Universally Composable Privacy Amplification Against Quantum Adversaries

By Renato Renner, Robert T. König. Theory of Cryptography Conference, 2004

377 citations recorded by the source corpus.

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 Z. Our result has applications in quantum cryptography. In particular, it implies that many of the known quantum key distribution protocols are universally composable.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/221b2570f46d7b3995fb4d38acbf0328c53901c6

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Citations in the corpus

Quantum random number generation (2015, background): “The composable extractor was ﬁrst introduced in classical cryptography 93,94 , and was later extended to quantum cryptography 95,96 .”
Phase-Matching Quantum Key Distribution (2018, background): “[41] Renato Renner and Robert König, “Universally composable privacy amplification against quantum adversaries,” in Theory of Cryptography: Second Theory of Cryptography Conference, TCC 2005, Cambridge, MA, USA, February 10-12, 2005.”
Quantum Cryptography (2006, positive): “The generalization to the quantum setting (Theorem 1) is due to Renner and König [49, 52].”
Quantum random number generators (2016, methodology): “These methods are also applied in privacy amplification in Quantum Key Distribution (Bennett et al., 1995, 1988; König et al., 2005; Renner and König, 2005).”
Min- and Max-Relative Entropies and a New Entanglement Monotone (2008, background): “The same holds if ρ is only a subnormalized density operator.”
A Fully Quantum Asymptotic Equipartition Property (2008, background): “Bounds on the convergence derived from this argument will depend on the convergence of the individual terms and thus in general on the Hilbert space dimensions of and (see [3]). where and are the identity operators on and , respectively.”
Tight finite-key analysis for quantum cryptography (2011, methodology): “Privacy Ampliﬁcation: Alice extracts (cid:96) bits of secret key S from X using a random universal 2 hash function [43, 44].”
Quantum And Relativistic Protocols For Secure Multi-Party Computation (2009, background): “(See [21, 72, 73] for a further discussion, and an explicit example.”
Secure quantum key distribution (2014, background): “Fortunately, QKD is composably secure [5, 6, 24].”