The deployment of Share Data Spaces in open, possibly hostile, environments arises the need of protecting the confidentiality of the data space content. Existing approaches focus on access control mechanisms that protect the data space from untrusted agents. The basic assumption is that the hosts (and their administrators) where the data space is deployed have to be trusted. Encryption schemes can be used to protect the data space content from malicious hosts. However, these schemes do not allow searching on encrypted data. In this paper we present a novel encryption scheme that allows tuple matching on completely encrypted tuples. Since the data space does not need to decrypt tuples to perform the search, tuple confidentiality can be guaranteed even when the data space is deployed on malicious hosts (or an adversary gains access to the host). Our scheme does not require authorised agents to share keys for inserting and retrieving tuples. Each authorised agent can encrypt, decrypt, and search encrypted tuples without having to know other agents’ keys. This is beneficial inasmuch as it simplifies the task of key management. An implementation of an encrypted data space based on this scheme is described and some preliminary performance results are given.