Matrix Algorithm via Subspace Decomposition

Our objective is to devise a comprehensive and effective methodology for offering software anti-tamper protection via algorithm obfuscation. A primary Phase I goal will be to apply our techniques in the Kalman Filter setting, and use this as a baseline against which we can compare their effectiveness when applied to other matrix-based algorithms. Necessarily, we will devote appropriate resources to deriving meaningful metrics for measuring their efficacy. Phase I will comprise a proof-of-concept stage. We begin by specifiying a ``recursive or iterative matrix intensive algorithm,'' e.g., a Kalman Fiter. Our ``algorithm level obfuscation technique'' consists of a systematic subspace decompostion applied to pairs of (in general) non-commuting matrices. This approach is similar to an application of the Baker-Campbell-Hausdorff formula when specialized to matrix Lie Groups. In Phase II and III, we will develop the concepts from Phase I into a functional prototype. This will include, but may not be limited to combining (our) matrix-level algorithm obfuscation with tradition software obfuscation techniques. In addition, we will investigate the feasibility of developing ``meta-algorithms'' that can be applied to large classes of matrix-based algorithms, and will thereby not require detailed knowledge of the particular algorithm for which obfuscation is desired.