Abstract. The combination of software-as-a-service and the increasing use of mobile devices gives rise to a considerable difference in computational power between servers and clients. Thus, there is a desire for clients to outsource the evaluation of complex functions to an external server. Servers providing such a service may be rewarded per computation, and as such have an incentive to cheat by returning garbage rather than devoting resources and time to compute a valid result. In this work, we introduce the notion of Revocable Publicly Verifiable Computation (RPVC), where a cheating server is revoked and may not perform future computations (thus incurring a financial penalty). We introduce a Key Distribution Center (KDC) to efficiently handle the generation and distribution of the keys required to support RPVC. The KDC is an authority over entities in the system and enables revocation. We also introduce a notion of blind verification such that results are verifiable (and hence servers can be rewarded or punished) without learning the value. We present a rigorous definitional framework, define a number of new security models and present a construction of such a scheme built upon Key-Policy Attribute-based Encryption.

Publicly Verifiable Outsourced Computation (PVC) allows devices with restricted resources to delegate expensive computations to more powerful external servers, and to verify the correctness of results. Whilst highlybeneficial in many situations, this increases the visibility and availability of potentially sensitive data, so we may wish to limit the sets of entities that can view input data and results. Additionally, it is highly unlikely that all users have identical and uncontrolled access to all functionality within an organization. Thus there is a need for access control mechanisms in PVC environments.In this work, we define a new framework for Publicly Verifiable Outsourced Computation with Access Control (PVC-AC). We formally define algorithms to provide different PVC functionality for each entity within a large outsourced computation environment, and discuss the forms of access control policies that are applicable, and necessary, in such environments, as well as formally modelling the resulting security properties. Finally, we give an example instantiation that (in a black-box and generic fashion) combines existing PVC schemes with symmetric Key Assignment Schemes to cryptographically enforce the policies of interest.

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Publicly Verifiable Outsourced Computation (PVC) allows weak devices to delegate computations to more powerful servers, and to verify the correctness of results. Delegation and verification rely only on public parameters, and thus PVC lends itself to large multi-user systems where entities need not be registered. In such settings, individual user requirements may be diverse and cannot be realised with current PVC solutions. In this paper, we introduce Hybrid PVC (HPVC) which, with a single setup stage, provides a flexible solution to outsourced computation supporting multiple modes: (i) standard PVC, (ii) PVC with cryptographically enforced access control policies restricting the servers that may perform a given computation, and (iii) a reversed model of PVC which we call Verifiable Delegable Computation (VDC) where data is held remotely by servers. Entities may dynamically play the role of delegators or servers as required.

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