We present strong evidence that the implication, "if one-way permutations exist, then secure secret key agreement is possible" is not provable by standard techniques. Since both sides of this implication are widely believed true in real life, to show that the implication is false requires a new model. We consider a world where dl parties have access to a black box or a randomly selected permutation. Being totally random, this permutation will be strongly oneway in provable, information-thevretic way. We show that, if P = NP, no protocol for secret key agreement is secure in such setting. Thus, to prove that a secret key greement protocol which uses a one-way permutation as a black box is secure is as hrd as proving F NP. We also obtain, as corollary, that there is an oracle relative to which the implication is false, i.e., there is a one-way permutation, yet secret-exchange is impossible. Thus, no technique which relativizes can prove that secret exchange can be based on any one-way permutation. Our results present a general framework for proving statements of the form, "Cryptographic application X is not likely possible based solely on complexity assumption Y." 1

With a public key cryptosystem, the key used to encipher a message can be made public without compromising the secrecy of a different key needed to decipher that message. I. COMMERCIAL NEED FOR ENCRYPTION This problem is compounded in remote computing Cryptography has been of great importance to the mil- because the entire “conversation”is in computer readable itary and diplomatic communities since antiquity but form. An eavesdropper can then cheaply sort messages failed, until recently,.to attract much commercial atten-not only on the basis of the called number, but also on the tion. Recent commercial interest, by contrast, has been content of’the message, and record all messages which almost explosive due to the rapid computerization of contain one or more keywords. By including a name or information storage, transmission, and spying.

Keyword search is a critical component in most content retrieval systems. Despite the emergence of completely decentralized and efficient peer-to-peer techniques for content distribution, there have not been similarly efficient, accurate, and decentralized mechanisms for contentdiscoverybasedonapproximatesearchkeys. Inthis paper, we present a scalable and efficient peer-to-peer system calledCubitwith anewsearchprimitivethat can efficientlyfindthe k dataitemswithkeysmostsimilarto a givensearchkey. Thesystem worksbycreatingakeyword metric space that encompasses both the nodes and theobjectsinthesystem,wherethedistancebetweentwo points is a measure of the similarity between the strings thatthepointsrepresent. It providesa loosely-structured overlaythat can efficientlynavigatethis space. We evaluate Cubit through both a real deployment as a search plugin for a popular BitTorrent client and a large-scale simulation and show that it provides an efficient, accurateandrobustmethodto handleimprecisestringsearch infilesharingapplications. 1