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The CORA (Coallocative, Oversubscribing Resource Allocation) architecture is an auction based resource reservation system that makes combinatorial allocations of resources to clients. The focus of this paper is on the use of cryptographic tools in CORA to remove the need for trust in the resource auctioneer. One of the nice properties of this approach is that the auctioneers can be drawn from an arbitrary pool of untrusted peers, without the need to establish pre-existing trust or restrict the role of auctioneer to a trusted system service. This approach results in more flexibility in the design of large economic systems, with the potential for wide distribution of load amongst many auctioneers. In addition, only the winners of the auction and the prices they pay are revealed while all other bid values are kept secret. It is our belief that future growth or commercialisation of large scale Grid systems requires the provision of such mechanisms to share the wide pool of Grid brokered resources such as computers, software, licences and peripherals amongst many users and organisations. This paper encapsulates an overview of our design, our experiences of implementing two different secure auction protocols and the performances that we have achieved.