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Lecture notes in computer science

Lattice-Based Completely Non-malleable PKE in the Standard Model (Poster)

Reza Sepahi, Ron Steinfeld, Josef Pieprzyk

Published Jan 1, 2011• 3 citations
Publisher
DOI
10.1007/978-3-642-22497-3_26

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Non-malleability is an important security property for public-key encryption (PKE). Its significance is due to the fundamental unachievability of integrity and authenticity guarantees in this setting, rendering it the strongest integrity-like property achievable using only PKE, without digital signatures. In this work, we generalize this notion to the setting of quantum public-key encryption. Overcoming the notorious "recording barrier" known from generalizing other integrity-like security notions to quantum encryption, we generalize one of the equivalent classical definitions, comparison-based non-malleability, and show how it can be fulfilled. In addition, we explore one-time non-malleability notions for symmetric-key encryption from the literature by defining plaintext and ciphertext variants and by characterizing their relation.
We construct two-message non-malleable commitments with respect to opening in the standard model, assuming only one-to-one one-way functions. Our protocol consists of two unidirectional messages by the committer (with no message from the receiver), and is secure against all polynomial-time adversaries in the standard synchronous setting. Pass (TCC 2013) proved that any commitment scheme with non-malleability with respect to commitment, using only 2 rounds of communication, cannot be proved secure via a black-box reduction to any "standard" intractability assumption. We extend this by showing a similar impossibility result for commitments with non-malleability with respect to opening, another standard notion of non-malleability for commitments, for any 2-message challenge-response protocol, as well. However, somewhat surprisingly, we show that this barrier breaks down in the setting of two unidirectional messages by the committer (with no message from the receiver), for non-malleability with respect to opening.°Our protocol makes only black-box use of any non-interactive statistically binding commitment scheme. Such a scheme can be based on any one-to-one one-way function.°Our techniques depart significantly from the commit-challenge-response structure followed by nearly all prior works on non-malleable protocols in the standard model. Our methods are combinatorial in nature.°Our protocol resolves the round complexity of commitments with non-malleability with respect to opening via natural (non-embedding) black-box security reductions. We show that completely non-interactive non-malleable commitments w.r.t. opening cannot be proved secure via most natural black-box reductions. This result extends to also rule out bi-directional two-message non-malleable commitments w.r.t. opening in the synchronous or asynchronous setting.°Our protocol, together with our impossibility result, also resolves the round complexity of block-wise non-malleable codes (Chandran et al) w.r.t. natural black-box reductions.