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

This technical point will prevent the reader from suspecting any measure-theoretic fallacy.