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Simple Watermarking Pseudorandom Functions from Extractable Pseudorandom Generators
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| Abstract: | Watermarking pseudorandom functions (PRF) allow an authority to embed an unforgeable and unremovable watermark into a PRF while preserving its functionality. In this work, we extend the work of Kim and Wu [Crypto'19] who gave a simple two-step construction of watermarking PRFs from a class of extractable PRFs satisfying several other properties – first construct a mark-embedding scheme, and then upgrade it to a message-embedding scheme. While the message-embedding scheme of Kim and Wu is based on complex homomorphic evaluation techniques, we observe that much simpler constructions can be obtained and from a wider range of assumptions, if we forego the strong requirement of security against the watermarking authority. Concretely, we introduce a new notion called extractable PRGs (xPRGs), from which extractable PRFs (without security against authorities) suitable for the Kim-Wu transformations can be simply obtained via the Goldreich-Goldwasser-Micali (GGM) construction. We provide simple constructions of xPRGs from a wide range of assumptions such as hardness of computational Diffie-Hellman (CDH) in the random oracle model, as well as LWE and RSA in the standard model. |
BibTeX
@article{cic-2024-34406,
title={Simple Watermarking Pseudorandom Functions from Extractable Pseudorandom Generators},
journal={cic},
publisher={International Association for Cryptologic Research},
volume={1, Issue 2},
url={https://cic.iacr.org//p/1/2/13},
doi={10.62056/aevur-10k},
author={Estuardo Alpirez Bock and Chris Brzuska and Russell W. F. Lai},
year=2024
}