Private and rateless adaptive coded matrix-vector multiplication

Abstract

Edge computing is emerging as a new paradigm to allow processing data near the edge of the network, where the data is typically generated and collected. This enables critical computations at the edge in applications such as Internet of Things (IoT), in which an increasing number of devices (sensors, cameras, health monitoring devices, etc.) collect data that needs to be processed through computationally intensive algorithms with stringent reliability, security and latency constraints. Our key tool is the theory of coded computation, which advocates mixing data in computationally intensive tasks by employing erasure codes and offloading these tasks to other devices for computation. Coded computation is recently gaining interest, thanks to its higher reliability, smaller delay, and lower communication costs. In this paper, we develop a private and rateless adaptive coded computation (PRAC) algorithm for distributed matrix-vector multiplication by taking into account (1) the privacy requirements of IoT applications and devices, and (2) the heterogeneous and time-varying resources of edge devices. We show that PRAC outperforms known secure coded computing methods when resources are heterogeneous. We provide theoretical guarantees on the performance of PRAC and its comparison to baselines. Moreover, we confirm our theoretical results through simulations and implementations on Android-based smartphones.

The Use of The High-Performance Computing in The Learning Process

“…In the paper «Private and rateless adaptive coded matrix-vector multiplication» authors develop a private and rateless adaptive coded computation (PRAC) algorithm for distributed matrix-vector multiplication by taking into account [16] the privacy requirements of IoT applications and devices, and [17] the heterogeneous and time-varying resources of edge devices. They show that PRAC outperforms known secure coded computing methods when resources are heterogeneous [18].…”

PolyDot Coded Privacy Preserving Multi-Party Computation at the Edge

“…In [32]- [34], the problem of matrix-matrix multiplication is considered for the case that a master possesses the input data and would like to perform multiplication on the data with the help of parallel workers, while the data is kept confidential from the workers. In [35] and [36], privacy is addressed for the same system model of master-worker setup, but for matrix-vector multiplication. As compared to this line of work, we focus on the MPC system setup, where there are multiple sources each having private input data, and the goal is that a master learns the result of computation of matrix multiplication on the input data with the help of parallel workers.…”

“…For this purpose, we decompose P(H(x)) based on the four components H(x) is composed of, i.e., C A (x)C B (x), C A (x)S B (x), S A (x)C B (x), and S A (x)S B (x). From (34), (35), (42) and (61), we have:…”

“…(i) Find all elements of P(S A (x)) satisfying C4 in (36). For this step, using (35) and C4 in (36), we have: i + t(s − 1) + tl(2s − 1) ∈ {t(s − 1) − tq + tl ′ (2s − 1)} ∈ Z + P(S A (x)), 0 ≤ q ≤ s − 1, 0 ≤ i, l, l ′ ≤ t − 1, s, t ∈ N (37)…”

Securely Straggler-Exploiting Coded Computation for Distributed Matrix Multiplication

“…Related Work: In the literature, several coded computation schemes have been proposed for matrix multiplication tasks considering security issues in distributed computing. Existing studies have focused on preserving data security [18]- [27], and some studies have assumed a stragglerexploiting scenario, but this was limited to matrix-vector multiplication tasks [21]. It should be noted that other schemes for preserving data security from colluding workers but not considering a straggler-exploiting scenario can be easily extended to this scenario by allocating multiple subtasks to each worker which were designed to be allocated to colluding workers.…”