-trivial PIR protocol, but also yields the following consequences:-Any non-trivial PIR is complete for all two-party and multi-party secure computations. -There exists a communication-efficient reduction from any PIR protocol to a 1-out-of-n Oblivious Transfer protocol (also called SPIR). -There is strong evidence that the assumption of the existence of a one-way function is necessary but not sufficient for any non-trivial PIR protocol.

We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the non-interactive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques.We show that interactive SZK for random self reducible languages (RSR) (and for CO-RSR) is closed under monotone boolean operations. Namely, we give SZK proofs for monotone boolean formulae whose atoms are statements about an SZK language which is RSR (or a complement of RSR).All previously known languages in SZK are in these classes. We then show that if a language L has a noninteractive SZK proof system then honest-verifier interactive SZK proof systems exist for all monotone boolean formulae whose atoms are statements about the complement of L.We also discuss extensions and generalizations.