Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1

DR.SGX: Hardening SGX Enclaves against Cache Attacks with Data Location Randomization

Recent research has demonstrated that Intel's SGX is vulnerable to various software-based side-channel attacks. In particular, attacks that monitor CPU caches shared between the victim enclave and untrusted software enable accurate leakage of secret enclave data. Known defenses assume developer assistance, require hardware changes, impose high overhead, or prevent only some of the known attacks. In this paper we propose data location randomization as a novel defensive approach to address the threat of side-channel attacks. Our main goal is to break the link between the cache observations by the privileged adversary and the actual data accesses by the victim. We design and implement a compiler-based tool called DR.SGX that instruments enclave code such that data locations are permuted at the granularity of cache lines. We realize the permutation with the CPU's cryptographic hardware-acceleration units providing secure randomization. To prevent correlation of repeated memory accesses we continuously re-randomize all enclave data during execution. Our solution effectively protects many (but not all) enclaves from cache attacks and provides a complementary enclave hardening technique that is especially useful against unpredictable information leakage

SANNS: Scaling Up Secure Approximate k-Nearest Neighbors Search

The $k$-Nearest Neighbor Search ($k$-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud server and receives the response in which case the query and response are revealed to the service provider. Such data disclosures are unacceptable in several scenarios due to the sensitivity of data and/or privacy laws. In this paper, we introduce SANNS, a system for secure $k$-NNS that keeps client's query and the search result confidential. SANNS comprises two protocols: an optimized linear scan and a protocol based on a novel sublinear time clustering-based algorithm. We prove the security of both protocols in the standard semi-honest model. The protocols are built upon several state-of-the-art cryptographic primitives such as lattice-based additively homomorphic encryption, distributed oblivious RAM, and garbled circuits. We provide several contributions to each of these primitives which are applicable to other secure computation tasks. Both of our protocols rely on a new circuit for the approximate top-$k$ selection from $n$ numbers that is built from $O(n + k^2)$ comparators. We have implemented our proposed system and performed extensive experimental results on four datasets in two different computation environments, demonstrating more than $18-31\times$ faster response time compared to optimally implemented protocols from the prior work. Moreover, SANNS is the first work that scales to the database of 10 million entries, pushing the limit by more than two orders of magnitude.Comment: 18 pages, to appear at USENIX Security Symposium 202