Correcting errors without leaking partial information (original) (raw)

This paper explores what kinds of information two parties must communicate in order to correct errors which occur in a shared secret string W . Any bits they communicate must leak a significant amount of information about W -that is, from the adversary's point of view, the entropy of W will drop significantly. Nevertheless, we construct schemes with which Alice and Bob can prevent an adversary from learning any useful information about W . Specifically, if the entropy of W is sufficiently high, then there is no function f (W ) which the adversary can learn from the error-correction information with significant probability. This leads to several new results: