Information Security and Cryptography Research Group

Universally Composable Privacy Amplification Against Quantum Adversaries

Renato Renner and Robert Koenig

Theory of Cryptography Conference — TCC 2005, Lecture Notes in Computer Science, Springer-Verlag, vol. 3378, pp. 407–425, Feb 2005, Also available at

Privacy amplification is the art of shrinking a partially secret string Z to a highly secret key S. We show that, even if an adversary holds quantum information about the initial string Z, the key S obtained by two-universal hashing is secure, according to a universally composable security definition. Additionally, we give an asymptotically optimal lower bound on the length of the extractable key S in terms of the adversary's (quantum) knowledge about S. Our result has applications in quantum cryptography. In particular, it implies that many of the known quantum key distribution protocols are universally composable.

BibTeX Citation

    author       = {Renato Renner and Robert Koenig},
    title        = {Universally Composable Privacy Amplification Against Quantum Adversaries},
    editor       = {Joe Kilian},
    booktitle    = {Theory of Cryptography Conference --- TCC 2005},
    pages        = {407--425},
    series       = {Lecture Notes in Computer Science},
    volume       = {3378},
    year         = {2005},
    month        = {2},
    note         = {Also available at},
    publisher    = {Springer-Verlag},

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