Secret-key agreement between two parties Alice and Bob, connected by an insecure channel, can be realized in an information-theoretic sense if the parties share many independent pairs of correlated and partially secure bits. We study the special case where only one-way communication from Alice to Bob is allowed and where, for each of the bit pairs, with a certain probability, the adversary has no information on Alice’s bit. We give an expression which, for this situation, exactly characterizes the rate at which Alice and Bob can generate secret key bits.