HOW TO GENERATE AND EXCHANGE SECRETS.

A tool for controlling the knowledge transfer process in cryptographic protocol design is introduced and used to solve a general class of problems that include most of the two-party cryptographic problems in the literature. Specifically, it is shown how two parties A and B can interactively generate a random integer N equals p multiplied by q such that its secret (i. e. , the prime factors p, q) is hidden from either party individually but is recoverable jointly if desired. This can be utilized to give a protocol for two parties with private values i and j to compute any polynomial computable functions f(i,j) and g(i,j) with minimal knowledge transfer and a strong fairness property. As a special case, A and B can exchange a pair of secrets S//A , S//B in such a way that S//A becomes computable by B when and only when S//B becomes computable by A.