Abstract-This is the first part of a three-part paper on secret-key agreement secure against active adversaries. In all three parts, we address the question whether two parties, knowing some correlated pieces of information X and Y , respectively, can generate a string S about which an adversary, knowing some information Z and having read and write access to the communication channel used by the legitimate partners, is almost completely ignorant. Whether such key agreement is possible, and if yes at which rate, is an inherent property of the joint probability distribution P XY Z . In this part, we first prove a number of general impossibility results. We then consider the important special case where the legitimate partners as well as the adversary have access to the outcomes of many independent repetitions of a fixed tripartite random experiment. In this case, the result characterizing the possibility of secret-key agreement secure against active adversaries is of all-or-nothing nature: Either a secret key can be generated at the same rate as in the (well-studied) passive-adversary case, or such secret-key agreement is completely impossible. The exact condition characterizing the two cases is presented.
The adversary can be a passive eavesdropper (as is also the case for the DH protocol); the possibility of key establishment in the presence of active adversaries is proven REF .
Secret-key agreement over unauthenticated public channels I: Definitions and a completeness result
IEEE Trans. Inf. Theory
IEEE Trans. Inf. Theory
Computer Science