The circulant hash revisited

AbstractAt ProvSec 2013, Minematsu presented the circulant hash, an almost-xor universal hash using only the xor and rotation operations. The circulant hash is a variant of Carter and Wegman’s H3 hash as well as Krawczyk’s Toeplitz hash, both of which are hashes based on matrix-vector multiplication over 𝔽2. In this paper we revisit the circulant hash and reinterpret it as a multiplication in the polynomial ring 𝔽2[x]/(xn + 1). This leads to simpler proofs, faster implementations in modern computer chips, and newer variants with practical implementation advantages.

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SpaceA: Sparse Matrix Vector Multiplication on Processing-in-Memory Accelerator

2021 IEEE International Symposium on High-Performance Computer Architecture (HPCA) ◽

10.1109/hpca51647.2021.00055 ◽

2021 ◽

Author(s):

Xinfeng Xie ◽

Zheng Liang ◽

Peng Gu ◽

Abanti Basak ◽

Lei Deng ◽

...

Keyword(s):

Sparse Matrix ◽

Matrix Vector Multiplication ◽

Matrix Vector

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Conflict-free symmetric sparse matrix-vector multiplication on multicore architectures

Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis ◽

10.1145/3295500.3356148 ◽

2019 ◽

Cited By ~ 1

Author(s):

Athena Elafrou ◽

Georgios Goumas ◽

Nectarios Koziris

Keyword(s):

Sparse Matrix ◽

Multicore Architectures ◽

Matrix Vector Multiplication ◽

Matrix Vector

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Sparse Matrix-Vector Multiplication on GPGPUs

ACM Transactions on Mathematical Software ◽

10.1145/3017994 ◽

2017 ◽

Vol 43 (4) ◽

pp. 1-49 ◽

Cited By ~ 34

Author(s):

Salvatore Filippone ◽

Valeria Cardellini ◽

Davide Barbieri ◽

Alessandro Fanfarillo

Keyword(s):

Sparse Matrix ◽

Matrix Vector Multiplication ◽

Matrix Vector

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Private and rateless adaptive coded matrix-vector multiplication

EURASIP Journal on Wireless Communications and Networking ◽

10.1186/s13638-020-01887-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Rawad Bitar ◽

Yuxuan Xing ◽

Yasaman Keshtkarjahromi ◽

Venkat Dasari ◽

Salim El Rouayheb ◽

...

Keyword(s):

Computing Methods ◽

Erasure Codes ◽

Time Varying ◽

New Paradigm ◽

Matrix Vector Multiplication ◽

Processing Data ◽

Computationally Intensive ◽

Matrix Vector ◽

Monitoring Devices ◽

Theoretical Results

AbstractEdge 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.

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