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arXiv:1504.05255 · Lecture notes in computer science

Semantic Security and Indistinguishability in the Quantum World

Tommaso Gagliardoni, Andreas Hülsing, Christian Schaffner

Published Jan 1, 2016• 46 citations
arXivHTMLPDF
DOI
10.1007/978-3-662-53015-3_3

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We investigate the definition of security for encryption scheme in quantum context. We systematically define the indistinguishability and semantic security for quantum public-key and private-key encryption schemes, and for computational security, physical security and information-theoretic security. Based on our definition, we present a necessary and sufficient condition that leads to information-theoretic indistinguishability for quantum encryption scheme. The equivalence between the indistinguishability and semantic security of quantum encryption scheme is also proved.
We provide a formalization of the emergent notion of “functional encryption,” as well as introduce various security notions for it, and study relations among the latter. In particular, we show that indistinguishability and semantic security based notions of security are inequivalent for functional encryption in general; in fact, “adaptive” indistinguishability does not even imply “non-adaptive” semantic security. This is alarming given the large body of work employing (special cases of) the former. We go on to show, however, that in the “non-adaptive” case an equivalence does hold between indistinguishability and semantic security for what we call preimage sampleable schemes. We take this as evidence that for preimage sampleable schemes an indistinguishability based notion may be acceptable in practice. We show that some common functionalities considered in the literature satisfy this requirement.
Contrary to expectation, we show that there is no general reduction from simulation-based selective opening security (SSO) to indistinguishability-based selective opening security (ISO) in the CCA setting. In particular, we show that when restricted to certain message distributions, SSO-CCA is incomparable with ISO-CCA. This contrasts the CPA case, where SSO-CPA is known to be strictly stronger than ISO-CPA relative to any message sampler. Any sampler with high enough min-entropy suffices for this “semi-separation” to appear. On the other hand, we show that restricting to distributions with very low min-entropy gives rise to an implication. Our main result does not rely on the presence of selective openings, but rather follow from subtleties in the game structures. At a glance, this may seem to contradict known equivalences between indistinguishability, semantic security, and selective opening security under trivial openings. We reconcile the apparent contradiction by showing that the CCA landscape splits into a “high-entropy” and a “low-entropy” world, which for notions of SOA must be treated separately.