Since the discovery of simple power attacks, the cryptographic research community has developed significantly more advanced attack methods. The idea behind most algorithms remains to perform a statistical analysis by correlating the power trace obtained when executing a cryptographic primitive to a key-dependent guess. With the advancements of cryptographic countermeasures, it is not uncommon that sophisticated (higher order) power attacks require computation on many millions of power traces to find the desired correlation. In this paper, we study the computational aspects of calculating the most widely used correlation coefficient: the Pearson product-moment correlation coefficient. We study various time-memory trade-off techniques which apply specifically to the cryptologic setting and present methods to extend already completed computations using incremental versions. Moreover, we show how this technique can be applied to second-order attacks, reducing the attack cost significantly when adding new traces to an existing dataset. We also present methods which allow one to split the potentially huge trace set into smaller, more manageable chunks to reduce the memory requirements. Our parallel implementation of these techniques highlights the benefits of this approach as it allows efficient computations on power measurements consisting of hundreds of gigabytes on a single modern workstation.

We motivate and address the problem of testing for properties of interest in real-world implementations of authorization systems. We adopt a 4-stage process: (1) express a property precisely using existential second-order logic, (2) establish types of traces that are necessary and sufficient to establish a property, (3) adopt finitizing assumptions and show that under those assumptions, verifying a property is in PSPACE, and, (4) use a model-checker as a tracegenerator to generate instances of traces, and exercise the implementation to check for those traces. We discuss our design of a corresponding testing-system, and its use to test for qualitatively different kinds of properties in two commercial authorization systems. One is a database system that we call the D System, and the other is a file-sharing system that we call the I System. (We use pseudonyms at the request of the respective vendors.) In the context of the D System, our testing has uncovered several issues with its authorization system in the context of procedures that aggregate SQL statements that, to our knowledge, are new to the research literature. For the I System, we have established that it possesses several properties of interest.

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