A secure, tamper proof execution environment is critical for trustworthy network computing. Newly emerging hardware, such as those developed as part of the TCPA and Palladium initiatives, enables operating systems to implement such an environment through Merkle hash trees. We examine the selection of optimal parameters, namely blocksize and tree depth, for Merkle hash trees based on the size of the memory region to be protected and the number of memory updates between updates of the hash tree. We analytically derive an expression for the cost of updating the hash tree, show that there is an optimal block size for the leaves of a Merkle tree for a given file size and update interval that minimizes the cost of update operations, and describe a general method by which the parameters of such a tree can be determined optimally.