Walsh Spectrum Analysis on Sampling Distributions

Citation Author(s):
Navid Ghaedi Bardeh, Isaac Andrés Canales Martinez, Stian Fauskanger, Chunlei Li, Nian Li, Xiaxi Li, Yi LU, Bo Sun, Andrea Tenti, Ziran Tu, Srimathi Varadharajan, Irene Villa, Dong Yang, Dan Zhang, Xiaokang Zhang
Submitted by:
Yi LU
Last updated:
Sat, 06/16/2018 - 23:18
DOI:
10.21227/H2RC7M
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Creative Commons Attribution
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Abstract 

The dataset stores a random sampling distribution with cardinality of support of 4,294,967,296 (i.e., two raised to the power of thirty-two). Specifically, the source generator is fixed as a symmetric-key cryptographic function with 64-bit input and 32-bit output. A total of 17,179,869,184 (i.e., two raised to the power of thirty-four) randomly chosen inputs are used to produce the sampling distribution as the dataset. The integer-valued sampling distribution is formatted as 4,294,967,296 (i.e., two raised to the power of thirty-two) entries, and each entry occupies one byte in storage.

The dataset is used as the experimental analysis subject of an interdisciplinary project "Noisy Sparse Walsh-Hadamard Transform". The project initiates the study of finding the largest (and/or significantly large) Walsh coefficients and the index positions of an unknown distribution by sampling.

References:

[1] R. Scheibler, S. Haghighatshoar, M. Vetterli, "A Fast Hadamard Transform for Signals With Sublinear Sparsity in the Transform Domain", IEEE Transactions on Information Theory, vol. 61, no. 4, pp. 2115 - 2132, 2015 (https://doi.org/10.1109/TIT.2015.2404441).

[2] X. Chen, D. Guo, "Robust Sublinear Complexity Walsh-Hadamard Transform with Arbitrary Sparse Support", in Proc. IEEE Int. Symp. Information Theory, pp. 2573-2577, 2015 (https://doi.org/10.1109/ISIT.2015.7282921).

[3] M. Cheraghchi, P. Indyk, "Nearly Optimal Deterministic Algorithm for Sparse Walsh-Hadamard Transform", arXiv:1504.07648v1, 2015.

[4] X. Li, J. K. Bradley, S. Pawar, K. Ramchandran, "SPRIGHT: A Fast and Robust Framework for Sparse Walsh-Hadamard Transform", arXiv:1508.06336, 2015.

[5] Y. Lu, Y. Desmedt, "Walsh-Hadamard Transform and Cryptographic Applications in Bias Computing", IACR eprint, 2016 (https://eprint.iacr.org/2016/419).

[6] Y. Lu, "Practical Tera-scale Walsh-Hadamard Transform", FTC'2016, IEEE, pp. 1230 - 1236, 2017 (http://ieeexplore.ieee.org/document/7821757/).

Instructions: 

The big dataset file is 4GB in size. The dataset contains 4,294,967,296 entries and each entry occupies one byte in storage. The MD5 checksum is 4ee9 a09a a509 fd70 4152 2fd2 f263 ae25. The SHA256 checksum is d9a4 fb8d d9f0 de29 b1e2 3316 c78d 8e65 4ec7 d60f 7ebc ec9e ee57 6fa2 e392 3b57. Note that the above hash checksum results are displayed in groups of four digits.

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