The diffeomorphism type of small hyperplane arrangements is combinatorially determined

It is known that there exist hyperplane arrangements with the same underlying matroid that admit non-homotopy equivalent complement manifolds. Here we show that, in any rank, complex central hyperplane arrangements with up to 7 hyperplanes and the same underlying matroid are isotopic. In particular, the diffeomorphism type of the complement manifold and the Milnor fiber and fibration of these arrangements are combinatorially determined, that is, they depend only on the underlying matroid. To prove this, we associate to every such matroid a topological space, that we call the reduced realization space; its connectedness, shown by means of symbolic computation, implies the desired result

Strongly Secure and Efficient Data Shuffle On Hardware Enclaves

Mitigating memory-access attacks on the Intel SGX architecture is an important and open research problem. A natural notion of the mitigation is cache-miss obliviousness which requires the cache-misses emitted during an enclave execution are oblivious to sensitive data. This work realizes the cache-miss obliviousness for the computation of data shuffling. The proposed approach is to software-engineer the oblivious algorithm of Melbourne shuffle on the Intel SGX/TSX architecture, where the Transaction Synchronization eXtension (TSX) is (ab)used to detect the occurrence of cache misses. In the system building, we propose software techniques to prefetch memory data prior to the TSX transaction to defend the physical bus-tapping attacks. Our evaluation based on real implementation shows that our system achieves superior performance and lower transaction abort rate than the related work in the existing literature.Comment: Systex'1