Secret-key agreement over unauthenticated public channels-part III: privacy amplification

TLDR

The paper examines privacy amplification when legitimate parties share a partially known string, a scenario previously studied in passive‑adversary models such as quantum key agreement. The study proposes two protocols—universal hashing and extractor‑based—to achieve privacy amplification against an active adversary who knows at most one‑third of the initial string. The protocols rely on novel authentication techniques that remain secure even when the adversary knows a substantial portion of the secret key. References: For pt.; see ibid., vol.49, no.4, p.832‑38 (2003).

Abstract

For pt. II see ibid., vol.49, no.4, p.832-38 (2003). Here, we consider the special case where the legitimate partners already share a mutual string which might, however, be partially known to the adversary. The problem of generating a secret key in this case has been well studied in the passive-adversary model - for instance, in the context of quantum key agreement - under the name of privacy amplification. We consider the same problem with respect to an active adversary and propose two protocols, one based on universal hashing and one based on extractors, allowing for privacy amplification secure against an adversary whose knowledge about the initial partially secret string is limited to one third of the length of this string. Our results are based on novel techniques for authentication secure even against adversaries knowing a substantial amount of the "secret" key.