Strategies for protecting intellectual property when using CUDA applications on graphics processing units

Recent advances in the massively parallel computational abilities of graphical processing units (GPUs) have increased their use for general purpose computation, as companies look to take advantage of big data processing techniques. This has given rise to the potential for malicious software targeting GPUs, which is of interest to forensic investigators examining the operation of software. The ability to carry out reverse-engineering of software is of great importance within the security and forensics elds, particularly when investigating malicious software or carrying out forensic analysis following a successful security breach. Due to the complexity of the Nvidia CUDA (Compute Uni ed Device Architecture) framework, it is not clear how best to approach the reverse engineering of a piece of CUDA software. We carry out a review of the di erent binary output formats which may be encountered from the CUDA compiler, and their implications on reverse engineering. We then demonstrate the process of carrying out disassembly of an example CUDA application, to establish the various techniques available to forensic investigators carrying out black-box disassembly and reverse engineering of CUDA binaries. We show that the Nvidia compiler, using default settings, leaks useful information. Finally, we demonstrate techniques to better protect intellectual property in CUDA algorithm implementations from reverse engineering.

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.