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arXiv:quant-ph/0403133 · Lecture notes in computer science

Universally Composable Privacy Amplification Against Quantum Adversaries

Renato Renner, Robert König

Published Jan 1, 2005• 330 citations
arXivHTMLPDF
DOI
10.1007/978-3-540-30576-7_22

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This paper examines classical privacy amplification using a universal family of hash functions. In quantum key distribution, the adversary's measurement can wait until the choice of hash functions is announced, and so the adversary's information may depend on the choice. Therefore the existing result on classical privacy amplification, which assumes the independence of the choice from the other random variables, is not applicable to this case. This paper provides a security proof of privacy amplification which is valid even when the adversary's information may depend on the choice of hash functions. The compression rate of the proposed privacy amplification can be taken to be the same as that of the existing one with an exponentially small loss in secrecy of a final key.
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.