Multi-Dimensional Range Query over Encrypted Data

Abstract

We design an encryption scheme called Multi-dimensional Range Query over Encrypted Data (MRQED), to address the privacy concerns related to the sharing of network audit logs and various other applications. Our scheme allows a network gateway to encrypt summaries of network flows before submitting them to an untrusted repository. When network intrusions are suspected, an authority can release a key to an auditor, allowing the auditor to decrypt flows whose attributes (e.g., source and destination addresses, port numbers, etc.) fall within specific ranges. However, the privacy of all irrelevant flows are still preserved. We formally define the security for MRQED and prove the security of our construction under the decision bilinear Diffie-Hellman and decision linear assumptions in certain bilinear groups. We study the practical performance of our construction in the context of network audit logs. Apart from network audit logs, our scheme also has interesting applications for financial audit logs, medical privacy, untrusted remote storage, etc. In particular, we show that MRQED implies a solution to its dual problem, which enables investors to trade stocks through a broker in a privacy-preserving manner.Recently, the network intrusion detection community has made large-scale efforts to collect network audit logs from different sites [25,35,24]. In this application, a network gateway or an Internet Service Provider (ISP) can submit network traces to an audit log repository. However, due to the presence of privacy sensitive information in the network traces, the gateway will allow only authorized parties to search their audit logs. We consider the following four types of entities: a gateway, an untrusted repository, an authority, and an auditor. We design a cryptographic primitive that allows the gateway to submit encrypted audit logs to the untrusted repository. Normally, no one is able to decrypt these audit logs. However, when malicious behavior is suspected, an auditor may ask the authority for a search capability. With this search capability, the auditor can decrypt entries satisfying certain properties, e.g., network flows whose destination address and port number fall within a certain range. However, the privacy of all other flows should still be preserved. Note that in practice, to avoid a central point of trust, we can have multiple parties to jointly act as the authority. Only when a sufficient number of the parities collaborate, can they generate a valid search capability.We name our encryption scheme Multi-dimensional Range Query over Encrypted Data (MRQED). In MRQED, we encrypt a message with a set of attributes. For example, in the network audit log application, the attributes are the fields of a network flow, e.g., source and destination addresses, port numbers, time-stamp, protocol number, etc. Among these attributes, suppose that we would like to support queries on the time-stamp t, the source address a and the destination port number p. Our encryption scheme provides the following properties:• Range ...

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