We analyze how fast we can solve general systems of multivariate equations of various low degrees over F2; this is a well known hard problem which is important both in itself and as part of many types of algebraic cryptanalysis. Compared to the standard exhaustive search technique, our improved approach is more efficient both asymptotically and practically. We implemented several optimized versions of our techniques on CPUs and GPUs. Our technique runs more than 10 times faster on modern graphic cards than on the most powerful CPU available. Today, we can solve 48+ quadratic equations in 48 binary variables on a 500-dollar NVIDIA GTX 295 graphics card in 21 minutes. With this level of performance, solving systems of equations supposed to ensure a security level of 64 bits turns out to be feasible in practice with a modest budget. This is a clear demonstration of the computational power of GPUs in solving many types of combinatorial and cryptanalytic problems.
Abstract-Spectrum sensing is of fundamental importance to many wireless applications including cognitive radio channel assignment and radiolocation. However, conventional spectrum sensing can be prohibitively expensive in computation and network bandwidth when the bands under scanning are wide and highly contested. In this paper we propose distributed spectrum sensing with multiple sensing nodes in a UAV environment. The ground nodes in our scheme sense the spectrum in parallel using compressive sensing. Each sensor node transmits compressive measurements to a nearby UAV in the air. The UAV performs decoding on the received measurements; it decodes information with increasing resolution as it receives more measurements. Furthermore, by a property of compressive sensing decoding, frequencies of large magnitude responses are recovered first. In the proposed scheme, as soon as the UAV detects the presence of such high-power frequencies from a sensor, this information is used to aid decoding for other sensors. We argue that such collaboration enabled by UAV will greatly enhance the decoding accuracy of compressive sensing. We use packet-loss traces acquired in UAV flight experiments in the field, as well as field experiments involving software-defined radios, to validate the effectiveness of this distributed compressive sensing approach.
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