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Quantum commitments from complexity assumptions

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Abstract

Bit commitment schemes are at the basis of modern cryptography. Since information-theoretic security is impossible both in the classical and in the quantum regime, we examine computationally secure commitment schemes. In this paper we study worst-case complexity assumptions that imply quantum bit commitment schemes. First, we show that QSZK \({\not\subseteq}\) QMA implies a computationally hiding and statistically binding auxiliary-input quantum commitment scheme. We then extend our result to show that the much weaker assumption QIP \({\not\subseteq}\) QMA (which is weaker than PSPACE \({\not\subseteq}\) PP) implies the existence of auxiliary-input commitment schemes with quantum advice. Finally, to strengthen the plausibility of the separation QSZK \({\not\subseteq}\) QMA, we find a quantum oracle relative to which honest-verifier QSZK is not contained in QCMA, the class of languages that can be verified using a classical proof in quantum polynomial time.

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Authors and Affiliations

  1. INRIA, Paris Rocquencourt, Rocquencourt, France

    André Chailloux

  2. LIAFA, CNRS, Université Paris 7, Paris, France

    Iordanis Kerenidis

  3. CQT, National University of Singapore, Singapore, Singapore

    Bill Rosgen

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  1. André Chailloux
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  2. Iordanis Kerenidis
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  3. Bill Rosgen
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Correspondence to André Chailloux.

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Chailloux, A., Kerenidis, I. & Rosgen, B. Quantum commitments from complexity assumptions. comput. complex. 25, 103–151 (2016). https://doi.org/10.1007/s00037-015-0116-5

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  • DOI: https://doi.org/10.1007/s00037-015-0116-5

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