On cryptography with auxiliary input

Abstract

We study the question of designing cryptographic schemes which are secure even if an arbitrary function f(sk) of the secret key is leaked, as long as the secret key sk is still (exponentially) hard to compute from this auxiliary input. This setting of auxiliary input is more general than the more traditional setting, which assumes that some of information about the secret key sk may be leaked, but sk still has high min-entropy left. In particular, we deal with situations where f(sk) information-theoretically determines the entire secret key sk.