11 research outputs found

    Accumulators in (and Beyond) Generic Groups: Non-Trivial Batch Verification Requires Interaction

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    We prove a tight lower bound on the number of group operations required for batch verification by any generic-group accumulator that stores a less-than-trivial amount of information. Specifically, we show that Ω(t⋅(λ/log⁥λ))\Omega(t \cdot (\lambda / \log \lambda)) group operations are required for the batch verification of any subset of t≄1t \geq 1 elements, where λ∈N\lambda \in \mathbb{N} is the security parameter, thus ruling out non-trivial batch verification in the standard non-interactive manner. Our lower bound applies already to the most basic form of accumulators (i.e., static accumulators that support membership proofs), and holds both for known-order (and even multilinear) groups and for unknown-order groups, where it matches the asymptotic performance of the known bilinear and RSA accumulators, respectively. In addition, it complements the techniques underlying the generic-group accumulators of Boneh, B{ĂŒ}nz and Fisch (CRYPTO \u2719) and Thakur (ePrint \u2719) by justifying their application of the Fiat-Shamir heuristic for transforming their interactive batch-verification protocols into non-interactive procedures. Moreover, motivated by a fundamental challenge introduced by Aggarwal and Maurer (EUROCRYPT \u2709), we propose an extension of the generic-group model that enables us to capture a bounded amount of arbitrary non-generic information (e.g., least-significant bits or Jacobi symbols that are hard to compute generically but are easy to compute non-generically). We prove our lower bound within this extended model, which may be of independent interest for strengthening the implications of impossibility results in idealized models

    Invisible Sanitizable Signatures and Public-Key Encryption are Equivalent

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    Sanitizable signature schemes are signature schemes which support the delegation of modification rights. The signer can allow a sanitizer to perform a set of admissible operations on the original message and then to update the signature, in such a way that basic security properties like unforgeability or accountability are preserved. Recently, Camenisch et al. (PKC 2017) devised new schemes with the previously unattained invisibility property. This property says that the set of admissible operations for the sanitizer remains hidden from outsiders. Subsequently, Beck et al. (ACISP 2017) gave an even stronger version of this notion and constructions achieving it. Here we characterize the invisibility property in both forms by showing that invisible sanitizable signatures are equivalent to IND-CPA-secure encryption schemes, and strongly invisible signatures are equivalent to IND-CCA2-secure encryption schemes. The equivalence is established by proving that invisible (resp. strongly invisible) sanitizable signature schemes yield IND-CPA-secure (resp. IND-CCA2-secure) public-key encryption schemes and that, vice versa, we can build (strongly) invisible sanitizable signatures given a corresponding public-key encryption scheme
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