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We study verifiable outsourcing of computation in a model where the verifier has black-box access to the function being computed. We introduce the problem of oracle-aided batch verification of computation (OBVC) for a function class $$\mathcal{F}$$. This allows a verifier to efficiently verify the correctness of any $$f \in \mathcal{F}$$ evaluated on a batch of $$n$$ instances $$x_1, \ldots, x_n$$, while only making $$\lambda$$ calls to an oracle for $$f$$ (along with $$O(n \lambda)$$ calls to low-complexity helper oracles), for security parameter $$\lambda$$. We obtain the following positive and negative results: - We build OBVC protocols for the class of all functions that admit {\em random-self-reductions}. Some of our protocols rely on homomorphic encryption schemes. - We show that there cannot exist OBVC schemes for the class of all functions mapping $$\lambda$$-bit inputs to $$\lambda$$-bit outputs, for any $$n = \mathsf{poly}(\lambda)$$.
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Gray-box monitoring of hyperproperties with an application to privacy
Abstract Runtime verification is a complementary approach to testing, model checking and other static verification techniques to verify software properties. Monitorability characterizes what can be verified (monitored) at run time. Different definitions of monitorability have been given both for trace properties and for hyperproperties (properties defined over sets of traces), but these definitions usually cover only some aspects of what is important when characterizing the notion of monitorability. The first contribution of this paper is a refinement of classic notions of monitorability both for trace properties and hyperproperties, taking into account, among other things, the computability of the monitor. A second contribution of our work is to show that black-box monitoring of HyperLTL (a logic for hyperproperties) is in general unfeasible, and to suggest a gray-box approach in which we combine static and runtime verification. The main idea is to call a static verifier as an oracle at run time allowing, in some cases, to give a final verdict for properties that are considered to be non-monitorable under a black-box approach. Our third contribution is the instantiation of this solution to a privacy property called distributed data minimization which cannot be verified using black-box runtime verification. We use an SMT-based static verifier as an oracle at run time. We have implemented our gray-box approach for monitoring data minimization into the proof-of-concept tool Minion . We describe the tool and apply it to a few case studies to show its feasibility.
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- Award ID(s):
- 2100989
- PAR ID:
- 10384537
- Date Published:
- Journal Name:
- Formal Methods in System Design
- Volume:
- 58
- Issue:
- 1-2
- ISSN:
- 0925-9856
- Page Range / eLocation ID:
- 126 to 159
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10703-020-00358-w
