Abstract
The low-degree method postulates that no efficient algorithm outperforms low-degree polynomials in certain hypothesis-testing tasks. It has been used to understand computational indistinguishability in high-dimensional statistics.
We explore the use of the low-degree method in the context of cryptography. To this end, we apply it in the design and analysis of a new public-key encryption scheme whose security is based on Goldreich’s pseudorandom generator. The scheme is a combination of two proposals of Applebaum, Barak, and Wigderson, and inherits desirable features from both.
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Acknowledgments
We thank Caicai Chen, Yuval Ishai, and Chris Jones for their advice and feedback. Part of this work done when the first and second authors visited Bocconi University. Andrej Bogdanov is supported by an NSERC Discovery Grant and Hong Kong RGC GRF CUHK14209920. Pravesh Kothari is supported by NSF CAREER Award #2047933, Alfred P. Sloan Fellowship and a Google Research Scholar Award. Alon Rosen is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019547) and Cariplo CRYPTONOMEX grant.
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Bogdanov, A., Kothari, P.K., Rosen, A. (2023). Public-Key Encryption, Local Pseudorandom Generators, and the Low-Degree Method. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14369. Springer, Cham. https://doi.org/10.1007/978-3-031-48615-9_10
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DOI: https://doi.org/10.1007/978-3-031-48615-9_10
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